Theorems · Theorem · commutative algebra

Submodule.smul_mem_pointwise_smul

∀ {α : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : Monoid α] [inst_4 : DistribMulAction α M] [inst_5 : SMulCommClass α R M] (m : M) (a : α)
  (S : Submodule R M), m ∈ S → a • m ∈ a • S

Defined in

Mathlib.Algebra.Module.Submodule.Pointwise

Cited by

6 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulActionSMulCommClass