proposition: Lemma Mho0 G : 'Mho^0(G) = G.
proof: Proof. apply/eqP; rewrite eqEsubset Mho_sub /=. apply/subsetP=> x Gx; rewrite -[x]prod_constt group_prod // => p _. exact: Mho_p_elt (groupX _ Gx) (p_elt_constt _ _). 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)