End DecField.
Module PreClosedField.
Section UseAxiom.
Variable F : fieldType.
Hypothesis closedF : GRing.ClosedField.axiom F.
Implicit Type p : {poly F}.

(* Specifications: *)
Lemma closed_rootP p : reflect (exists x, root p x) (size p != 1%N).
Lemma closed_nonrootP p : reflect (exists x, ~~ root p x) (p != 0).
End UseAxiom.