proposition: Lemma nt_prime_order p x : prime p -> x ^+ p = 1 -> x != 1 -> #[x] = p.
proof: Proof. move=> p_pr xp ntx; apply/prime_nt_dvdP; rewrite ?order_eq1 //. by rewrite order_dvdn xp. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice div) mathcomp(fintype bigop prime finset fingroup morphism) mathcomp(perm automorphism quotient gproduct ssralg) mathcomp(finalg zmodp poly)