--- /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 *********************)
+
+include "LambdaDelta-1/sn3/props.ma".
+
+include "LambdaDelta-1/drop1/fwd.ma".
+
+include "LambdaDelta-1/lift1/fwd.ma".
+
+theorem sns3_lifts1:
+ \forall (e: C).(\forall (hds: PList).(\forall (c: C).((drop1 hds c e) \to
+(\forall (ts: TList).((sns3 e ts) \to (sns3 c (lifts1 hds ts)))))))
+\def
+ \lambda (e: C).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
+(c: C).((drop1 p c e) \to (\forall (ts: TList).((sns3 e ts) \to (sns3 c
+(lifts1 p ts))))))) (\lambda (c: C).(\lambda (H: (drop1 PNil c e)).(\lambda
+(ts: TList).(\lambda (H0: (sns3 e ts)).(let H_y \def (drop1_gen_pnil c e H)
+in (eq_ind_r C e (\lambda (c0: C).(sns3 c0 (lifts1 PNil ts))) (eq_ind_r TList
+ts (\lambda (t: TList).(sns3 e t)) H0 (lifts1 PNil ts) (lifts1_nil ts)) c
+H_y)))))) (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda
+(H: ((\forall (c: C).((drop1 p c e) \to (\forall (ts: TList).((sns3 e ts) \to
+(sns3 c (lifts1 p ts)))))))).(\lambda (c: C).(\lambda (H0: (drop1 (PCons n n0
+p) c e)).(\lambda (ts: TList).(\lambda (H1: (sns3 e ts)).(let H_x \def
+(drop1_gen_pcons c e p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda
+(c2: C).(drop n n0 c c2)) (\lambda (c2: C).(drop1 p c2 e)) (sns3 c (lifts1
+(PCons n n0 p) ts)) (\lambda (x: C).(\lambda (H3: (drop n n0 c x)).(\lambda
+(H4: (drop1 p x e)).(eq_ind_r TList (lifts n n0 (lifts1 p ts)) (\lambda (t:
+TList).(sns3 c t)) (sns3_lifts c x n n0 H3 (lifts1 p ts) (H x H4 ts H1))
+(lifts1 (PCons n n0 p) ts) (lifts1_cons n n0 p ts))))) H2))))))))))) hds)).
+