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[helm.git] / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / subst / fwd.ma

diff --git a/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/subst/fwd.ma b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/subst/fwd.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/subst/defs.ma".
+
+theorem subst_sort:
+ \forall (v: T).(\forall (d: nat).(\forall (k: nat).(eq T (subst d v (TSort 
+k)) (TSort k))))
+\def
+ \lambda (_: T).(\lambda (_: nat).(\lambda (k: nat).(refl_equal T (TSort 
+k)))).
+
+theorem subst_lref_lt:
+ \forall (v: T).(\forall (d: nat).(\forall (i: nat).((lt i d) \to (eq T 
+(subst d v (TLRef i)) (TLRef i)))))
+\def
+ \lambda (v: T).(\lambda (d: nat).(\lambda (i: nat).(\lambda (H: (lt i 
+d)).(eq_ind_r bool true (\lambda (b: bool).(eq T (match b with [true 
+\Rightarrow (TLRef i) | false \Rightarrow (match (blt d i) with [true 
+\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)])]) (TLRef i))) 
+(refl_equal T (TLRef i)) (blt i d) (lt_blt d i H))))).
+
+theorem subst_lref_eq:
+ \forall (v: T).(\forall (i: nat).(eq T (subst i v (TLRef i)) (lift i O v)))
+\def
+ \lambda (v: T).(\lambda (i: nat).(eq_ind_r bool false (\lambda (b: bool).(eq 
+T (match b with [true \Rightarrow (TLRef i) | false \Rightarrow (match b with 
+[true \Rightarrow (TLRef (pred i)) | false \Rightarrow (lift i O v)])]) (lift 
+i O v))) (refl_equal T (lift i O v)) (blt i i) (le_bge i i (le_n i)))).
+
+theorem subst_lref_gt:
+ \forall (v: T).(\forall (d: nat).(\forall (i: nat).((lt d i) \to (eq T 
+(subst d v (TLRef i)) (TLRef (pred i))))))
+\def
+ \lambda (v: T).(\lambda (d: nat).(\lambda (i: nat).(\lambda (H: (lt d 
+i)).(eq_ind_r bool false (\lambda (b: bool).(eq T (match b with [true 
+\Rightarrow (TLRef i) | false \Rightarrow (match (blt d i) with [true 
+\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)])]) (TLRef 
+(pred i)))) (eq_ind_r bool true (\lambda (b: bool).(eq T (match b with [true 
+\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)]) (TLRef (pred 
+i)))) (refl_equal T (TLRef (pred i))) (blt d i) (lt_blt i d H)) (blt i d) 
+(le_bge d i (lt_le_weak d i H)))))).
+
+theorem subst_head:
+ \forall (k: K).(\forall (w: T).(\forall (u: T).(\forall (t: T).(\forall (d: 
+nat).(eq T (subst d w (THead k u t)) (THead k (subst d w u) (subst (s k d) w 
+t)))))))
+\def
+ \lambda (k: K).(\lambda (w: T).(\lambda (u: T).(\lambda (t: T).(\lambda (d: 
+nat).(refl_equal T (THead k (subst d w u) (subst (s k d) w t))))))).
+