proposition: Lemma galS K M E : (K <= M)%VS -> 'Gal(E / M) \subset 'Gal(E / K).
proof: Proof. rewrite gal_cap (gal_cap K E) => sKM; apply/subsetP=> x. by rewrite !gal_kAut ?capvSr //; apply: kAutS; apply: capvS. 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)