Mathlib Map

Theorems · Definition · group theory

Con.subgroup

{G : Type u_1} → [inst : Group G] → Con G → Subgroup G

The subgroup defined by the class of 1 for a congruence relation on a group.

Defined in
Mathlib.GroupTheory.QuotientGroup.Defs
Cited by
4 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
Group
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup.orderIsoCon · cited by 3Subgroup.orderIsoConCon.mem_subgroup_iff · cited by 1Con.mem_subgroup_iffCon.subgroup_quotientGroupCon · cited by 0Con.subgroup_quotientGrou…QuotientGroup.con_subgroup · cited by 0QuotientGroup.con_subgroupSubgroup.orderIsoCon_symm_apply_coe · cited by 0Subgroup.orderIsoCon_symm…DFunLike.coe · cited by 62936DFunLike.coeGroup · cited by 6238GroupSet.ofPred · cited by 6101Set.ofPredSubgroup · cited by 3593SubgroupCon · cited by 152ConCon.subgroupCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.