Theorems · Definition · group theory
AddSubmonoid.FG
{M : Type u_1} → [inst : AddMonoid M] → AddSubmonoid M → PropAn additive submonoid of N is finitely generated if it is the closure of a
finite subset of M.
- Defined in
- Mathlib.GroupTheory.Finiteness
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 54 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.closureproof · cited by 224
Cited by38
Results whose statement or proof uses this declaration.
- AddMonoid.FG.fg_topstatement · cited by 10
- AddMonoid.fg_defstatement and proof · cited by 6
- AddSubgroup.fg_iff_addSubmonoid_fgstatement and proof · cited by 6
- AddSubmonoid.fg_iffstatement and proof · cited by 5
- AddSubmonoid.fg_iff_exists_fin_addMonoidHomstatement and proof · cited by 4
- Submodule.fg_iff_addSubmonoid_fgstatement and proof · cited by 3
- Submonoid.fg_iff_add_fgstatement and proof · cited by 3
- AddMonoid.fg_iff_addSubmonoid_fgstatement and proof · cited by 3
- AddSubmonoid.FG.supstatement and proof · cited by 2
- IsSemilinearSet.exists_fg_eq_subtypeVal₂statement and proof · cited by 2
- IsSemilinearSet.interproof · cited by 2
- IsLinearSet.of_fgstatement and proof · cited by 2