(* The typing judgement is compatible with substitution, i.e., substituting a well-typed term for a term variable. *)

(* Specifications: *)
Lemma substitution:
forall E x t2 T1 T2,
j (insert x T1 E) t2 T2 ->
forall t1,
j E t1 T1 ->
j E (subst t1 x t2) T2.