--- /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 *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pr3/pr3".
+
+include "pr3/props.ma".
+
+include "pr2/pr2.ma".
+
+theorem pr3_strip:
+ \forall (c: C).(\forall (t0: T).(\forall (t1: T).((pr3 c t0 t1) \to (\forall
+(t2: T).((pr2 c t0 t2) \to (ex2 T (\lambda (t: T).(pr3 c t1 t)) (\lambda (t:
+T).(pr3 c t2 t))))))))
+\def
+ \lambda (c: C).(\lambda (t0: T).(\lambda (t1: T).(\lambda (H: (pr3 c t0
+t1)).(pr3_ind c (\lambda (t: T).(\lambda (t2: T).(\forall (t3: T).((pr2 c t
+t3) \to (ex2 T (\lambda (t4: T).(pr3 c t2 t4)) (\lambda (t4: T).(pr3 c t3
+t4))))))) (\lambda (t: T).(\lambda (t2: T).(\lambda (H0: (pr2 c t
+t2)).(ex_intro2 T (\lambda (t3: T).(pr3 c t t3)) (\lambda (t3: T).(pr3 c t2
+t3)) t2 (pr3_pr2 c t t2 H0) (pr3_refl c t2))))) (\lambda (t2: T).(\lambda
+(t3: T).(\lambda (H0: (pr2 c t3 t2)).(\lambda (t4: T).(\lambda (_: (pr3 c t2
+t4)).(\lambda (H2: ((\forall (t5: T).((pr2 c t2 t5) \to (ex2 T (\lambda (t:
+T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c t5 t))))))).(\lambda (t5: T).(\lambda
+(H3: (pr2 c t3 t5)).(ex2_ind T (\lambda (t: T).(pr2 c t5 t)) (\lambda (t:
+T).(pr2 c t2 t)) (ex2 T (\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c
+t5 t))) (\lambda (x: T).(\lambda (H4: (pr2 c t5 x)).(\lambda (H5: (pr2 c t2
+x)).(ex2_ind T (\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c x t))
+(ex2 T (\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c t5 t))) (\lambda
+(x0: T).(\lambda (H6: (pr3 c t4 x0)).(\lambda (H7: (pr3 c x x0)).(ex_intro2 T
+(\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c t5 t)) x0 H6 (pr3_sing c
+x t5 H4 x0 H7))))) (H2 x H5))))) (pr2_confluence c t3 t5 H3 t2 H0))))))))))
+t0 t1 H)))).
+
+theorem pr3_confluence:
+ \forall (c: C).(\forall (t0: T).(\forall (t1: T).((pr3 c t0 t1) \to (\forall
+(t2: T).((pr3 c t0 t2) \to (ex2 T (\lambda (t: T).(pr3 c t1 t)) (\lambda (t:
+T).(pr3 c t2 t))))))))
+\def
+ \lambda (c: C).(\lambda (t0: T).(\lambda (t1: T).(\lambda (H: (pr3 c t0
+t1)).(pr3_ind c (\lambda (t: T).(\lambda (t2: T).(\forall (t3: T).((pr3 c t
+t3) \to (ex2 T (\lambda (t4: T).(pr3 c t2 t4)) (\lambda (t4: T).(pr3 c t3
+t4))))))) (\lambda (t: T).(\lambda (t2: T).(\lambda (H0: (pr3 c t
+t2)).(ex_intro2 T (\lambda (t3: T).(pr3 c t t3)) (\lambda (t3: T).(pr3 c t2
+t3)) t2 H0 (pr3_refl c t2))))) (\lambda (t2: T).(\lambda (t3: T).(\lambda
+(H0: (pr2 c t3 t2)).(\lambda (t4: T).(\lambda (_: (pr3 c t2 t4)).(\lambda
+(H2: ((\forall (t5: T).((pr3 c t2 t5) \to (ex2 T (\lambda (t: T).(pr3 c t4
+t)) (\lambda (t: T).(pr3 c t5 t))))))).(\lambda (t5: T).(\lambda (H3: (pr3 c
+t3 t5)).(ex2_ind T (\lambda (t: T).(pr3 c t5 t)) (\lambda (t: T).(pr3 c t2
+t)) (ex2 T (\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c t5 t)))
+(\lambda (x: T).(\lambda (H4: (pr3 c t5 x)).(\lambda (H5: (pr3 c t2
+x)).(ex2_ind T (\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c x t))
+(ex2 T (\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c t5 t))) (\lambda
+(x0: T).(\lambda (H6: (pr3 c t4 x0)).(\lambda (H7: (pr3 c x x0)).(ex_intro2 T
+(\lambda (t: T).(pr3 c t4 t)) (\lambda (t: T).(pr3 c t5 t)) x0 H6 (pr3_t x t5
+c H4 x0 H7))))) (H2 x H5))))) (pr3_strip c t3 t5 H3 t2 H0)))))))))) t0 t1
+H)))).
+