proposition: Lemma galoisClosureP E F K' : (F <= K')%VS -> galois E K' -> (normalClosure E F <= K')%VS.
proof: Proof. by move=> EK' /and3P[FK' _ ] /normalClosureP; apply. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field) Abel(various char0)