--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "LambdaDelta-1/G/defs.ma".
+
+include "LambdaDelta-1/pc3/defs.ma".
+
+inductive ty3 (g: G): C \to (T \to (T \to Prop)) \def
+| ty3_conv: \forall (c: C).(\forall (t2: T).(\forall (t: T).((ty3 g c t2 t)
+\to (\forall (u: T).(\forall (t1: T).((ty3 g c u t1) \to ((pc3 c t1 t2) \to
+(ty3 g c u t2))))))))
+| ty3_sort: \forall (c: C).(\forall (m: nat).(ty3 g c (TSort m) (TSort (next
+g m))))
+| ty3_abbr: \forall (n: nat).(\forall (c: C).(\forall (d: C).(\forall (u:
+T).((getl n c (CHead d (Bind Abbr) u)) \to (\forall (t: T).((ty3 g d u t) \to
+(ty3 g c (TLRef n) (lift (S n) O t))))))))
+| ty3_abst: \forall (n: nat).(\forall (c: C).(\forall (d: C).(\forall (u:
+T).((getl n c (CHead d (Bind Abst) u)) \to (\forall (t: T).((ty3 g d u t) \to
+(ty3 g c (TLRef n) (lift (S n) O u))))))))
+| ty3_bind: \forall (c: C).(\forall (u: T).(\forall (t: T).((ty3 g c u t) \to
+(\forall (b: B).(\forall (t1: T).(\forall (t2: T).((ty3 g (CHead c (Bind b)
+u) t1 t2) \to (ty3 g c (THead (Bind b) u t1) (THead (Bind b) u t2)))))))))
+| ty3_appl: \forall (c: C).(\forall (w: T).(\forall (u: T).((ty3 g c w u) \to
+(\forall (v: T).(\forall (t: T).((ty3 g c v (THead (Bind Abst) u t)) \to (ty3
+g c (THead (Flat Appl) w v) (THead (Flat Appl) w (THead (Bind Abst) u
+t)))))))))
+| ty3_cast: \forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c t1 t2)
+\to (\forall (t0: T).((ty3 g c t2 t0) \to (ty3 g c (THead (Flat Cast) t2 t1)
+(THead (Flat Cast) t0 t2))))))).
+