Theorems · Theorem · group theory
Subgroup.map_mono
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} {K K' : Subgroup G},
K ≤ K' → Subgroup.map f K ≤ Subgroup.map f K'- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 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.
- 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_monoproof · cited by 197
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.map_le_rangeproof · cited by 5
- Subgroup.IsSubnormal.mapproof · cited by 2
- Subgroup.IsSubnormal.trans'proof · cited by 2
- Subgroup.Normal.conjActproof · cited by 2
- Subgroup.normalCore_eq_iInf_map_conjproof · cited by 1
- Subgroup.commutator_le_focalSubgroupproof · cited by 0
- IsConj.normalClosure_eq_top_ofproof · cited by 0
- Subgroup.map_inf_leproof · cited by 0