proposition: Lemma splittingFieldForS (K M E : {subfield L}) p : (K <= M)%VS -> (M <= E)%VS -> splittingFieldFor K p E -> splittingFieldFor M p E.
proof: Proof. move=> sKM sKE [rs Dp genL]; exists rs => //; apply/eqP. rewrite eqEsubv -[in X in _ && (X <= _)%VS]genL adjoin_seqSl // andbT. by apply/Fadjoin_seqP; split; rewrite // -genL; apply: seqv_sub_adjoin. 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)