Theorems · Theorem · group theory
Submonoid.exists_multiset_of_mem_closure
∀ {M : Type u_4} [inst : CommMonoid M] {s : Set M} {x : M}, x ∈ Submonoid.closure s → ∃ l, (∀ y ∈ l, y ∈ s) ∧ l.prod = x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Submonoidstatement · cited by 3,086
- Multisetstatement · cited by 2,627
- CommMonoidstatement and proof · cited by 2,264
- Multiset.prodstatement · cited by 528
- Multiset.ofListproof · cited by 290
- Submonoid.closurestatement and proof · cited by 167
- Multiset.prod_coeproof · cited by 12
- Submonoid.exists_list_of_mem_closureproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.splits_iff_exists_multiset'proof · cited by 4
- divisor_closure_eq_closureproof · cited by 0