Theorems · Theorem · linear algebra

Submodule.mem_span

∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {x : M}
  {s : Set M}, x ∈ Submodule.span R s ↔ ∀ (p : Submodule R M), s ⊆ ↑p → x ∈ p

Defined in

Mathlib.LinearAlgebra.Span.Defs

Cited by

5 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModule