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[helm.git] / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / arity / lift1.ma

diff --git a/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/arity/lift1.ma b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/arity/lift1.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/arity/props.ma".
+
+include "LambdaDelta-1/drop1/fwd.ma".
+
+theorem arity_lift1:
+ \forall (g: G).(\forall (a: A).(\forall (c2: C).(\forall (hds: 
+PList).(\forall (c1: C).(\forall (t: T).((drop1 hds c1 c2) \to ((arity g c2 t 
+a) \to (arity g c1 (lift1 hds t) a))))))))
+\def
+ \lambda (g: G).(\lambda (a: A).(\lambda (c2: C).(\lambda (hds: 
+PList).(PList_ind (\lambda (p: PList).(\forall (c1: C).(\forall (t: 
+T).((drop1 p c1 c2) \to ((arity g c2 t a) \to (arity g c1 (lift1 p t) a)))))) 
+(\lambda (c1: C).(\lambda (t: T).(\lambda (H: (drop1 PNil c1 c2)).(\lambda 
+(H0: (arity g c2 t a)).(let H_y \def (drop1_gen_pnil c1 c2 H) in (eq_ind_r C 
+c2 (\lambda (c: C).(arity g c t a)) H0 c1 H_y)))))) (\lambda (n: 
+nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c1: 
+C).(\forall (t: T).((drop1 p c1 c2) \to ((arity g c2 t a) \to (arity g c1 
+(lift1 p t) a))))))).(\lambda (c1: C).(\lambda (t: T).(\lambda (H0: (drop1 
+(PCons n n0 p) c1 c2)).(\lambda (H1: (arity g c2 t a)).(let H_x \def 
+(drop1_gen_pcons c1 c2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda 
+(c3: C).(drop n n0 c1 c3)) (\lambda (c3: C).(drop1 p c3 c2)) (arity g c1 
+(lift n n0 (lift1 p t)) a) (\lambda (x: C).(\lambda (H3: (drop n n0 c1 
+x)).(\lambda (H4: (drop1 p x c2)).(arity_lift g x (lift1 p t) a (H x t H4 H1) 
+c1 n n0 H3)))) H2))))))))))) hds)))).
+