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[helm.git] / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / csubst0 / props.ma

diff --git a/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/props.ma b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/props.ma
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+++ b/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubst0/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 "LambdaDelta-1/csubst0/defs.ma".
+
+theorem csubst0_snd_bind:
+ \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall 
+(u2: T).((subst0 i v u1 u2) \to (\forall (c: C).(csubst0 (S i) v (CHead c 
+(Bind b) u1) (CHead c (Bind b) u2))))))))
+\def
+ \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
+(u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c: C).(eq_ind nat (s (Bind 
+b) i) (\lambda (n: nat).(csubst0 n v (CHead c (Bind b) u1) (CHead c (Bind b) 
+u2))) (csubst0_snd (Bind b) i v u1 u2 H c) (S i) (refl_equal nat (S 
+i))))))))).
+
+theorem csubst0_fst_bind:
+ \forall (b: B).(\forall (i: nat).(\forall (c1: C).(\forall (c2: C).(\forall 
+(v: T).((csubst0 i v c1 c2) \to (\forall (u: T).(csubst0 (S i) v (CHead c1 
+(Bind b) u) (CHead c2 (Bind b) u))))))))
+\def
+ \lambda (b: B).(\lambda (i: nat).(\lambda (c1: C).(\lambda (c2: C).(\lambda 
+(v: T).(\lambda (H: (csubst0 i v c1 c2)).(\lambda (u: T).(eq_ind nat (s (Bind 
+b) i) (\lambda (n: nat).(csubst0 n v (CHead c1 (Bind b) u) (CHead c2 (Bind b) 
+u))) (csubst0_fst (Bind b) i c1 c2 v H u) (S i) (refl_equal nat (S i))))))))).
+
+theorem csubst0_both_bind:
+ \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall 
+(u2: T).((subst0 i v u1 u2) \to (\forall (c1: C).(\forall (c2: C).((csubst0 i 
+v c1 c2) \to (csubst0 (S i) v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) 
+u2))))))))))
+\def
+ \lambda (b: B).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda 
+(u2: T).(\lambda (H: (subst0 i v u1 u2)).(\lambda (c1: C).(\lambda (c2: 
+C).(\lambda (H0: (csubst0 i v c1 c2)).(eq_ind nat (s (Bind b) i) (\lambda (n: 
+nat).(csubst0 n v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) u2))) 
+(csubst0_both (Bind b) i v u1 u2 H c1 c2 H0) (S i) (refl_equal nat (S 
+i))))))))))).
+