Mathlib Map

Theorems · Inductive type · commutative algebra

RingConGen.Rel

{R : Type u_1} → [Add R] → [Mul R] → (R → R → Prop) → R → R → Prop

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

Defined in
Mathlib.RingTheory.Congruence.Defs
Cited by
5 results in Mathlib
Foundations
Depth 1 from the axioms · uses no axioms
Assumes
AddMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ringConGen · cited by 18ringConGenRingCon.ringConGen_eq · cited by 2RingCon.ringConGen_eqRingConGen.Rel.below · cited by 2Rel.belowRingCon.mapGen_eq_map_of_surjective · cited by 1RingCon.mapGen_eq_map_of_…RingConGen.Rel.recOn · cited by 1Rel.recOnRingConGen.Rel.star · cited by 1Rel.starRingConGen.Rel.brecOn · cited by 1Rel.brecOnRingConGen.Rel.casesOn · cited by 0Rel.casesOnRingConGen.Rel.below.casesOn · cited by 0below.casesOnRingQuot.eqvGen_rel_eq · cited by 0RingQuot.eqvGen_rel_eqRingConGen.RelCITED BYCITES

Cites0

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

Nothing in Mathlib beyond the foundations.

Cited by10

Results whose statement or proof uses this declaration.