Physlib.Particles.SuperSymmetry.MSSMNu.AnomalyCancellation.B3

Imports

/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module

public import Physlib.Particles.SuperSymmetry.MSSMNu.AnomalyCancellation.Basic
public import Mathlib.Tactic.LinearCombination

The definition of the solution B₃ and properties thereof

We define B₃ and show that it is a double point of the cubic.

References

The main reference for the material in this file is:

[Allanach, Madigan and Tooby-Smith][Allanach:2021yjy]

@[expose] public section

B₃ is the charge which is $B-L$ in all families, but with the third family of the opposite sign.

def B₃AsCharge : MSSMACC.Charges := toSpecies.symm
  ⟨fun s => fun i =>
    match s, i with
    | 0, 0 => 1
    | 0, 1 => 1
    | 0, 2 => - 1
    | 1, 0 => - 1
    | 1, 1 => - 1
    | 1, 2 => 1
    | 2, 0 => - 1
    | 2, 1 => - 1
    | 2, 2 => 1
    | 3, 0 => - 3
    | 3, 1 => - 3
    | 3, 2 => 3
    | 4, 0 => 3
    | 4, 1 => 3
    | 4, 2 => - 3
    | 5, 0 => 3
    | 5, 1 => 3
    | 5, 2 => - 3,
  fun s =>
    match s with
    | 0 => -3
    | 1 => 3⟩

B₃ as a solution.

def B₃ : MSSMACC.Sols :=
  MSSMACC.AnomalyFreeMk B₃AsCharge (by⊢ accGrav B₃AsCharge = 0 with_unfolding_all rflAll goals completed! 🐙)
    (by⊢ accSU2 B₃AsCharge = 0 with_unfolding_all rflAll goals completed! 🐙) (by⊢ accSU3 B₃AsCharge = 0 with_unfolding_all rflAll goals completed! 🐙) (by⊢ accYY B₃AsCharge = 0 with_unfolding_all rflAll goals completed! 🐙)
    (by⊢ accQuad B₃AsCharge = 0 with_unfolding_all rflAll goals completed! 🐙) (by⊢ accCube B₃AsCharge = 0 with_unfolding_all rflAll goals completed! 🐙)

lemma B₃_val : B₃.val = B₃AsCharge := by⊢ B₃.val = B₃AsCharge
  rflAll goals completed! 🐙



set_option backward.isDefEq.respectTransparency false in
lemma doublePoint_B₃_B₃ (R : MSSMACC.LinSols) : cubeTriLin B₃.val B₃.val R.val = 0 := byR:MSSMACC.LinSols⊢ ((cubeTriLin B₃.val) B₃.val) R.val = 0
  simp only [cubeTriLin, TriLinearSymm.mk₃_toFun_apply_apply, cubeTriLinToFun]R:MSSMACC.LinSols⊢ ∑ x,
      (6 * (Q B₃.val x * Q B₃.val x * Q R.val x) + 3 * (U B₃.val x * U B₃.val x * U R.val x) +
              3 * (D B₃.val x * D B₃.val x * D R.val x) +
            2 * (L B₃.val x * L B₃.val x * L R.val x) +
          E B₃.val x * E B₃.val x * E R.val x +
        N B₃.val x * N B₃.val x * N R.val x) +
    (2 * Hd B₃.val * Hd B₃.val * Hd R.val + 2 * Hu B₃.val * Hu B₃.val * Hu R.val) =
  0
  erw [Fin.sum_univ_threeR:MSSMACC.LinSols⊢ 6 * (Q B₃.val 0 * Q B₃.val 0 * Q R.val 0) + 3 * (U B₃.val 0 * U B₃.val 0 * U R.val 0) +
                3 * (D B₃.val 0 * D B₃.val 0 * D R.val 0) +
              2 * (L B₃.val 0 * L B₃.val 0 * L R.val 0) +
            E B₃.val 0 * E B₃.val 0 * E R.val 0 +
          N B₃.val 0 * N B₃.val 0 * N R.val 0 +
        (6 * (Q B₃.val 1 * Q B₃.val 1 * Q R.val 1) + 3 * (U B₃.val 1 * U B₃.val 1 * U R.val 1) +
                3 * (D B₃.val 1 * D B₃.val 1 * D R.val 1) +
              2 * (L B₃.val 1 * L B₃.val 1 * L R.val 1) +
            E B₃.val 1 * E B₃.val 1 * E R.val 1 +
          N B₃.val 1 * N B₃.val 1 * N R.val 1) +
      (6 * (Q B₃.val 2 * Q B₃.val 2 * Q R.val 2) + 3 * (U B₃.val 2 * U B₃.val 2 * U R.val 2) +
              3 * (D B₃.val 2 * D B₃.val 2 * D R.val 2) +
            2 * (L B₃.val 2 * L B₃.val 2 * L R.val 2) +
          E B₃.val 2 * E B₃.val 2 * E R.val 2 +
        N B₃.val 2 * N B₃.val 2 * N R.val 2) +
    (2 * Hd B₃.val * Hd B₃.val * Hd R.val + 2 * Hu B₃.val * Hu B₃.val * Hu R.val) =
  0]R:MSSMACC.LinSols⊢ 6 * (Q B₃.val 0 * Q B₃.val 0 * Q R.val 0) + 3 * (U B₃.val 0 * U B₃.val 0 * U R.val 0) +
                3 * (D B₃.val 0 * D B₃.val 0 * D R.val 0) +
              2 * (L B₃.val 0 * L B₃.val 0 * L R.val 0) +
            E B₃.val 0 * E B₃.val 0 * E R.val 0 +
          N B₃.val 0 * N B₃.val 0 * N R.val 0 +
        (6 * (Q B₃.val 1 * Q B₃.val 1 * Q R.val 1) + 3 * (U B₃.val 1 * U B₃.val 1 * U R.val 1) +
                3 * (D B₃.val 1 * D B₃.val 1 * D R.val 1) +
              2 * (L B₃.val 1 * L B₃.val 1 * L R.val 1) +
            E B₃.val 1 * E B₃.val 1 * E R.val 1 +
          N B₃.val 1 * N B₃.val 1 * N R.val 1) +
      (6 * (Q B₃.val 2 * Q B₃.val 2 * Q R.val 2) + 3 * (U B₃.val 2 * U B₃.val 2 * U R.val 2) +
              3 * (D B₃.val 2 * D B₃.val 2 * D R.val 2) +
            2 * (L B₃.val 2 * L B₃.val 2 * L R.val 2) +
          E B₃.val 2 * E B₃.val 2 * E R.val 2 +
        N B₃.val 2 * N B₃.val 2 * N R.val 2) +
    (2 * Hd B₃.val * Hd B₃.val * Hd R.val + 2 * Hu B₃.val * Hu B₃.val * Hu R.val) =
  0
  rw [B₃_valR:MSSMACC.LinSols⊢ 6 * (Q B₃AsCharge 0 * Q B₃AsCharge 0 * Q R.val 0) + 3 * (U B₃AsCharge 0 * U B₃AsCharge 0 * U R.val 0) +
                3 * (D B₃AsCharge 0 * D B₃AsCharge 0 * D R.val 0) +
              2 * (L B₃AsCharge 0 * L B₃AsCharge 0 * L R.val 0) +
            E B₃AsCharge 0 * E B₃AsCharge 0 * E R.val 0 +
          N B₃AsCharge 0 * N B₃AsCharge 0 * N R.val 0 +
        (6 * (Q B₃AsCharge 1 * Q B₃AsCharge 1 * Q R.val 1) + 3 * (U B₃AsCharge 1 * U B₃AsCharge 1 * U R.val 1) +
                3 * (D B₃AsCharge 1 * D B₃AsCharge 1 * D R.val 1) +
              2 * (L B₃AsCharge 1 * L B₃AsCharge 1 * L R.val 1) +
            E B₃AsCharge 1 * E B₃AsCharge 1 * E R.val 1 +
          N B₃AsCharge 1 * N B₃AsCharge 1 * N R.val 1) +
      (6 * (Q B₃AsCharge 2 * Q B₃AsCharge 2 * Q R.val 2) + 3 * (U B₃AsCharge 2 * U B₃AsCharge 2 * U R.val 2) +
              3 * (D B₃AsCharge 2 * D B₃AsCharge 2 * D R.val 2) +
            2 * (L B₃AsCharge 2 * L B₃AsCharge 2 * L R.val 2) +
          E B₃AsCharge 2 * E B₃AsCharge 2 * E R.val 2 +
        N B₃AsCharge 2 * N B₃AsCharge 2 * N R.val 2) +
    (2 * Hd B₃AsCharge * Hd B₃AsCharge * Hd R.val + 2 * Hu B₃AsCharge * Hu B₃AsCharge * Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 * (Q B₃AsCharge 0 * Q B₃AsCharge 0 * Q R.val 0) + 3 * (U B₃AsCharge 0 * U B₃AsCharge 0 * U R.val 0) +
                3 * (D B₃AsCharge 0 * D B₃AsCharge 0 * D R.val 0) +
              2 * (L B₃AsCharge 0 * L B₃AsCharge 0 * L R.val 0) +
            E B₃AsCharge 0 * E B₃AsCharge 0 * E R.val 0 +
          N B₃AsCharge 0 * N B₃AsCharge 0 * N R.val 0 +
        (6 * (Q B₃AsCharge 1 * Q B₃AsCharge 1 * Q R.val 1) + 3 * (U B₃AsCharge 1 * U B₃AsCharge 1 * U R.val 1) +
                3 * (D B₃AsCharge 1 * D B₃AsCharge 1 * D R.val 1) +
              2 * (L B₃AsCharge 1 * L B₃AsCharge 1 * L R.val 1) +
            E B₃AsCharge 1 * E B₃AsCharge 1 * E R.val 1 +
          N B₃AsCharge 1 * N B₃AsCharge 1 * N R.val 1) +
      (6 * (Q B₃AsCharge 2 * Q B₃AsCharge 2 * Q R.val 2) + 3 * (U B₃AsCharge 2 * U B₃AsCharge 2 * U R.val 2) +
              3 * (D B₃AsCharge 2 * D B₃AsCharge 2 * D R.val 2) +
            2 * (L B₃AsCharge 2 * L B₃AsCharge 2 * L R.val 2) +
          E B₃AsCharge 2 * E B₃AsCharge 2 * E R.val 2 +
        N B₃AsCharge 2 * N B₃AsCharge 2 * N R.val 2) +
    (2 * Hd B₃AsCharge * Hd B₃AsCharge * Hd R.val + 2 * Hu B₃AsCharge * Hu B₃AsCharge * Hu R.val) =
