Theorems · Theorem · group theory
Submonoid.fg_iff_add_fg
∀ {M : Type u_1} [inst : Monoid M] (P : Submonoid M), P.FG ↔ (Submonoid.toAddSubmonoid P).FG- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Set.preimageproof · cited by 4,946
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- Set.Finiteproof · cited by 1,814
- AddSubmonoidstatement · cited by 1,178
- OrderIsostatement · cited by 874
- Additivestatement and proof · cited by 356
- AddSubmonoid.closureproof · cited by 224
- Submonoid.closureproof · cited by 167
- Additive.ofMulproof · cited by 155
Cited by3
Results whose statement or proof uses this declaration.
- AddSubmonoid.fg_iff_mul_fgproof · cited by 2
- Monoid.fg_iff_add_fgproof · cited by 1
- Subgroup.fg_iff_add_fgproof · cited by 1