proposition: Lemma card_pX1p2 : #|p^{1+2}| = (p ^ 3)%N.
proof: Proof. rewrite [@gtype _]unlock -(sdprod_card (sdprod_sdpair _)). rewrite !card_injm ?injm_sdpair1 ?injm_sdpair2 // !cardsT card_prod card_ord. by rewrite -mulnA Zp_cast. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism presentation) mathcomp(quotient action commutator gproduct gfunctor) mathcomp(ssralg finalg zmodp cyclic pgroup center gseries) mathcomp(nilpotent sylow abelian finmodule matrix maximal) mathcomp(extremal)