proposition: Lemma rcosets_cycle_partition : partition (HG :* <[g]>) G.
proof: Proof. by rewrite defHGg; have [] := partition_partition partHG partHGg. 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)