Theorems · Theorem · nonassociative algebras

LieSubmodule.tmul_mem_baseChange_of_mem

∀ {R : Type u_1} {A : Type u_2} {L : Type u_3} {M : Type u_4} [inst : CommRing R] [inst_1 : LieRing L]
  [inst_2 : LieAlgebra R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M]
  [inst_6 : LieModule R L M] [inst_7 : CommRing A] [inst_8 : Algebra R A] {N : LieSubmodule R L M} (a : A) {m : M},
  m ∈ N → a ⊗ₜ[R] m ∈ LieSubmodule.baseChange A N

Defined in

Mathlib.Algebra.Lie.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleCommRingAlgebra