proposition: Lemma lcosetP A x y : reflect (exists2 a, a \in A & y = x * a) (y \in x *: A).
proof: Proof. by rewrite -lcosetE; apply: imsetP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)