Theorems · Theorem · group theory
AddSubgroup.map_le_iff_le_comap
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {f : G →+ N} {K : AddSubgroup G}
{H : AddSubgroup N}, AddSubgroup.map f K ≤ H ↔ K ≤ AddSubgroup.comap f H- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- Set.image_subset_iffproof · cited by 203
- AddSubgroup.mapstatement · cited by 189
- AddSubgroup.comapstatement · cited by 123
Cited by10
Results whose statement or proof uses this declaration.
- AddSubgroup.gc_map_comapproof · cited by 12
- AddSubgroup.map_addCommutatorproof · cited by 6
- AddSubgroup.comap_normalizer_eq_of_le_rangeproof · cited by 2
- AddSubgroup.map_le_map_iff_of_injectiveproof · cited by 2
- AddSubgroup.map_le_map_iffproof · cited by 1
- AddSubgroup.map_normalClosure_leproof · cited by 1
- AddMonoidHom.range_eq_bot_iffproof · cited by 1
- AddSubgroup.comap_le_comap_of_le_rangeproof · cited by 1
- AddCommGroup.map_torsion_leproof · cited by 0
- AddSubgroup.closure_prodproof · cited by 0