Theorems · Theorem · nonassociative algebras

LieAlgebra.Extension.oneCochainOfTwoSplitting.congr_simp

∀ {R : Type u_1} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : LieRing M] [inst_4 : LieAlgebra R M] (E : LieAlgebra.Extension R M L) {s₁ s₁_1 : L →ₗ[R] E.L}
  (e_s₁ : s₁ = s₁_1) {s₂ s₂_1 : L →ₗ[R] E.L} (e_s₂ : s₂ = s₂_1) (hs₁ : Function.LeftInverse ⇑E.proj ⇑s₁)
  (hs₂ : Function.LeftInverse ⇑E.proj ⇑s₂), E.oneCochainOfTwoSplitting hs₁ hs₂ = E.oneCochainOfTwoSplitting ⋯ ⋯

Defined in

Mathlib.Algebra.Lie.Extension

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraLieRingLieAlgebra