Admitted. (* Prop *)

(* Specifications: *)
Lemma orb_true_iff : forall b1 b2,
b1 || b2 = true <-> b1 = true \/ b2 = true.
Theorem beq_nat_false_iff : forall x y : nat,
beq_nat x y = false <-> x <> y.
Theorem beq_id_false_iff : forall x y : id,
beq_id x y = false
<-> x <> y.
Theorem false_beq_id : forall x y : id,
x <> y
-> beq_id x y = false.
Theorem beq_id_false_iff : forall x y : id,
beq_id x y = false
<-> x <> y.
Lemma lookup_bind : forall Gamma i T, lookup Gamma i = Some T <-> bind Gamma i T.
induction Gamma => i T; split; intros; eauto.