Theorems · Theorem · linear algebra

LinearMap.IsAlt.eq_of_add_add_eq_zero

∀ {R : Type u_1} {R₁ : Type u_2} {M : Type u_5} {M₁ : Type u_6} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : CommSemiring R₁] [inst_4 : AddCommMonoid M₁] [inst_5 : Module R₁ M₁]
  {I₁ I₂ : R₁ →+* R} {B : M₁ →ₛₗ[I₁] M₁ →ₛₗ[I₂] M},
  B.IsAlt → ∀ [IsCancelAdd M] {a b c : M₁}, a + b + c = 0 → (B a) b = (B b) c

Defined in

Mathlib.LinearAlgebra.SesquilinearForm.Basic

Cited by

2 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAddCommMonoidModuleIsCancelAdd