X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Fnf2%2Flift1.ma;h=240c48d0efeb71e8caca765785a49a3d0d6f002b;hb=89519c7b52e06304a94019dd528925300380cdc0;hp=33c44778da31ab61f7cf21b451ea455f99ed4fbe;hpb=831af787465e1bff886e22ee14b68c8f1bb0177c;p=helm.git

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/nf2/lift1.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/nf2/lift1.ma
index 33c44778d..240c48d0e 100644
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/nf2/lift1.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/nf2/lift1.ma
@@ -14,11 +14,9 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/nf2/lift1".
+include "LambdaDelta-1/nf2/props.ma".
 
-include "nf2/props.ma".
-
-include "drop1/defs.ma".
+include "LambdaDelta-1/drop1/fwd.ma".
 
 theorem nf2_lift1:
  \forall (e: C).(\forall (hds: PList).(\forall (c: C).(\forall (t: T).((drop1 
@@ -27,58 +25,14 @@ hds c e) \to ((nf2 e t) \to (nf2 c (lift1 hds t)))))))
  \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 H1 \def (match H in drop1 return (\lambda 
-(p: PList).(\lambda (c0: C).(\lambda (c1: C).(\lambda (_: (drop1 p c0 
-c1)).((eq PList p PNil) \to ((eq C c0 c) \to ((eq C c1 e) \to (nf2 c 
-t)))))))) with [(drop1_nil c0) \Rightarrow (\lambda (_: (eq PList PNil 
-PNil)).(\lambda (H2: (eq C c0 c)).(\lambda (H3: (eq C c0 e)).(eq_ind C c 
-(\lambda (c1: C).((eq C c1 e) \to (nf2 c t))) (\lambda (H4: (eq C c 
-e)).(eq_ind C e (\lambda (c1: C).(nf2 c1 t)) H0 c (sym_eq C c e H4))) c0 
-(sym_eq C c0 c H2) H3)))) | (drop1_cons c1 c2 h d H1 c3 hds0 H2) \Rightarrow 
-(\lambda (H3: (eq PList (PCons h d hds0) PNil)).(\lambda (H4: (eq C c1 
-c)).(\lambda (H5: (eq C c3 e)).((let H6 \def (eq_ind PList (PCons h d hds0) 
-(\lambda (e0: PList).(match e0 in PList return (\lambda (_: PList).Prop) with 
-[PNil \Rightarrow False | (PCons _ _ _) \Rightarrow True])) I PNil H3) in 
-(False_ind ((eq C c1 c) \to ((eq C c3 e) \to ((drop h d c1 c2) \to ((drop1 
-hds0 c2 c3) \to (nf2 c t))))) H6)) H4 H5 H1 H2))))]) in (H1 (refl_equal PList 
-PNil) (refl_equal C c) (refl_equal C e))))))) (\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 H2 \def (match H0 in drop1 return (\lambda (p0: 
-PList).(\lambda (c0: C).(\lambda (c1: C).(\lambda (_: (drop1 p0 c0 c1)).((eq 
-PList p0 (PCons n n0 p)) \to ((eq C c0 c) \to ((eq C c1 e) \to (nf2 c (lift n 
-n0 (lift1 p t)))))))))) with [(drop1_nil c0) \Rightarrow (\lambda (H2: (eq 
-PList PNil (PCons n n0 p))).(\lambda (H3: (eq C c0 c)).(\lambda (H4: (eq C c0 
-e)).((let H5 \def (eq_ind PList PNil (\lambda (e0: PList).(match e0 in PList 
-return (\lambda (_: PList).Prop) with [PNil \Rightarrow True | (PCons _ _ _) 
-\Rightarrow False])) I (PCons n n0 p) H2) in (False_ind ((eq C c0 c) \to ((eq 
-C c0 e) \to (nf2 c (lift n n0 (lift1 p t))))) H5)) H3 H4)))) | (drop1_cons c1 
-c2 h d H2 c3 hds0 H3) \Rightarrow (\lambda (H4: (eq PList (PCons h d hds0) 
-(PCons n n0 p))).(\lambda (H5: (eq C c1 c)).(\lambda (H6: (eq C c3 e)).((let 
-H7 \def (f_equal PList PList (\lambda (e0: PList).(match e0 in PList return 
-(\lambda (_: PList).PList) with [PNil \Rightarrow hds0 | (PCons _ _ p0) 
-\Rightarrow p0])) (PCons h d hds0) (PCons n n0 p) H4) in ((let H8 \def 
-(f_equal PList nat (\lambda (e0: PList).(match e0 in PList return (\lambda 
-(_: PList).nat) with [PNil \Rightarrow d | (PCons _ n1 _) \Rightarrow n1])) 
-(PCons h d hds0) (PCons n n0 p) H4) in ((let H9 \def (f_equal PList nat 
-(\lambda (e0: PList).(match e0 in PList return (\lambda (_: PList).nat) with 
-[PNil \Rightarrow h | (PCons n1 _ _) \Rightarrow n1])) (PCons h d hds0) 
-(PCons n n0 p) H4) in (eq_ind nat n (\lambda (n1: nat).((eq nat d n0) \to 
-((eq PList hds0 p) \to ((eq C c1 c) \to ((eq C c3 e) \to ((drop n1 d c1 c2) 
-\to ((drop1 hds0 c2 c3) \to (nf2 c (lift n n0 (lift1 p t)))))))))) (\lambda 
-(H10: (eq nat d n0)).(eq_ind nat n0 (\lambda (n1: nat).((eq PList hds0 p) \to 
-((eq C c1 c) \to ((eq C c3 e) \to ((drop n n1 c1 c2) \to ((drop1 hds0 c2 c3) 
-\to (nf2 c (lift n n0 (lift1 p t))))))))) (\lambda (H11: (eq PList hds0 
-p)).(eq_ind PList p (\lambda (p0: PList).((eq C c1 c) \to ((eq C c3 e) \to 
-((drop n n0 c1 c2) \to ((drop1 p0 c2 c3) \to (nf2 c (lift n n0 (lift1 p 
-t)))))))) (\lambda (H12: (eq C c1 c)).(eq_ind C c (\lambda (c0: C).((eq C c3 
-e) \to ((drop n n0 c0 c2) \to ((drop1 p c2 c3) \to (nf2 c (lift n n0 (lift1 p 
-t))))))) (\lambda (H13: (eq C c3 e)).(eq_ind C e (\lambda (c0: C).((drop n n0 
-c c2) \to ((drop1 p c2 c0) \to (nf2 c (lift n n0 (lift1 p t)))))) (\lambda 
-(H14: (drop n n0 c c2)).(\lambda (H15: (drop1 p c2 e)).(nf2_lift c2 (lift1 p 
-t) (H c2 t H15 H1) c n n0 H14))) c3 (sym_eq C c3 e H13))) c1 (sym_eq C c1 c 
-H12))) hds0 (sym_eq PList hds0 p H11))) d (sym_eq nat d n0 H10))) h (sym_eq 
-nat h n H9))) H8)) H7)) H5 H6 H2 H3))))]) in (H2 (refl_equal PList (PCons n 
-n0 p)) (refl_equal C c) (refl_equal C e))))))))))) hds)).
+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)).