  0]R:MSSMACC.LinSols⊢ 6 * (Q B₃AsCharge 0 * Q B₃AsCharge 0 * Q R.val 0) + 3 * (U B₃AsCharge 0 * U B₃AsCharge 0 * U R.val 0) +
                3 * (D B₃AsCharge 0 * D B₃AsCharge 0 * D R.val 0) +
              2 * (L B₃AsCharge 0 * L B₃AsCharge 0 * L R.val 0) +
            E B₃AsCharge 0 * E B₃AsCharge 0 * E R.val 0 +
          N B₃AsCharge 0 * N B₃AsCharge 0 * N R.val 0 +
        (6 * (Q B₃AsCharge 1 * Q B₃AsCharge 1 * Q R.val 1) + 3 * (U B₃AsCharge 1 * U B₃AsCharge 1 * U R.val 1) +
                3 * (D B₃AsCharge 1 * D B₃AsCharge 1 * D R.val 1) +
              2 * (L B₃AsCharge 1 * L B₃AsCharge 1 * L R.val 1) +
            E B₃AsCharge 1 * E B₃AsCharge 1 * E R.val 1 +
          N B₃AsCharge 1 * N B₃AsCharge 1 * N R.val 1) +
      (6 * (Q B₃AsCharge 2 * Q B₃AsCharge 2 * Q R.val 2) + 3 * (U B₃AsCharge 2 * U B₃AsCharge 2 * U R.val 2) +
              3 * (D B₃AsCharge 2 * D B₃AsCharge 2 * D R.val 2) +
            2 * (L B₃AsCharge 2 * L B₃AsCharge 2 * L R.val 2) +
          E B₃AsCharge 2 * E B₃AsCharge 2 * E R.val 2 +
        N B₃AsCharge 2 * N B₃AsCharge 2 * N R.val 2) +
    (2 * Hd B₃AsCharge * Hd B₃AsCharge * Hd R.val + 2 * Hu B₃AsCharge * Hu B₃AsCharge * Hu R.val) =
  0
  rw [B₃AsChargeR:MSSMACC.LinSols⊢ 6 *
                    (Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      Q R.val 0) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      U R.val 0) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                    D R.val 0) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                  L R.val 0) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
              E R.val 0 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
            N R.val 0 +
        (6 *
                    (Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      Q R.val 1) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      U R.val 1) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                    D R.val 1) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                  L R.val 1) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
              E R.val 1 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
            N R.val 1) +
      (6 *
                  (Q
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      Q
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    Q R.val 2) +
                3 *
                  (U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    U R.val 2) +
              3 *
                (D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                    D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                  D R.val 2) +
            2 *
              (L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                  L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                L R.val 2) +
          E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
              E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
            E R.val 2 +
        N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
            N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 *
                    (Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      Q R.val 0) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      U R.val 0) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                    D R.val 0) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                  L R.val 0) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
              E R.val 0 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
            N R.val 0 +
        (6 *
                    (Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      Q R.val 1) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      U R.val 1) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                    D R.val 1) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                  L R.val 1) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
              E R.val 1 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
            N R.val 1) +
      (6 *
                  (Q
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      Q
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    Q R.val 2) +
                3 *
                  (U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    U R.val 2) +
              3 *
                (D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                    D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                  D R.val 2) +
            2 *
              (L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                  L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                L R.val 2) +
          E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
              E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
            E R.val 2 +
        N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
            N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0]R:MSSMACC.LinSols⊢ 6 *
