Canonical subfx_unitAlgType (F L : fieldType) iota (z : L) p :=
Eval hnf in [unitAlgType F of subFExtend iota z p].

Lemma num_field_exists (s : seq algC) :
{Qs : fieldExtType rat & {QsC : {rmorphism Qs -> algC}
& {s1 : seq Qs | map QsC s1 = s & <<1 & s1>>%VS = fullv}}}.