Theorems · Theorem · nonassociative algebras

LieModuleEquiv.symm_apply_eq

∀ {R : Type u} {L : Type v} {M : Type w} {N : Type w₁} [inst : CommRing R] [inst_1 : LieRing L]
  [inst_2 : AddCommGroup M] [inst_3 : AddCommGroup N] [inst_4 : Module R M] [inst_5 : Module R N]
  [inst_6 : LieRingModule L M] [inst_7 : LieRingModule L N] {m : M} {n : N} (e : M ≃ₗ⁅R,L⁆ N), e.symm n = m ↔ n = e m

Defined in

Mathlib.Algebra.Lie.Basic

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupAddCommGroupModuleModuleLieRingModuleLieRingModule