proposition: Lemma normalFieldf K : normalField K {:L}.
proof: Proof. apply/normalFieldP=> a _; have [r /eqP->] := splitting_field_normal K a. by exists r => //; apply/allP=> b; rewrite /= memvf. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop ssralg poly) mathcomp(polydiv finset fingroup morphism quotient perm) mathcomp(action zmodp cyclic matrix mxalgebra vector) mathcomp(falgebra fieldext separable)