proposition: Lemma card_rot : #|rot| = 4.
proof: Proof. rewrite -[4]/(size [:: id1; r1; r2; r3]) -(card_uniqP _). by apply: eq_card => x; rewrite rot_is_rot !inE -!orbA. by apply: map_uniq (fun p : {perm square} => p c0) _ _; rewrite /= !permE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype tuple finfun bigop finset fingroup) mathcomp(action perm primitive_action)