proposition: Lemma galNorm_gal a x : a \in E -> x \in 'Gal(E / K) -> galNorm K E (x a) = galNorm K E a.
proof: Proof. move=> Ea galEx; rewrite {2}/galNorm (reindex_inj (mulgI x)). by apply: eq_big => [b | b _]; rewrite ?groupMl // galM ?lfunE. 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)