Theorems · Theorem · group theory
Subgroup.ext
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, (∀ (x : G), x ∈ H ↔ x ∈ K) → H = KTwo subgroups are equal if they have the same elements.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 108 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 76 definitions · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.extproof · cited by 92
Cited by108
Results whose statement or proof uses this declaration.
- MonoidHom.range_eq_mapproof · cited by 37
- QuotientGroup.ker_mk'proof · cited by 18
- Subgroup.upperCentralSeries_oneproof · cited by 7
- Matrix.GeneralLinearGroup.center_eq_range_scalarproof · cited by 6
- Subgroup.zpowers_eq_closureproof · cited by 5
- IntermediateField.fixingSubgroup_botproof · cited by 4
- MulAction.stabilizer_coe_finsetproof · cited by 4
- Submodule.range_unitsToPicproof · cited by 4
- CongruenceSubgroup.Gamma_one_topproof · cited by 3
- Subgroup.comap_idproof · cited by 3
- Subgroup.bot_subgroupOfproof · cited by 2
- Subgroup.subsingleton_iffproof · cited by 2