∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {ι₂ : Type u_5} {M₂ : Type u_6} {N₂ : Type u_7}
  [inst_5 : AddCommGroup M₂] [inst_6 : Module R M₂] [inst_7 : AddCommGroup N₂] [inst_8 : Module R N₂]
  {P : RootPairing ι R M N} {Q : RootPairing ι₂ R M₂ N₂} (weightMap : M →ₗ[R] M₂) (coweightMap : N₂ →ₗ[R] N)
  (indexEquiv : ι ≃ ι₂)
  (weight_coweight_transpose : weightMap.dualMap ∘ₗ ↑Q.flip.toPerfPair = ↑P.flip.toPerfPair ∘ₗ coweightMap)
  (root_weightMap : ⇑weightMap ∘ ⇑P.root = ⇑Q.root ∘ ⇑indexEquiv)
  (coroot_coweightMap : ⇑coweightMap ∘ ⇑Q.coroot = ⇑P.coroot ∘ ⇑indexEquiv.symm) (weightMap_1 : M →ₗ[R] M₂)
  (coweightMap_1 : N₂ →ₗ[R] N) (indexEquiv_1 : ι ≃ ι₂)
  (weight_coweight_transpose_1 : weightMap_1.dualMap ∘ₗ ↑Q.flip.toPerfPair = ↑P.flip.toPerfPair ∘ₗ coweightMap_1)
  (root_weightMap_1 : ⇑weightMap_1 ∘ ⇑P.root = ⇑Q.root ∘ ⇑indexEquiv_1)
  (coroot_coweightMap_1 : ⇑coweightMap_1 ∘ ⇑Q.coroot = ⇑P.coroot ∘ ⇑indexEquiv_1.symm),
  ({ weightMap := weightMap, coweightMap := coweightMap, indexEquiv := indexEquiv,
        weight_coweight_transpose := weight_coweight_transpose, root_weightMap := root_weightMap,
        coroot_coweightMap := coroot_coweightMap } =
      { weightMap := weightMap_1, coweightMap := coweightMap_1, indexEquiv := indexEquiv_1,
        weight_coweight_transpose := weight_coweight_transpose_1, root_weightMap := root_weightMap_1,
        coroot_coweightMap := coroot_coweightMap_1 }) =
    (weightMap = weightMap_1 ∧ coweightMap = coweightMap_1 ∧ indexEquiv = indexEquiv_1)