update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / drop1 / fwd.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/drop1/fwd.ma b/matita/matita/contribs/lambdadelta/basic_1/drop1/fwd.ma
index 6e4d1789e832997e10cb8be5ae44488a6fdd0b68..3195918959af365def7b86753c8411be4f649020 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/drop1/fwd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/drop1/fwd.ma
@@ -14,9 +14,18 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/drop1/defs.ma".
+include "basic_1/drop1/defs.ma".
 
-theorem drop1_gen_pnil:
+implied rec lemma drop1_ind (P: (PList \to (C \to (C \to Prop)))) (f: 
+(\forall (c: C).(P PNil c c))) (f0: (\forall (c1: C).(\forall (c2: 
+C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c2) \to (\forall (c3: 
+C).(\forall (hds: PList).((drop1 hds c2 c3) \to ((P hds c2 c3) \to (P (PCons 
+h d hds) c1 c3))))))))))) (p: PList) (c: C) (c0: C) (d: drop1 p c c0) on d: P 
+p c c0 \def match d with [(drop1_nil c1) \Rightarrow (f c1) | (drop1_cons c1 
+c2 h d0 d1 c3 hds d2) \Rightarrow (f0 c1 c2 h d0 d1 c3 hds d2 ((drop1_ind P f 
+f0) hds c2 c3 d2))].
+
+lemma drop1_gen_pnil:
  \forall (c1: C).(\forall (c2: C).((drop1 PNil c1 c2) \to (eq C c1 c2)))
 \def
  \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (drop1 PNil c1 c2)).(insert_eq 
@@ -28,15 +37,11 @@ c0))))) (\lambda (c: C).(\lambda (_: (eq PList PNil PNil)).(refl_equal C c)))
 nat).(\lambda (_: (drop h d c3 c4)).(\lambda (c5: C).(\lambda (hds: 
 PList).(\lambda (_: (drop1 hds c4 c5)).(\lambda (_: (((eq PList hds PNil) \to 
 (eq C c4 c5)))).(\lambda (H4: (eq PList (PCons h d hds) PNil)).(let H5 \def 
-(eq_ind PList (PCons h d hds) (\lambda (ee: PList).(match ee in PList return 
-(\lambda (_: PList).Prop) with [PNil \Rightarrow False | (PCons _ _ _) 
-\Rightarrow True])) I PNil H4) in (False_ind (eq C c3 c5) H5)))))))))))) y c1 
-c2 H0))) H))).
-(* COMMENTS
-Initial nodes: 198
-END *)
+(eq_ind PList (PCons h d hds) (\lambda (ee: PList).(match ee with [PNil 
+\Rightarrow False | (PCons _ _ _) \Rightarrow True])) I PNil H4) in 
+(False_ind (eq C c3 c5) H5)))))))))))) y c1 c2 H0))) H))).
 
-theorem drop1_gen_pcons:
+lemma drop1_gen_pcons:
  \forall (c1: C).(\forall (c3: C).(\forall (hds: PList).(\forall (h: 
 nat).(\forall (d: nat).((drop1 (PCons h d hds) c1 c3) \to (ex2 C (\lambda 
 (c2: C).(drop h d c1 c2)) (\lambda (c2: C).(drop1 hds c2 c3))))))))
@@ -49,33 +54,28 @@ c2 c3)))) (\lambda (y: PList).(\lambda (H0: (drop1 y c1 c3)).(drop1_ind
 (\lambda (p: PList).(\lambda (c: C).(\lambda (c0: C).((eq PList p (PCons h d 
 hds)) \to (ex2 C (\lambda (c2: C).(drop h d c c2)) (\lambda (c2: C).(drop1 
 hds c2 c0))))))) (\lambda (c: C).(\lambda (H1: (eq PList PNil (PCons h d 
-hds))).(let H2 \def (eq_ind PList PNil (\lambda (ee: PList).(match ee in 
-PList return (\lambda (_: PList).Prop) with [PNil \Rightarrow True | (PCons _ 
-_ _) \Rightarrow False])) I (PCons h d hds) H1) in (False_ind (ex2 C (\lambda 
-(c2: C).(drop h d c c2)) (\lambda (c2: C).(drop1 hds c2 c))) H2)))) (\lambda 
-(c2: C).(\lambda (c4: C).(\lambda (h0: nat).(\lambda (d0: nat).(\lambda (H1: 
-(drop h0 d0 c2 c4)).(\lambda (c5: C).(\lambda (hds0: PList).(\lambda (H2: 