                    (Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      Q R.val 0) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      U R.val 0) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                    D R.val 0) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                  L R.val 0) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
              E R.val 0 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
            N R.val 0 +
        (6 *
                    (Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        Q
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      Q R.val 1) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      U R.val 1) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                    D R.val 1) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                  L R.val 1) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
              E R.val 1 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
            N R.val 1) +
      (6 *
                  (Q
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      Q
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    Q R.val 2) +
                3 *
                  (U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    U R.val 2) +
              3 *
                (D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                    D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                  D R.val 2) +
            2 *
              (L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                  L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                L R.val 2) +
          E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
              E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
            E R.val 2 +
        N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
            N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0
  repeat rw [toSMSpecies_toSpecies_invR:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          0 *
                      U R.val 0) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        0 *
                    D R.val 0) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      0 *
                  L R.val 0) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  0 *
              E R.val 0 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    (U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                        U
                          (toSpecies.symm
                            (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3))
                          1 *
                      U R.val 1) +
                3 *
                  (D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                      D
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        1 *
                    D R.val 1) +
              2 *
                (L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                    L
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      1 *
                  L R.val 1) +
            E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
                E
                  (toSpecies.symm
                    (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3))
                  1 *
              E R.val 1 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  (U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                      U
                        (toSpecies.symm
                          (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3))
                        2 *
                    U R.val 2) +
              3 *
                (D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                    D
                      (toSpecies.symm
                        (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3))
                      2 *
                  D R.val 2) +
            2 *
              (L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                  L
                    (toSpecies.symm
                      (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3))
                    2 *
                L R.val 2) +
          E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
              E
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                2 *
            E R.val 2 +
        N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
            N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
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                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0]R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
              N
                (toSpecies.symm
                  (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3))
                1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
            N
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3))
              2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            Hd
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hd
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0
  rw [Hd_toSpecies_inv,R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              0 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            0 *
