Theorems · Theorem · group theory
AddMonoidHom.mrange_eq_top
∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {F : Type u_4}
[inst_2 : FunLike F M N] [mc : AddMonoidHomClass F M N] {f : F}, AddMonoidHom.mrange f = ⊤ ↔ Function.Surjective ⇑f- Cited by
- 9 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.rangeproof · cited by 4,705
- Set.univproof · cited by 3,945
- FunLikestatement and proof · cited by 2,560
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement · cited by 1,178
- AddMonoidHomClassstatement and proof · cited by 252
- SetLike.ext'_iffproof · cited by 78
- AddMonoidHom.mrangestatement · cited by 61
Cited by9
Results whose statement or proof uses this declaration.
- AddMonoidHom.mrange_eq_top_of_surjectiveproof · cited by 6
- AddMonoid.fg_of_surjectiveproof · cited by 3
- IsSemilinearSet.interproof · cited by 2
- AddCon.mrange_mk'proof · cited by 1
- DirectSum.IsInternal.addSubmonoid_iSup_eq_topproof · cited by 1
- isSemilinearSet_setOfPred_eqproof · cited by 1
- IsSemilinearSet.sdiffproof · cited by 1
- AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjectiveproof · cited by 1
- IsSemilinearSet.preimageproof · cited by 0