Theorems · Theorem · linear algebra

Submodule.set_smul_span

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {α : Type u_8}
  [inst_3 : Monoid α] [inst_4 : DistribMulAction α M] [SMulCommClass α R M] (s : Set α) (t : Set M),
  s • Submodule.span R t = Submodule.span R (s • t)

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

3 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulActionSMulCommClass