Lemma vars_with_type_le_length_aux: forall e x tau n, In (Id x) (map (fun p : type * var => Id (snd p)) (filter (fun p : type * nat => proj1_sig (Sumbool.bool_of_sumbool (type_eq_dec tau (fst p)))) (combine e (seq n (length e))))) -> x < n + (length e).