Theorems · Theorem · nonassociative algebras

LieSubmodule.mk.congr_simp

∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : LieRingModule L M] (toSubmodule toSubmodule_1 : Submodule R M)
  (e_toSubmodule : toSubmodule = toSubmodule_1)
  (lie_mem : ∀ {x : L} {m : M}, m ∈ toSubmodule.carrier → ⁅x, m⁆ ∈ toSubmodule.carrier),
  { toSubmodule := toSubmodule, lie_mem := lie_mem } = { toSubmodule := toSubmodule_1, lie_mem := ⋯ }

Defined in

Mathlib.Algebra.Lie.BaseChange

Cited by

5 results in Mathlib

Foundations

Depth 8 from the axioms · uses no axioms

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule