Canonical Crat_span_opprPred s := OpprPred (Crat_span_zmod_closed s).
Canonical Crat_span_addrPred s := AddrPred (Crat_span_zmod_closed s).
Canonical Crat_span_zmodPred s := ZmodPred (Crat_span_zmod_closed s).
Section MoreAlgCaut.
Implicit Type rR : unitRingType.

(* Specifications: *)
Lemma alg_num_field (Qz : fieldExtType rat) a : a%:A = ratr a :> Qz.
Lemma Crat_spanM b : {in Crat & Crat_span b, forall a x, a * x \in Crat_span b}.
Lemma restrict_aut_to_num_field (nu : {rmorphism algC -> algC}) :
(forall x, exists y, nu (QnC x) = QnC y) ->
{nu0 : {lrmorphism Qn -> Qn} | {morph QnC : x / nu0 x >-> nu x}}.
Lemma map_Qnum_poly (nu : {rmorphism algC -> algC}) p :
p \in polyOver 1%VS -> map_poly (nu \o QnC) p = (map_poly QnC p).