Theorems · Theorem · group theory
Subgroup.map_le_iff_le_comap
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} {K : Subgroup G} {H : Subgroup N},
Subgroup.map f K ≤ H ↔ K ≤ Subgroup.comap f H- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 13 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.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- Set.image_subset_iffproof · cited by 203
- Subgroup.comapstatement · cited by 154
Cited by13
Results whose statement or proof uses this declaration.
- Subgroup.gc_map_comapproof · cited by 12
- Subgroup.comap_normalizer_eq_of_le_rangeproof · cited by 2
- Subgroup.isPretransitive_of_stabilizer_ltproof · cited by 2
- Subgroup.map_le_map_iff_of_injectiveproof · cited by 2
- Sylow.mapSurjective_surjectiveproof · cited by 2
- Sylow.exists_comap_eq_of_ker_isPGroupproof · cited by 2
- Subgroup.Normal.conjActproof · cited by 2
- Subgroup.comap_le_comap_of_le_rangeproof · cited by 1
- MonoidHom.range_eq_bot_iffproof · cited by 1
- CommGroup.map_torsion_leproof · cited by 0
- IsConj.normalClosure_eq_top_ofproof · cited by 0
- Subgroup.map_le_map_iffproof · cited by 0