Theorems · Theorem · group theory
Monoid.fg_iff_submonoid_fg
∀ {M : Type u_1} [inst : Monoid M] (N : Submonoid M), Monoid.FG ↥N ↔ N.FG- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- Subtype.coe_injectiveproof · cited by 205
- Submonoid.mapproof · cited by 190
- Submonoid.subtypeproof · cited by 26
- Submonoid.FGstatement and proof · cited by 24
- Monoid.FGstatement and proof · cited by 19
- MonoidHom.mrange_eq_mapproof · cited by 13
- Monoid.FG.fg_topproof · cited by 7
- Submonoid.mrange_subtypeproof · cited by 4
- Submonoid.FG.map_injectiveproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Group.fg_iff_subgroup_fgproof · cited by 2
- IsLocalization.finiteType_of_monoid_fgproof · cited by 2