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Theorems · Theorem · group theory

AddCon.addConGen_le

∀ {M : Type u_1} [inst : Add M] {r : M → M → Prop} {c : AddCon M}, addConGen r ≤ c ↔ r ≤ ⇑c

The smallest additive congruence relation containing a binary relation r is contained in any additive congruence relation containing r.

Defined in
Mathlib.GroupTheory.Congruence.Defs
Cited by
2 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Quot.sound
Assumes
Add
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Around this declaration

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

AddCon.gi · cited by 5AddCon.giAddCon.le_comap_addConGen · cited by 1AddCon.le_comap_addConGenPresentedAddMonoid.toMonoid.unique · cited by 0toMonoid.uniqueDFunLike.coe · cited by 62936DFunLike.coele_trans · cited by 985le_transAddCon · cited by 138AddConsInf_le · cited by 110sInf_leaddConGen · cited by 28addConGenAddCon.le_addConGen · cited by 1AddCon.le_addConGenAddCon.addConGen_eq · cited by 1AddCon.addConGen_eqAddCon.addConGen_leCITED BYCITES

Cites7

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

Cited by3

Results whose statement or proof uses this declaration.