Theorems · Theorem · linear algebra

Submodule.mem_span_iff_exists_finset_subset

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Set M}
  {x : M}, x ∈ Submodule.span R s ↔ ∃ f t, ↑t ⊆ s ∧ Function.support f ⊆ ↑t ∧ ∑ a ∈ t, f a • a = x

Defined in

Mathlib.LinearAlgebra.Finsupp.LinearCombination

Cited by

3 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule