Local Notation ZtoQ := (intr : int -> rat).Local Notation ZtoC := (intr : int -> algC).Local Notation QtoC := (ratr : rat -> algC).Local Notation intrp := (map_poly intr).Local Notation pZtoQ := (map_poly ZtoQ).Local Notation pZtoC := (map_poly ZtoC).Local Notation pQtoC := (map_poly ratr).Fact Crat_span_subproof s x : decidable (in_Crat_span s x).Definition Crat_span s : pred algC := Crat_span_subproof s.Fact Crat_span_key s : pred_key (Crat_span s).Canonical Crat_span_keyed s := KeyedPred (Crat_span_key s).

Lemma mem_Crat_span s : {subset s <= Crat_span s}.