Theorems · Theorem · linear algebra
Submodule.mem_span_finset
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Finset M}
{x : M}, x ∈ Submodule.span R ↑s ↔ ∃ f, Function.support f ⊆ ↑s ∧ ∑ a ∈ s, f a • a = x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Finset.sumstatement and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- Submodule.spanstatement and proof · cited by 1,504
- zero_smulproof · cited by 716
- Function.supportstatement and proof · cited by 610
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.span_singleton_inf_orthogonal_eq_botproof · cited by 2