Theorems · Theorem · group theory
AddMonoidHom.mem_range
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {f : G →+ N} {y : N},
y ∈ f.range ↔ ∃ x, f x = y- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidHom.rangestatement · cited by 142
Cited by16
Results whose statement or proof uses this declaration.
- AddMonoidHom.range_eq_mapproof · cited by 15
- AddMonoidHom.noncommPiCoprod_rangeproof · cited by 2
- AddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHomproof · cited by 2
- AddMonoidHom.domRestrict_rangeproof · cited by 1
- AddMonoidHom.injective_noncommPiCoprod_of_iSupIndepproof · cited by 1
- AddGroupExtension.rightHom_inlproof · cited by 1
- AddSubgroup.isFiniteRelIndex_map_nsmulAddMonoidHom_of_fgproof · cited by 1
- AddMonoidHom.exists_addEquiv_range_eq_graphproof · cited by 1
- Submodule.goursat_surjectiveproof · cited by 1
- AddSubgroup.addSubgroupOf_map_nsmulAddMonoidHom_eq_rangeproof · cited by 1
- AddMonoidHom.range_zeroproof · cited by 1
- AddMonoidHom.graph_eq_range_prodproof · cited by 0