(* This file was automatically generated: do not edit *********************)
-include "Basic-1/nf2/props.ma".
+include "basic_1/nf2/props.ma".
-include "Basic-1/drop1/fwd.ma".
+include "basic_1/drop1/fwd.ma".
theorem nf2_lift1:
\forall (e: C).(\forall (hds: PList).(\forall (c: C).(\forall (t: T).((drop1
hds c e) \to ((nf2 e t) \to (nf2 c (lift1 hds t)))))))
\def
- \lambda (e: C).(\lambda (hds: PList).(PList_ind (\lambda (p: PList).(\forall
-(c: C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c (lift1 p
-t))))))) (\lambda (c: C).(\lambda (t: T).(\lambda (H: (drop1 PNil c
-e)).(\lambda (H0: (nf2 e t)).(let H_y \def (drop1_gen_pnil c e H) in
-(eq_ind_r C e (\lambda (c0: C).(nf2 c0 t)) H0 c H_y)))))) (\lambda (n:
-nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c:
-C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c (lift1 p
-t)))))))).(\lambda (c: C).(\lambda (t: T).(\lambda (H0: (drop1 (PCons n n0 p)
-c e)).(\lambda (H1: (nf2 e t)).(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)) (nf2 c (lift n n0 (lift1 p t))) (\lambda (x:
-C).(\lambda (H3: (drop n n0 c x)).(\lambda (H4: (drop1 p x e)).(nf2_lift x
-(lift1 p t) (H x t H4 H1) c n n0 H3)))) H2))))))))))) hds)).
-(* COMMENTS
-Initial nodes: 249
-END *)
+ \lambda (e: C).(\lambda (hds: PList).(let TMP_2 \def (\lambda (p:
+PList).(\forall (c: C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (let
+TMP_1 \def (lift1 p t) in (nf2 c TMP_1))))))) in (let TMP_4 \def (\lambda (c:
+C).(\lambda (t: T).(\lambda (H: (drop1 PNil c e)).(\lambda (H0: (nf2 e
+t)).(let H_y \def (drop1_gen_pnil c e H) in (let TMP_3 \def (\lambda (c0:
+C).(nf2 c0 t)) in (eq_ind_r C e TMP_3 H0 c H_y))))))) in (let TMP_13 \def
+(\lambda (n: nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H:
+((\forall (c: C).(\forall (t: T).((drop1 p c e) \to ((nf2 e t) \to (nf2 c
+(lift1 p t)))))))).(\lambda (c: C).(\lambda (t: T).(\lambda (H0: (drop1
+(PCons n n0 p) c e)).(\lambda (H1: (nf2 e t)).(let H_x \def (drop1_gen_pcons
+c e p n n0 H0) in (let H2 \def H_x in (let TMP_5 \def (\lambda (c2: C).(drop
+n n0 c c2)) in (let TMP_6 \def (\lambda (c2: C).(drop1 p c2 e)) in (let TMP_7
+\def (lift1 p t) in (let TMP_8 \def (lift n n0 TMP_7) in (let TMP_9 \def (nf2
+c TMP_8) in (let TMP_12 \def (\lambda (x: C).(\lambda (H3: (drop n n0 c
+x)).(\lambda (H4: (drop1 p x e)).(let TMP_10 \def (lift1 p t) in (let TMP_11
+\def (H x t H4 H1) in (nf2_lift x TMP_10 TMP_11 c n n0 H3)))))) in (ex2_ind C
+TMP_5 TMP_6 TMP_9 TMP_12 H2))))))))))))))))) in (PList_ind TMP_2 TMP_4 TMP_13
+hds))))).