proposition: Lemma nub_In_cons:forall x xs, In x xs -> nub (x :: xs)=nub xs.
proof: Proof. intros x [|y ys]; simpl; [intros H_; contradiction H_|]; intros [H1|H1]. destruct (eq_dec y x) as [H2|H2];[destruct (In_dec eq_dec y ys) as [H3|H3]; trivial|contradiction H2]. destruct (eq_dec y x) as [H2|H2];[destruct (In_dec eq_dec y ys) as [H3|H3]; trivial|]; destruct (In_dec eq_dec x ys) as [H3|H3]; trivial; contradiction H3. Qed.
imports: List Streams Omega