        Hd R.val +
      2 *
            Hu
              (toSpecies.symm
                (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3)) *
          Hu
            (toSpecies.symm
              (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3)) *
        Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              0 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            0 *
        Hd R.val +
      2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              1 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            1 *
        Hu R.val) =
  0 Hu_toSpecies_invR:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              0 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            0 *
        Hd R.val +
      2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              1 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            1 *
        Hu R.val) =
  0R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              0 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            0 *
        Hd R.val +
      2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              1 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            1 *
        Hu R.val) =
  0]R:MSSMACC.LinSols⊢ 6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 0 *
                      Q R.val 0) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 0 *
                      U R.val 0) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 0 *
                    D R.val 0) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 0 *
                  L R.val 0) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 0 *
              E R.val 0 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 0 *
            N R.val 0 +
        (6 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          0 1 *
                      Q R.val 1) +
                  3 *
                    ((fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                        (fun s i =>
                              match s, i with
                              | 0, 0 => 1
                              | 0, 1 => 1
                              | 0, 2 => -1
                              | 1, 0 => -1
                              | 1, 1 => -1
                              | 1, 2 => 1
                              | 2, 0 => -1
                              | 2, 1 => -1
                              | 2, 2 => 1
                              | 3, 0 => -3
                              | 3, 1 => -3
                              | 3, 2 => 3
                              | 4, 0 => 3
                              | 4, 1 => 3
                              | 4, 2 => -3
                              | 5, 0 => 3
                              | 5, 1 => 3
                              | 5, 2 => -3,
                              fun s =>
                              match s with
                              | 0 => -3
                              | 1 => 3).1
                          1 1 *
                      U R.val 1) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        2 1 *
                    D R.val 1) +
              2 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      3 1 *
                  L R.val 1) +
            (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
                (fun s i =>
                      match s, i with
                      | 0, 0 => 1
                      | 0, 1 => 1
                      | 0, 2 => -1
                      | 1, 0 => -1
                      | 1, 1 => -1
                      | 1, 2 => 1
                      | 2, 0 => -1
                      | 2, 1 => -1
                      | 2, 2 => 1
                      | 3, 0 => -3
                      | 3, 1 => -3
                      | 3, 2 => 3
                      | 4, 0 => 3
                      | 4, 1 => 3
                      | 4, 2 => -3
                      | 5, 0 => 3
                      | 5, 1 => 3
                      | 5, 2 => -3,
                      fun s =>
                      match s with
                      | 0 => -3
                      | 1 => 3).1
                  4 1 *
              E R.val 1 +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                5 1 *
            N R.val 1) +
      (6 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        0 2 *
                    Q R.val 2) +
                3 *
                  ((fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                      (fun s i =>
                            match s, i with
                            | 0, 0 => 1
                            | 0, 1 => 1
                            | 0, 2 => -1
                            | 1, 0 => -1
                            | 1, 1 => -1
                            | 1, 2 => 1
                            | 2, 0 => -1
                            | 2, 1 => -1
                            | 2, 2 => 1
                            | 3, 0 => -3
                            | 3, 1 => -3
                            | 3, 2 => 3
