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Theorems · Definition · group theory

conGen

{M : Type u_1} → [inst : Mul M] → (M → M → Prop) → Con M

The inductively defined smallest multiplicative congruence relation containing a given binary relation.

Defined in
Mathlib.GroupTheory.Congruence.Defs
Cited by
23 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
Mul
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Around this declaration

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

Monoid.CoprodI · cited by 52Monoid.CoprodIMonoid.CoprodI.of · cited by 45CoprodI.ofMonoid.CoprodI.lift · cited by 21CoprodI.liftPresentedMonoid · cited by 10PresentedMonoidCon.gi · cited by 8Con.giPresentedMonoid.mk · cited by 7PresentedMonoid.mkMonoid.PushoutI.con · cited by 2PushoutI.conMonoid.CoprodI.ext_hom · cited by 2CoprodI.ext_homPresentedMonoid.lift · cited by 2PresentedMonoid.liftCon.conGen_le · cited by 2Con.conGen_leHNNExtension.con · cited by 1HNNExtension.conCon.le_comap_conGen · cited by 1Con.le_comap_conGenCon.le_conGen · cited by 1Con.le_conGenPresentedMonoid.mk_eq_mk_iff · cited by 1PresentedMonoid.mk_eq_mk_…Monoid.CoprodI.mrange_eq_iSup · cited by 1CoprodI.mrange_eq_iSupCon · cited by 152ConConGen.Rel · cited by 4ConGen.RelconGenCITED BYCITES

Cites2

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

Cited by33

Results whose statement or proof uses this declaration.