Theorems · Theorem · group theory
Subgroup.map_subgroupOf_eq_of_le
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H ≤ K → Subgroup.map K.subtype (H.subgroupOf K) = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- Subgroup.subtypestatement · cited by 185
- Subgroup.subgroupOfstatement · cited by 122
- inf_eq_leftproof · cited by 41
- Subgroup.subgroupOf_map_subtypeproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.map_focalSubgroupOfproof · cited by 3
- IsZGroup.isCyclic_commutatorproof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- Subgroup.IsSubnormal.transproof · cited by 0