Theorems · Theorem · group theory
Submonoid.mem_closure_range_iff_of_fintype
∀ {M : Type u_1} [inst : CommMonoid M] {ι : Type u_2} {f : ι → M} {x : M} [inst_1 : Fintype ι],
x ∈ Submonoid.closure (Set.range f) ↔ ∃ a, x = ∏ i, f i ^ a i- Defined in
- Mathlib.Algebra.Group.Submonoid.Finsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Finsuppproof · cited by 5,255
- Set.rangestatement and proof · cited by 4,705
- Equiv.symmproof · cited by 3,681
- Finset.univstatement and proof · cited by 3,473
- Submonoidstatement · cited by 3,086
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_congrproof · cited by 646
- Submonoid.closurestatement and proof · cited by 167
- Finsupp.equivFunOnFiniteproof · cited by 50
Cited by1
Results whose statement or proof uses this declaration.
- Submonoid.mem_closure_iff_of_fintypeproof · cited by 1