proposition: Lemma F_Sv : 'Fix_to[sv] = [set x | (coin0 x == coin3 x) && (coin2 x == coin1 x)].
proof: Proof. apply/setP=> x; rewrite (sameP afix1P eqP) !inE eqperm_map /=. rewrite /act_f sv_inv !ffunE !permE /=. by rewrite eq_sym andbT andbC (eq_sym (x c1)) andbA -andbA !andbb andbC. 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)