Theorems · Theorem · group theory
Subgroup.map_eq_range_iff
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} {H : Subgroup G},
Subgroup.map f H = f.range ↔ Codisjoint H f.ker- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- MonoidHom.rangestatement · cited by 314
- Subgroup.mapstatement and proof · cited by 301
- MonoidHom.kerstatement and proof · cited by 212
- Codisjointstatement and proof · cited by 197
- codisjoint_iffproof · cited by 53
- MonoidHom.range_eq_mapproof · cited by 37
- top_sup_eqproof · cited by 8
- Subgroup.map_eq_map_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- map_commutator_eqproof · cited by 0