proposition: Lemma galoisS K M E : (K <= M <= E)%VS -> galois K E -> galois M E.
proof: Proof. case/andP=> sKM sME /and3P[_ sepUV nUV]. by rewrite /galois sME (separableSl sKM) ?(normalFieldS sKM). 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)