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[helm.git] / matita / contribs / LAMBDA-TYPES / Base-1 / types / props.ma

diff --git a/matita/contribs/LAMBDA-TYPES/Base-1/types/props.ma b/matita/contribs/LAMBDA-TYPES/Base-1/types/props.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 "Base-1/types/defs.ma".
+
+theorem ex2_sym:
+ \forall (A: Set).(\forall (P: ((A \to Prop))).(\forall (Q: ((A \to 
+Prop))).((ex2 A (\lambda (x: A).(P x)) (\lambda (x: A).(Q x))) \to (ex2 A 
+(\lambda (x: A).(Q x)) (\lambda (x: A).(P x))))))
+\def
+ \lambda (A: Set).(\lambda (P: ((A \to Prop))).(\lambda (Q: ((A \to 
+Prop))).(\lambda (H: (ex2 A (\lambda (x: A).(P x)) (\lambda (x: A).(Q 
+x)))).(ex2_ind A (\lambda (x: A).(P x)) (\lambda (x: A).(Q x)) (ex2 A 
+(\lambda (x: A).(Q x)) (\lambda (x: A).(P x))) (\lambda (x: A).(\lambda (H0: 
+(P x)).(\lambda (H1: (Q x)).(ex_intro2 A (\lambda (x0: A).(Q x0)) (\lambda 
+(x0: A).(P x0)) x H1 H0)))) H)))).
+