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[helm.git] / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / pc3 / nf2.ma

diff --git a/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/pc3/nf2.ma b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/pc3/nf2.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/pc3/defs.ma".
+
+include "LambdaDelta-1/nf2/pr3.ma".
+
+theorem pc3_nf2:
+ \forall (c: C).(\forall (t1: T).(\forall (t2: T).((pc3 c t1 t2) \to ((nf2 c 
+t1) \to ((nf2 c t2) \to (eq T t1 t2))))))
+\def
+ \lambda (c: C).(\lambda (t1: T).(\lambda (t2: T).(\lambda (H: (pc3 c t1 
+t2)).(\lambda (H0: (nf2 c t1)).(\lambda (H1: (nf2 c t2)).(let H2 \def H in 
+(ex2_ind T (\lambda (t: T).(pr3 c t1 t)) (\lambda (t: T).(pr3 c t2 t)) (eq T 
+t1 t2) (\lambda (x: T).(\lambda (H3: (pr3 c t1 x)).(\lambda (H4: (pr3 c t2 
+x)).(let H_y \def (nf2_pr3_unfold c t1 x H3 H0) in (let H5 \def (eq_ind_r T x 
+(\lambda (t: T).(pr3 c t2 t)) H4 t1 H_y) in (let H6 \def (eq_ind_r T x 
+(\lambda (t: T).(pr3 c t1 t)) H3 t1 H_y) in (let H_y0 \def (nf2_pr3_unfold c 
+t2 t1 H5 H1) in (let H7 \def (eq_ind T t2 (\lambda (t: T).(pr3 c t t1)) H5 t1 
+H_y0) in (eq_ind_r T t1 (\lambda (t: T).(eq T t1 t)) (refl_equal T t1) t2 
+H_y0))))))))) H2))))))).
+