                            | 4, 0 => 3
                            | 4, 1 => 3
                            | 4, 2 => -3
                            | 5, 0 => 3
                            | 5, 1 => 3
                            | 5, 2 => -3,
                            fun s =>
                            match s with
                            | 0 => -3
                            | 1 => 3).1
                        1 2 *
                    U R.val 2) +
              3 *
                ((fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                    (fun s i =>
                          match s, i with
                          | 0, 0 => 1
                          | 0, 1 => 1
                          | 0, 2 => -1
                          | 1, 0 => -1
                          | 1, 1 => -1
                          | 1, 2 => 1
                          | 2, 0 => -1
                          | 2, 1 => -1
                          | 2, 2 => 1
                          | 3, 0 => -3
                          | 3, 1 => -3
                          | 3, 2 => 3
                          | 4, 0 => 3
                          | 4, 1 => 3
                          | 4, 2 => -3
                          | 5, 0 => 3
                          | 5, 1 => 3
                          | 5, 2 => -3,
                          fun s =>
                          match s with
                          | 0 => -3
                          | 1 => 3).1
                      2 2 *
                  D R.val 2) +
            2 *
              ((fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                  (fun s i =>
                        match s, i with
                        | 0, 0 => 1
                        | 0, 1 => 1
                        | 0, 2 => -1
                        | 1, 0 => -1
                        | 1, 1 => -1
                        | 1, 2 => 1
                        | 2, 0 => -1
                        | 2, 1 => -1
                        | 2, 2 => 1
                        | 3, 0 => -3
                        | 3, 1 => -3
                        | 3, 2 => 3
                        | 4, 0 => 3
                        | 4, 1 => 3
                        | 4, 2 => -3
                        | 5, 0 => 3
                        | 5, 1 => 3
                        | 5, 2 => -3,
                        fun s =>
                        match s with
                        | 0 => -3
                        | 1 => 3).1
                    3 2 *
                L R.val 2) +
          (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
              (fun s i =>
                    match s, i with
                    | 0, 0 => 1
                    | 0, 1 => 1
                    | 0, 2 => -1
                    | 1, 0 => -1
                    | 1, 1 => -1
                    | 1, 2 => 1
                    | 2, 0 => -1
                    | 2, 1 => -1
                    | 2, 2 => 1
                    | 3, 0 => -3
                    | 3, 1 => -3
                    | 3, 2 => 3
                    | 4, 0 => 3
                    | 4, 1 => 3
                    | 4, 2 => -3
                    | 5, 0 => 3
                    | 5, 1 => 3
                    | 5, 2 => -3,
                    fun s =>
                    match s with
                    | 0 => -3
                    | 1 => 3).1
                4 2 *
            E R.val 2 +
        (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).1
              5 2 *
          N R.val 2) +
    (2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              0 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            0 *
        Hd R.val +
      2 *
            (fun s i =>
                  match s, i with
                  | 0, 0 => 1
                  | 0, 1 => 1
                  | 0, 2 => -1
                  | 1, 0 => -1
                  | 1, 1 => -1
                  | 1, 2 => 1
                  | 2, 0 => -1
                  | 2, 1 => -1
                  | 2, 2 => 1
                  | 3, 0 => -3
                  | 3, 1 => -3
                  | 3, 2 => 3
                  | 4, 0 => 3
                  | 4, 1 => 3
                  | 4, 2 => -3
                  | 5, 0 => 3
                  | 5, 1 => 3
                  | 5, 2 => -3,
                  fun s =>
                  match s with
                  | 0 => -3
                  | 1 => 3).2
              1 *
          (fun s i =>
                match s, i with
                | 0, 0 => 1
                | 0, 1 => 1
                | 0, 2 => -1
                | 1, 0 => -1
                | 1, 1 => -1
                | 1, 2 => 1
                | 2, 0 => -1
                | 2, 1 => -1
                | 2, 2 => 1
                | 3, 0 => -3
                | 3, 1 => -3
                | 3, 2 => 3
                | 4, 0 => 3
                | 4, 1 => 3
                | 4, 2 => -3
                | 5, 0 => 3
                | 5, 1 => 3
                | 5, 2 => -3,
                fun s =>
                match s with
                | 0 => -3
                | 1 => 3).2
            1 *
        Hu R.val) =
  0
