Theorems · Theorem · nonassociative algebras

LieSubmodule.lie_coe_mem_lie

∀ {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] {N : LieSubmodule R L M} [inst_5 : LieAlgebra R L]
  {I : LieIdeal R L} (x : ↥I) (m : ↥N), ⁅↑x, ↑m⁆ ∈ ⁅I, N⁆

Defined in

Mathlib.Algebra.Lie.IdealOperations

Cited by

5 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModuleLieAlgebra