1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1/nf2/props.ma".
19 include "basic_1/drop1/fwd.ma".
22 \forall (e: C).(\forall (hds: PList).(\forall (c: C).(\forall (t: T).((drop1
23 hds c e) \to ((nf2 e t) \to (nf2 c (lift1 hds t)))))))
25 \lambda (e: C).(\lambda (hds: PList).(let TMP_2 \def (\lambda (p:
26 PList).(\forall (c: C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (let
27 TMP_1 \def (lift1 p t) in (nf2 c TMP_1))))))) in (let TMP_4 \def (\lambda (c:
28 C).(\lambda (t: T).(\lambda (H: (drop1 PNil c e)).(\lambda (H0: (nf2 e
29 t)).(let H_y \def (drop1_gen_pnil c e H) in (let TMP_3 \def (\lambda (c0:
30 C).(nf2 c0 t)) in (eq_ind_r C e TMP_3 H0 c H_y))))))) in (let TMP_13 \def
31 (\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H:
32 ((\forall (c: C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c
33 (lift1 p t)))))))).(\lambda (c: C).(\lambda (t: T).(\lambda (H0: (drop1
34 (PCons n n0 p) c e)).(\lambda (H1: (nf2 e t)).(let H_x \def (drop1_gen_pcons
35 c e p n n0 H0) in (let H2 \def H_x in (let TMP_5 \def (\lambda (c2: C).(drop
36 n n0 c c2)) in (let TMP_6 \def (\lambda (c2: C).(drop1 p c2 e)) in (let TMP_7
37 \def (lift1 p t) in (let TMP_8 \def (lift n n0 TMP_7) in (let TMP_9 \def (nf2
38 c TMP_8) in (let TMP_12 \def (\lambda (x: C).(\lambda (H3: (drop n n0 c
39 x)).(\lambda (H4: (drop1 p x e)).(let TMP_10 \def (lift1 p t) in (let TMP_11
40 \def (H x t H4 H1) in (nf2_lift x TMP_10 TMP_11 c n n0 H3)))))) in (ex2_ind C
41 TMP_5 TMP_6 TMP_9 TMP_12 H2))))))))))))))))) in (PList_ind TMP_2 TMP_4 TMP_13