Theorems · Theorem · group theory
AddSubmonoid.mem_closure_finset
∀ {M : Type u_1} [inst : AddCommMonoid M] {x : M} {s : Finset M},
x ∈ AddSubmonoid.closure ↑s ↔ ∃ f, Function.support f ⊆ ↑s ∧ ∑ a ∈ s, f a • a = x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement and proof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- AddSubmonoidstatement · cited by 1,178
- Function.supportstatement and proof · cited by 610
- SetLike.mem_coeproof · cited by 302
- AddSubmonoid.closurestatement and proof · cited by 224
- zero_nsmulproof · cited by 137
- Finset.sum_subsetproof · cited by 79
Cited by2
Results whose statement or proof uses this declaration.
- IsLinearSet.isProperSemilinearSetproof · cited by 1
- AddSubmonoid.closure_addIrreducibleproof · cited by 0