Theorems · Theorem · linear algebra

Submodule.iSup_eq_span

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

Defined in

Mathlib.LinearAlgebra.Span.Defs

Cited by

3 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule