Theorems · Theorem · group theory
Subgroup.range_subtype
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), H.subtype.range = H- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 24 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
- SetLike.coe_injectiveproof · cited by 374
- MonoidHom.rangestatement and proof · cited by 314
- Subgroup.subtypestatement and proof · cited by 185
- Subtype.range_coeproof · cited by 98
- MonoidHom.coe_rangeproof · cited by 4
Cited by28
Results whose statement or proof uses this declaration.
- Subgroup.relIndex_comapproof · cited by 7
- Subgroup.map_subtype_commutatorproof · cited by 7
- Subgroup.map_subtype_leproof · cited by 5
- IsPGroup.mapproof · cited by 4
- Subgroup.isCyclic_iff_exists_zpowers_eq_topproof · cited by 4
- Subgroup.subtype_rangeproof · cited by 3
- Group.IsSolvable.commutator_lt_of_ne_botproof · cited by 2
- MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2
- Subgroup.isPerfect_iffproof · cited by 2
- Subgroup.isPretransitive_of_stabilizer_ltproof · cited by 2
- Subgroup.noncommPiCoprod_rangeproof · cited by 2
- Subgroup.IsSubnormal.trans'proof · cited by 2