--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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 *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/csubst1/props".
+
+include "csubst1/defs.ma".
+
+include "subst1/defs.ma".
+
+theorem csubst1_head:
+ \forall (k: K).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
+(u2: T).((subst1 i v u1 u2) \to (\forall (c1: C).(\forall (c2: C).((csubst1 i
+v c1 c2) \to (csubst1 (s k i) v (CHead c1 k u1) (CHead c2 k u2))))))))))
+\def
+ \lambda (k: K).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda
+(u2: T).(\lambda (H: (subst1 i v u1 u2)).(subst1_ind i v u1 (\lambda (t:
+T).(\forall (c1: C).(\forall (c2: C).((csubst1 i v c1 c2) \to (csubst1 (s k
+i) v (CHead c1 k u1) (CHead c2 k t)))))) (\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H0: (csubst1 i v c1 c2)).(csubst1_ind i v c1 (\lambda (c:
+C).(csubst1 (s k i) v (CHead c1 k u1) (CHead c k u1))) (csubst1_refl (s k i)
+v (CHead c1 k u1)) (\lambda (c3: C).(\lambda (H1: (csubst0 i v c1
+c3)).(csubst1_sing (s k i) v (CHead c1 k u1) (CHead c3 k u1) (csubst0_fst k i
+c1 c3 v H1 u1)))) c2 H0)))) (\lambda (t2: T).(\lambda (H0: (subst0 i v u1
+t2)).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csubst1 i v c1
+c2)).(csubst1_ind i v c1 (\lambda (c: C).(csubst1 (s k i) v (CHead c1 k u1)
+(CHead c k t2))) (csubst1_sing (s k i) v (CHead c1 k u1) (CHead c1 k t2)
+(csubst0_snd k i v u1 t2 H0 c1)) (\lambda (c3: C).(\lambda (H2: (csubst0 i v
+c1 c3)).(csubst1_sing (s k i) v (CHead c1 k u1) (CHead c3 k t2) (csubst0_both
+k i v u1 t2 H0 c1 c3 H2)))) c2 H1)))))) u2 H)))))).
+
+theorem csubst1_bind:
+ \forall (b: B).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
+(u2: T).((subst1 i v u1 u2) \to (\forall (c1: C).(\forall (c2: C).((csubst1 i
+v c1 c2) \to (csubst1 (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: (subst1 i v u1 u2)).(\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H0: (csubst1 i v c1 c2)).(eq_ind nat (s (Bind b) i) (\lambda (n:
+nat).(csubst1 n v (CHead c1 (Bind b) u1) (CHead c2 (Bind b) u2)))
+(csubst1_head (Bind b) i v u1 u2 H c1 c2 H0) (S i) (refl_equal nat (S
+i))))))))))).
+
+theorem csubst1_flat:
+ \forall (f: F).(\forall (i: nat).(\forall (v: T).(\forall (u1: T).(\forall
+(u2: T).((subst1 i v u1 u2) \to (\forall (c1: C).(\forall (c2: C).((csubst1 i
+v c1 c2) \to (csubst1 i v (CHead c1 (Flat f) u1) (CHead c2 (Flat f)
+u2))))))))))
+\def
+ \lambda (f: F).(\lambda (i: nat).(\lambda (v: T).(\lambda (u1: T).(\lambda
+(u2: T).(\lambda (H: (subst1 i v u1 u2)).(\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H0: (csubst1 i v c1 c2)).(eq_ind nat (s (Flat f) i) (\lambda (n:
+nat).(csubst1 n v (CHead c1 (Flat f) u1) (CHead c2 (Flat f) u2)))
+(csubst1_head (Flat f) i v u1 u2 H c1 c2 H0) i (refl_equal nat i)))))))))).
+