Theorems · Theorem · linear algebra

Submodule.span_iUnion

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Sort u_9}
  (s : ι → Set M), Submodule.span R (⋃ i, s i) = ⨆ i, Submodule.span R (s i)

Defined in

Mathlib.LinearAlgebra.Span.Defs

Cited by

6 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule