Theorems · Theorem · nonassociative algebras

RootPairing.InvariantForm.mk.injEq

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} {N : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] {P : RootPairing ι R M N}
  (form : LinearMap.BilinForm R M) (symm : LinearMap.IsSymm form)
  (ne_zero : ∀ (i : ι), (form (P.root i)) (P.root i) ≠ 0)
  (isOrthogonal_reflection : ∀ (i : ι), LinearMap.IsOrthogonal form ⇑(P.reflection i))
  (form_1 : LinearMap.BilinForm R M) (symm_1 : LinearMap.IsSymm form_1)
  (ne_zero_1 : ∀ (i : ι), (form_1 (P.root i)) (P.root i) ≠ 0)
  (isOrthogonal_reflection_1 : ∀ (i : ι), LinearMap.IsOrthogonal form_1 ⇑(P.reflection i)),
  ({ form := form, symm := symm, ne_zero := ne_zero, isOrthogonal_reflection := isOrthogonal_reflection } =
      { form := form_1, symm := symm_1, ne_zero := ne_zero_1, isOrthogonal_reflection := isOrthogonal_reflection_1 }) =
    (form = form_1)

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

0 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule