proposition: Lemma rcoset_inj : left_injective (fun A x => A :* x).
proof: Proof. by move=> x; apply: can_inj (rcosetK x). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)