-(drop1 hds0 c4 c5)).(\lambda (H3: (((eq PList hds0 (PCons h d hds)) \to (ex2 
-C (\lambda (c6: C).(drop h d c4 c6)) (\lambda (c6: C).(drop1 hds c6 
-c5)))))).(\lambda (H4: (eq PList (PCons h0 d0 hds0) (PCons h d hds))).(let H5 
-\def (f_equal PList nat (\lambda (e: PList).(match e in PList return (\lambda 
-(_: PList).nat) with [PNil \Rightarrow h0 | (PCons n _ _) \Rightarrow n])) 
+hds))).(let H2 \def (eq_ind PList PNil (\lambda (ee: PList).(match ee with 
+[PNil \Rightarrow True | (PCons _ _ _) \Rightarrow False])) I (PCons h d hds) 
+H1) in (False_ind (ex2 C (\lambda (c2: C).(drop h d c c2)) (\lambda (c2: 
+C).(drop1 hds c2 c))) H2)))) (\lambda (c2: C).(\lambda (c4: C).(\lambda (h0: 
+nat).(\lambda (d0: nat).(\lambda (H1: (drop h0 d0 c2 c4)).(\lambda (c5: 
+C).(\lambda (hds0: PList).(\lambda (H2: (drop1 hds0 c4 c5)).(\lambda (H3: 
+(((eq PList hds0 (PCons h d hds)) \to (ex2 C (\lambda (c6: C).(drop h d c4 
+c6)) (\lambda (c6: C).(drop1 hds c6 c5)))))).(\lambda (H4: (eq PList (PCons 
+h0 d0 hds0) (PCons h d hds))).(let H5 \def (f_equal PList nat (\lambda (e: 
+PList).(match e with [PNil \Rightarrow h0 | (PCons n _ _) \Rightarrow n])) 
 (PCons h0 d0 hds0) (PCons h d hds) H4) in ((let H6 \def (f_equal PList nat 
-(\lambda (e: PList).(match e in PList return (\lambda (_: PList).nat) with 
-[PNil \Rightarrow d0 | (PCons _ n _) \Rightarrow n])) (PCons h0 d0 hds0) 
-(PCons h d hds) H4) in ((let H7 \def (f_equal PList PList (\lambda (e: 
-PList).(match e in PList return (\lambda (_: PList).PList) with [PNil 
-\Rightarrow hds0 | (PCons _ _ p) \Rightarrow p])) (PCons h0 d0 hds0) (PCons h 
-d hds) H4) in (\lambda (H8: (eq nat d0 d)).(\lambda (H9: (eq nat h0 h)).(let 
-H10 \def (eq_ind PList hds0 (\lambda (p: PList).((eq PList p (PCons h d hds)) 
-\to (ex2 C (\lambda (c6: C).(drop h d c4 c6)) (\lambda (c6: C).(drop1 hds c6 
-c5))))) H3 hds H7) in (let H11 \def (eq_ind PList hds0 (\lambda (p: 
-PList).(drop1 p c4 c5)) H2 hds H7) in (let H12 \def (eq_ind nat d0 (\lambda 
-(n: nat).(drop h0 n c2 c4)) H1 d H8) in (let H13 \def (eq_ind nat h0 (\lambda 
-(n: nat).(drop n d c2 c4)) H12 h H9) in (ex_intro2 C (\lambda (c6: C).(drop h 
-d c2 c6)) (\lambda (c6: C).(drop1 hds c6 c5)) c4 H13 H11)))))))) H6)) 
-H5)))))))))))) y c1 c3 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 587
-END *)
+(\lambda (e: PList).(match e with [PNil \Rightarrow d0 | (PCons _ n _) 
+\Rightarrow n])) (PCons h0 d0 hds0) (PCons h d hds) H4) in ((let H7 \def 
+(f_equal PList PList (\lambda (e: PList).(match e with [PNil \Rightarrow hds0 
+| (PCons _ _ p) \Rightarrow p])) (PCons h0 d0 hds0) (PCons h d hds) H4) in 
+(\lambda (H8: (eq nat d0 d)).(\lambda (H9: (eq nat h0 h)).(let H10 \def 
+(eq_ind PList hds0 (\lambda (p: PList).((eq PList p (PCons h d hds)) \to (ex2 
+C (\lambda (c6: C).(drop h d c4 c6)) (\lambda (c6: C).(drop1 hds c6 c5))))) 
+H3 hds H7) in (let H11 \def (eq_ind PList hds0 (\lambda (p: PList).(drop1 p 
+c4 c5)) H2 hds H7) in (let H12 \def (eq_ind nat d0 (\lambda (n: nat).(drop h0 
+n c2 c4)) H1 d H8) in (let H13 \def (eq_ind nat h0 (\lambda (n: nat).(drop n 
+d c2 c4)) H12 h H9) in (ex_intro2 C (\lambda (c6: C).(drop h d c2 c6)) 
+(\lambda (c6: C).(drop1 hds c6 c5)) c4 H13 H11)))))))) H6)) H5)))))))))))) y 
+c1 c3 H0))) H)))))).