  simp only [mul_one, Fin.isValue, toSMSpecies_apply, one_mul, mul_neg, neg_neg, neg_mul, Hd_apply,
    Fin.reduceFinMk, Hu_apply]R:MSSMACC.LinSols⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  have hLin := R.linearSolR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear), (MSSMACC.linearACCs i) R.val = 0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  simp only [MSSMACC_linearACCs] at hLinR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  have h0 := hLin ⟨0, byR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0⊢ 0 < MSSMACC.numberLinearR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0 simpAll goals completed! 🐙R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0⟩R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  have h2 := hLin ⟨2, byR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 2 < MSSMACC.numberLinearR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0h2:(match ⟨2, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0 simpAll goals completed! 🐙R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0h2:(match ⟨2, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0⟩R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:(match ⟨0, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0h2:(match ⟨2, ⋯⟩ with
    | 0 => accGrav
    | 1 => accSU2
    | 2 => accSU3
    | 3 => accYY)
    R.val =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  simp only [accGrav, LinearMap.coe_mk, AddHom.coe_mk, accSU3] at h0 h2R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:∑ i, (6 * Q R.val i + 3 * U R.val i + 3 * D R.val i + 2 * L R.val i + E R.val i + N R.val i) +
    2 * (Hd R.val + Hu R.val) =
  0h2:∑ i, (2 * Q R.val i + U R.val i + D R.val i) = 0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  erw [Fin.sum_univ_threeR:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:6 * Q R.val 0 + 3 * U R.val 0 + 3 * D R.val 0 + 2 * L R.val 0 + E R.val 0 + N R.val 0 +
        (6 * Q R.val 1 + 3 * U R.val 1 + 3 * D R.val 1 + 2 * L R.val 1 + E R.val 1 + N R.val 1) +
      (6 * Q R.val 2 + 3 * U R.val 2 + 3 * D R.val 2 + 2 * L R.val 2 + E R.val 2 + N R.val 2) +
    2 * (Hd R.val + Hu R.val) =
  0h2:2 * Q R.val 0 + U R.val 0 + D R.val 0 + (2 * Q R.val 1 + U R.val 1 + D R.val 1) +
    (2 * Q R.val 2 + U R.val 2 + D R.val 2) =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0]R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:6 * Q R.val 0 + 3 * U R.val 0 + 3 * D R.val 0 + 2 * L R.val 0 + E R.val 0 + N R.val 0 +
        (6 * Q R.val 1 + 3 * U R.val 1 + 3 * D R.val 1 + 2 * L R.val 1 + E R.val 1 + N R.val 1) +
      (6 * Q R.val 2 + 3 * U R.val 2 + 3 * D R.val 2 + 2 * L R.val 2 + E R.val 2 + N R.val 2) +
    2 * (Hd R.val + Hu R.val) =
  0h2:2 * Q R.val 0 + U R.val 0 + D R.val 0 + (2 * Q R.val 1 + U R.val 1 + D R.val 1) +
    (2 * Q R.val 2 + U R.val 2 + D R.val 2) =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0 at h0 h2
  simp only [Fin.isValue, toSMSpecies_apply, Nat.reduceMul, Hd_apply, Fin.reduceFinMk,
    Hu_apply] at h0 h2R:MSSMACC.LinSolshLin:∀ (i : Fin MSSMACC.numberLinear),
  (match i with
      | 0 => accGrav
      | 1 => accSU2
      | 2 => accSU3
      | 3 => accYY)
      R.val =
    0h0:6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0))) +
            R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1))) +
            R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2))) +
          R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    2 * (R.val 18 + R.val 19) =
  0h2:2 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
        R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
      (2 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
        R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1)))) +
    (2 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
      R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2)))) =
  0⊢ 6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 0))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 0))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 0))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 0)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 0))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 0))) +
        (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 1))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 1))) +
                3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 1))) +
              2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 1)))) +
            3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 1))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 1)))) +
      (6 * R.val (Fin.castAdd 2 (finProdFinEquiv (0, 2))) + 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (1, 2))) +
              3 * R.val (Fin.castAdd 2 (finProdFinEquiv (2, 2))) +
            2 * (3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (3, 2)))) +
          3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (4, 2))) +
        3 * 3 * R.val (Fin.castAdd 2 (finProdFinEquiv (5, 2)))) +
    (2 * 3 * 3 * R.val 18 + 2 * 3 * 3 * R.val 19) =
  0
  linear_combination (norm := ring_nfAll goals completed! 🐙) 9 * (h0) - 24 * (h2)