proposition: Lemma F_Sh : 'Fix_to[sh] = [set x | (coin0 x == coin1 x) && (coin2 x == coin3 x)].
proof: Proof. apply/setP=> x; rewrite (sameP afix1P eqP) !inE eqperm_map /=. rewrite /act_f sh_inv !ffunE !permE /=. by rewrite eq_sym (eq_sym (x c3)) andbT andbA !andbb. 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)