proposition: Lemma act0r x : 0 ^@ x = 0.
proof: Proof. by rewrite /actr conj1g morph1 if_same. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype bigop ssralg finset fingroup) mathcomp(morphism perm finalg action gproduct commutator) mathcomp(cyclic)