proposition: Lemma F_r1 : 'Fix_to[r1] = [set x | (coin0 x == coin1 x)&&(coin1 x == coin2 x)&&(coin2 x == coin3 x)].
proof: Proof. apply/setP=> x; rewrite (sameP afix1P eqP) !inE eqperm_map /=. rewrite /act_f r1_inv !ffunE !permE andbC. by do 3![case E: {+}(_ == _); rewrite // {E}(eqP E)]; rewrite eqxx. 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)