Theorems · Theorem · group theory
AddMonoid.fg_iff
∀ {M : Type u_1} [inst : AddMonoid M], AddMonoid.FG M ↔ ∃ S, AddSubmonoid.closure S = ⊤ ∧ S.FiniteAn equivalent expression of AddMonoid.FG in terms of Set.Finite instead of Finset.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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
- Top.topstatement and proof · cited by 9,680
- AddMonoidstatement and proof · cited by 2,864
- Set.Finitestatement and proof · cited by 1,814
- AddSubmonoidstatement · cited by 1,178
- AddSubmonoid.closurestatement and proof · cited by 224
- AddMonoid.FGstatement and proof · cited by 31
- AddMonoid.FG.fg_topproof · cited by 10
- AddSubmonoid.fg_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjectiveproof · cited by 1