Theorems · Theorem · group theory
AddSubmonoid.mem_closure_iff_exists_finset_subset
∀ {M : Type u_1} [inst : AddCommMonoid M] {x : M} {s : Set M},
x ∈ AddSubmonoid.closure s ↔ ∃ f t, ↑t ⊆ s ∧ Function.support f ⊆ ↑t ∧ ∑ a ∈ t, f a • a = x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- Finset.sum_congrproof · cited by 2,323
- AddSubmonoidstatement · cited by 1,178
- one_ne_zeroproof · cited by 885
- Function.supportstatement and proof · cited by 610
- Pi.singleproof · cited by 518
- SetLike.mem_coeproof · cited by 302
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.mem_closure_finsetproof · cited by 2