proposition: Lemma Mho_p_elt (p : nat) x : x \in A -> p.-elt x -> x ^+ (p ^ n) \in Mho.
proof: Proof. move=> Ax p_x; have [-> | ntx] := eqVneq x 1; first by rewrite groupX. by apply/mem_gen/imsetP; exists x; rewrite ?inE ?Ax (pdiv_p_elt p_x). Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism action) mathcomp(quotient gfunctor gproduct ssralg countalg finalg zmodp) mathcomp(cyclic pgroup gseries nilpotent sylow)