X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Fclear%2Ffwd.ma;h=ede997e9537d028848be2d0996a0fd3c4c80ff9b;hb=89519c7b52e06304a94019dd528925300380cdc0;hp=c0316133067cde403eff274368ed93692876cbce;hpb=e92710b1d9774a6491122668c8463b8658114610;p=helm.git

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/clear/fwd.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/clear/fwd.ma
index c03161330..ede997e95 100644
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/clear/fwd.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/clear/fwd.ma
@@ -21,93 +21,85 @@ theorem clear_gen_sort:
 Prop).P)))
 \def
  \lambda (x: C).(\lambda (n: nat).(\lambda (H: (clear (CSort n) x)).(\lambda 
-(P: Prop).(let H0 \def (match H in clear return (\lambda (c: C).(\lambda (c0: 
-C).(\lambda (_: (clear c c0)).((eq C c (CSort n)) \to ((eq C c0 x) \to P))))) 
-with [(clear_bind b e u) \Rightarrow (\lambda (H0: (eq C (CHead e (Bind b) u) 
-(CSort n))).(\lambda (H1: (eq C (CHead e (Bind b) u) x)).((let H2 \def 
-(eq_ind C (CHead e (Bind b) u) (\lambda (e0: C).(match e0 in C return 
+(P: Prop).(insert_eq C (CSort n) (\lambda (c: C).(clear c x)) (\lambda (_: 
+C).P) (\lambda (y: C).(\lambda (H0: (clear y x)).(clear_ind (\lambda (c: 
+C).(\lambda (_: C).((eq C c (CSort n)) \to P))) (\lambda (b: B).(\lambda (e: 
+C).(\lambda (u: T).(\lambda (H1: (eq C (CHead e (Bind b) u) (CSort n))).(let 
+H2 \def (eq_ind C (CHead e (Bind b) u) (\lambda (ee: C).(match ee in C return 
 (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ _ _) 
-\Rightarrow True])) I (CSort n) H0) in (False_ind ((eq C (CHead e (Bind b) u) 
-x) \to P) H2)) H1))) | (clear_flat e c H0 f u) \Rightarrow (\lambda (H1: (eq 
-C (CHead e (Flat f) u) (CSort n))).(\lambda (H2: (eq C c x)).((let H3 \def 
-(eq_ind C (CHead e (Flat f) u) (\lambda (e0: C).(match e0 in C return 
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ _ _) 
-\Rightarrow True])) I (CSort n) H1) in (False_ind ((eq C c x) \to ((clear e 
-c) \to P)) H3)) H2 H0)))]) in (H0 (refl_equal C (CSort n)) (refl_equal C 
-x)))))).
+\Rightarrow True])) I (CSort n) H1) in (False_ind P H2)))))) (\lambda (e: 
+C).(\lambda (c: C).(\lambda (_: (clear e c)).(\lambda (_: (((eq C e (CSort 
+n)) \to P))).(\lambda (f: F).(\lambda (u: T).(\lambda (H3: (eq C (CHead e 
+(Flat f) u) (CSort n))).(let H4 \def (eq_ind C (CHead e (Flat f) u) (\lambda 
+(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) 
+\Rightarrow False | (CHead _ _ _) \Rightarrow True])) I (CSort n) H3) in 
+(False_ind P H4))))))))) y x H0))) H)))).
 
