Theorems · Inductive type · group theory
SubgroupClass
(S : Type u_3) → (G : outParam (Type u_4)) → [DivInvMonoid G] → [SetLike S G] → Prop
SubgroupClass S G states S is a type of subsets s ⊆ G that are subgroups of G.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- DivInvMonoidSetLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement · cited by 1,084
- DivInvMonoidstatement · cited by 103
Cited by39
Results whose statement or proof uses this declaration.
- mul_mem_cancel_rightstatement and proof · cited by 11
- mul_mem_cancel_leftstatement and proof · cited by 10
- div_memstatement and proof · cited by 9
- zpow_memstatement and proof · cited by 8
- SubgroupClass.inclusionstatement and proof · cited by 6
- SubgroupClass.subtypestatement and proof · cited by 4
- op_smul_coe_setstatement and proof · cited by 3
- smul_coe_setstatement and proof · cited by 3
- exists_inv_mem_iff_exists_memstatement and proof · cited by 1
- IsApproximateSubgroup.subgroupstatement and proof · cited by 1
- Subgroup.ofClassstatement and proof · cited by 1
- div_mem_comm_iffstatement and proof · cited by 1