(* ------------------------------------- *)

(* Specifications: *)
Lemma binds_concat: forall G F E x A, binds x (Tm A) (F ++ E ++ G) <-> binds x (Tm A) (F) \/ binds x (Tm A) (E) \/ binds x (Tm A) (G).
(* ------------------------------------- *)
Lemma fun_cong : forall A B (f : A -> B) (a b : A),  a = b -> f a = f b.
Lemma multi_preservation : forall G a b A, multi (head_reduction G) a b ->
AnnTyping G a A ->
AnnTyping G b A.