Theorems · Theorem · group theory
Subgroup.map_subtype_le_map_subtype
∀ {G : Type u_1} [inst : Group G] {G' : Subgroup G} {H K : Subgroup ↥G'},
Subgroup.map G'.subtype H ≤ Subgroup.map G'.subtype K ↔ H ≤ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 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.
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.mapstatement · cited by 301
- Subgroup.subtypestatement · cited by 185
- Subgroup.subtype_injectiveproof · cited by 18
- Subgroup.map_le_map_iff_of_injectiveproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsZGroup.isCyclic_commutatorproof · cited by 1
- Sylow.normalizer_le_centralizer_or_le_commutatorproof · cited by 1
- alternatingGroup.subgroup_eq_top_of_isPreprimitiveproof · cited by 1
- Subgroup.closure_mul_image_eq_topproof · cited by 1