proposition: Lemma imsetAC E F G : [set prodAC x | x in E `* F `* G] = E `* G `* F.
proof: Proof. apply/setP => -[[a c] b]; apply/imsetP/idP. - rewrite ex2C; move=> [[[a' b'] c']] /eqP. by rewrite /f !inE !xpair_eqE /= => /andP [] /andP [] /eqP -> /eqP -> /eqP -> /andP [] /andP [] -> -> ->. - by rewrite !inE /= => /andP [] /andP [] aE cG bF; exists ((a, b), c); rewrite // !inE /= aE cG bF. Qed.
imports: mathcomp(all_ssreflect ssralg fingroup perm matrix) mathcomp(all_algebra vector reals normedtype) mathcomp(mathcomp_extra boolp) mathcomp(Rstruct) ssrR logb realType_ext ssr_ext ssralg_ext bigop_ext