--- /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 "Basic-1/pr3/defs.ma".
+
+definition pc3:
+ C \to (T \to (T \to Prop))
+\def
+ \lambda (c: C).(\lambda (t1: T).(\lambda (t2: T).(ex2 T (\lambda (t: T).(pr3
+c t1 t)) (\lambda (t: T).(pr3 c t2 t))))).
+
+inductive pc3_left (c: C): T \to (T \to Prop) \def
+| pc3_left_r: \forall (t: T).(pc3_left c t t)
+| pc3_left_ur: \forall (t1: T).(\forall (t2: T).((pr2 c t1 t2) \to (\forall
+(t3: T).((pc3_left c t2 t3) \to (pc3_left c t1 t3)))))
+| pc3_left_ux: \forall (t1: T).(\forall (t2: T).((pr2 c t1 t2) \to (\forall
+(t3: T).((pc3_left c t1 t3) \to (pc3_left c t2 t3))))).
+