Theorems · Theorem · nonassociative algebras

RootPairing.InvariantForm.mk.inj

∀ {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

1 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound