Theorems · Theorem · commutative algebra
AddSubmonoid.fg_iff_exists_fin_addMonoidHom
∀ {M : Type u_3} [inst : AddCommMonoid M] {S : AddSubmonoid M}, S.FG ↔ ∃ n f, AddMonoidHom.mrange f = S- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapproof · cited by 10,215
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubmonoidstatement and proof · cited by 1,178
- LinearMap.rangeproof · cited by 893
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- Submodule.toAddSubmonoidproof · cited by 162
- AddMonoidHom.mrangestatement and proof · cited by 61
- AddSubmonoid.FGstatement and proof · cited by 36
- AddSubmonoid.toNatSubmoduleproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- IsSemilinearSet.interproof · cited by 2
- IsSemilinearSet.sdiffproof · cited by 1
- isSemilinearSet_setOfPred_eqproof · cited by 1
- IsSemilinearSet.preimageproof · cited by 0