Theorems · Theorem · linear algebra

Submodule.span_smul

∀ {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] [inst_5 : SMulCommClass α R M] (a : α) (s : Set M),
  Submodule.span R (a • s) = a • Submodule.span R s

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

3 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulActionSMulCommClass