Theorems · Theorem · group theory
AddMonoidHom.mrange_eq_map
∀ {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 = AddSubmonoid.map f ⊤- Cited by
- 15 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- 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
- AddSubmonoid.mapstatement · cited by 99
- AddMonoidHom.mrangestatement · cited by 61
- AddSubmonoid.copy_eqproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- AddMonoid.fg_iff_addSubmonoid_fgproof · cited by 3
- AddMonoid.Coprod.mclosure_range_inl_union_inrproof · cited by 3
- AddMonoid.fg_of_surjectiveproof · cited by 3
- AddSubmonoid.mrange_inlproof · cited by 2
- AddMonoidHom.map_mrangeproof · cited by 2
- AddSubmonoid.mrange_inrproof · cited by 2
- FreeAddMonoid.mrange_liftproof · cited by 1
- AddSubmonoid.sup_eq_rangeproof · cited by 1
- AddMonoid.fg_iff_exists_freeAddMonoid_hom_surjectiveproof · cited by 1
- AddSubmonoid.FG.map_injectiveproof · cited by 1
- AddMonoid.Coprod.mrange_eqproof · cited by 1
- AddSubmonoid.codisjoint_mapproof · cited by 0