Theorems · Theorem · group theory
AddSubgroup.ext
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G}, (∀ (x : G), x ∈ H ↔ x ∈ K) → H = KTwo AddSubgroups are equal if they have the same elements.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 75 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- SetLike.extproof · cited by 92
Cited by75
Results whose statement or proof uses this declaration.
- AddMonoidHom.range_eq_mapproof · cited by 15
- QuotientAddGroup.ker_mk'proof · cited by 13
- AddSubgroup.zmultiples_eq_closureproof · cited by 9
- AddSubgroup.upperCentralSeries_oneproof · cited by 4
- Subgroup.strictPeriods_eq_zmultiples_one_of_T_memproof · cited by 4
- AddAction.stabilizer_coe_finsetproof · cited by 4
- AddSubgroup.subsingleton_iffproof · cited by 3
- isPointed_iff_support_eq_botproof · cited by 2
- AddSubgroup.bot_addSubgroupOfproof · cited by 2
- AddSubgroup.op_normalizerproof · cited by 2
- AddSubgroup.pi_topproof · cited by 2
- CongruenceSubgroup.strictPeriods_Gammaproof · cited by 2