Theorems · Theorem · group theory
AddSubmonoid.FG.iSup
∀ {M : Type u_1} [inst : AddMonoid M] {ι : Sort u_3} [Finite ι] (P : ι → AddSubmonoid M),
(∀ (i : ι), (P i).FG) → (iSup P).FG- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Set.univproof · cited by 3,945
- Finitestatement and proof · cited by 3,029
- AddMonoidstatement and proof · cited by 2,864
- iSupstatement and proof · cited by 2,415
- AddSubmonoidstatement and proof · cited by 1,178
- Set.mem_univproof · cited by 416
- iSup_congr_Propproof · cited by 247
- iSup_posproof · cited by 61
- Set.finite_univproof · cited by 52
- AddSubmonoid.FGstatement and proof · cited by 36
- iSup_plift_downproof · cited by 10
- AddSubmonoid.FG.biSupproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsSemilinearSet.exists_fg_eq_subtypeValproof · cited by 1