Theorems · Theorem · linear algebra

Submodule.span_range_subtype_eq_top_iff

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_9}
  (p : Submodule R M) {s : ι → M} (hs : ∀ (i : ι), s i ∈ p),
  Submodule.span R (Set.range fun i => ⟨s i, ⋯⟩) = ⊤ ↔ Submodule.span R (Set.range s) = p

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModule