Theorems · Theorem · group theory
AddSubmonoid.fg_iff_mul_fg
∀ {M : Type u_3} [inst : AddMonoid M] (P : AddSubmonoid M), P.FG ↔ (AddSubmonoid.toSubmonoid P).FG- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites12
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
- Submonoidstatement · cited by 3,086
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- Multiplicativestatement and proof · cited by 875
- OrderIsostatement · cited by 874
- Additiveproof · cited by 356
- AddSubmonoid.FGstatement and proof · cited by 36
- Submonoid.FGstatement and proof · cited by 24
- Submonoid.toAddSubmonoidproof · cited by 5
- AddSubmonoid.toSubmonoidstatement and proof · cited by 4
- Submonoid.fg_iff_add_fgproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.fg_iff_mul_fgproof · cited by 1
- AddMonoid.fg_iff_mul_fgproof · cited by 0