Fact Crat_key : pred_key Crat.Fact Crat_divring_closed : divring_closed Crat.Canonical Crat_keyed := KeyedPred Crat_key.Canonical Crat_opprPred := OpprPred Crat_divring_closed.Canonical Crat_addrPred := AddrPred Crat_divring_closed.Canonical Crat_mulrPred := MulrPred Crat_divring_closed.Canonical Crat_zmodPred := ZmodPred Crat_divring_closed.Canonical Crat_semiringPred := SemiringPred Crat_divring_closed.Canonical Crat_smulrPred := SmulrPred Crat_divring_closed.Canonical Crat_divrPred := DivrPred Crat_divring_closed.Canonical Crat_subringPred := SubringPred Crat_divring_closed.Canonical Crat_sdivrPred := SdivrPred Crat_divring_closed.Canonical Crat_divringPred := DivringPred Crat_divring_closed.

Lemma rpred_Crat S (ringS : divringPred S) (kS : keyed_pred ringS) : {subset Crat <= kS}.