 theorem clear_gen_bind:
  \forall (b: B).(\forall (e: C).(\forall (x: C).(\forall (u: T).((clear 
 (CHead e (Bind b) u) x) \to (eq C x (CHead e (Bind b) u))))))
 \def
  \lambda (b: B).(\lambda (e: C).(\lambda (x: C).(\lambda (u: T).(\lambda (H: 
-(clear (CHead e (Bind b) u) x)).(let H0 \def (match H in clear return 
-(\lambda (c: C).(\lambda (c0: C).(\lambda (_: (clear c c0)).((eq C c (CHead e 
-(Bind b) u)) \to ((eq C c0 x) \to (eq C x (CHead e (Bind b) u))))))) with 
-[(clear_bind b0 e0 u0) \Rightarrow (\lambda (H0: (eq C (CHead e0 (Bind b0) 
-u0) (CHead e (Bind b) u))).(\lambda (H1: (eq C (CHead e0 (Bind b0) u0) 
-x)).((let H2 \def (f_equal C T (\lambda (e1: C).(match e1 in C return 
-(\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow 
-t])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H0) in ((let H3 \def 
+(clear (CHead e (Bind b) u) x)).(insert_eq C (CHead e (Bind b) u) (\lambda 
+(c: C).(clear c x)) (\lambda (c: C).(eq C x c)) (\lambda (y: C).(\lambda (H0: 
+(clear y x)).(clear_ind (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead e 
+(Bind b) u)) \to (eq C c0 c)))) (\lambda (b0: B).(\lambda (e0: C).(\lambda 
+(u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b0) u0) (CHead e (Bind b) 
+u))).(let H2 \def (f_equal C C (\lambda (e1: C).(match e1 in C return 
+(\lambda (_: C).C) with [(CSort _) \Rightarrow e0 | (CHead c _ _) \Rightarrow 
+c])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H1) in ((let H3 \def 
 (f_equal C B (\lambda (e1: C).(match e1 in C return (\lambda (_: C).B) with 
 [(CSort _) \Rightarrow b0 | (CHead _ k _) \Rightarrow (match k in K return 
 (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow 
-b0])])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H0) in ((let H4 \def 
-(f_equal C C (\lambda (e1: C).(match e1 in C return (\lambda (_: C).C) with 
-[(CSort _) \Rightarrow e0 | (CHead c _ _) \Rightarrow c])) (CHead e0 (Bind 
-b0) u0) (CHead e (Bind b) u) H0) in (eq_ind C e (\lambda (c: C).((eq B b0 b) 
-\to ((eq T u0 u) \to ((eq C (CHead c (Bind b0) u0) x) \to (eq C x (CHead e 
-(Bind b) u)))))) (\lambda (H5: (eq B b0 b)).(eq_ind B b (\lambda (b1: B).((eq 
-T u0 u) \to ((eq C (CHead e (Bind b1) u0) x) \to (eq C x (CHead e (Bind b) 
-u))))) (\lambda (H6: (eq T u0 u)).(eq_ind T u (\lambda (t: T).((eq C (CHead e 
-(Bind b) t) x) \to (eq C x (CHead e (Bind b) u)))) (\lambda (H7: (eq C (CHead 
-e (Bind b) u) x)).(eq_ind C (CHead e (Bind b) u) (\lambda (c: C).(eq C c 
-(CHead e (Bind b) u))) (refl_equal C (CHead e (Bind b) u)) x H7)) u0 (sym_eq 
-T u0 u H6))) b0 (sym_eq B b0 b H5))) e0 (sym_eq C e0 e H4))) H3)) H2)) H1))) 
-| (clear_flat e0 c H0 f u0) \Rightarrow (\lambda (H1: (eq C (CHead e0 (Flat 
-f) u0) (CHead e (Bind b) u))).(\lambda (H2: (eq C c x)).((let H3 \def (eq_ind 
-C (CHead e0 (Flat f) u0) (\lambda (e1: C).(match e1 in C return (\lambda (_: 
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match 
-k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat 
-_) \Rightarrow True])])) I (CHead e (Bind b) u) H1) in (False_ind ((eq C c x) 
-\to ((clear e0 c) \to (eq C x (CHead e (Bind b) u)))) H3)) H2 H0)))]) in (H0 
-(refl_equal C (CHead e (Bind b) u)) (refl_equal C x))))))).
+b0])])) (CHead e0 (Bind b0) u0) (CHead e (Bind b) u) H1) in ((let H4 \def 
+(f_equal C T (\lambda (e1: C).(match e1 in C return (\lambda (_: C).T) with 
+[(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead e0 (Bind 
+b0) u0) (CHead e (Bind b) u) H1) in (\lambda (H5: (eq B b0 b)).(\lambda (H6: 
+(eq C e0 e)).(eq_ind_r T u (\lambda (t: T).(eq C (CHead e0 (Bind b0) t) 
+(CHead e0 (Bind b0) t))) (eq_ind_r C e (\lambda (c: C).(eq C (CHead c (Bind 
+b0) u) (CHead c (Bind b0) u))) (eq_ind_r B b (\lambda (b1: B).(eq C (CHead e 
+(Bind b1) u) (CHead e (Bind b1) u))) (refl_equal C (CHead e (Bind b) u)) b0 
+H5) e0 H6) u0 H4)))) H3)) H2)))))) (\lambda (e0: C).(\lambda (c: C).(\lambda 
+(_: (clear e0 c)).(\lambda (_: (((eq C e0 (CHead e (Bind b) u)) \to (eq C c 
+e0)))).(\lambda (f: F).(\lambda (u0: T).(\lambda (H3: (eq C (CHead e0 (Flat 
+f) u0) (CHead e (Bind b) u))).(let H4 \def (eq_ind C (CHead e0 (Flat f) u0) 
+(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) 
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda 
+(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow 
+True])])) I (CHead e (Bind b) u) H3) in (False_ind (eq C c (CHead e0 (Flat f) 
+u0)) H4))))))))) y x H0))) H))))).
 
 theorem clear_gen_flat:
  \forall (f: F).(\forall (e: C).(\forall (x: C).(\forall (u: T).((clear 
 (CHead e (Flat f) u) x) \to (clear e x)))))
 \def
  \lambda (f: F).(\lambda (e: C).(\lambda (x: C).(\lambda (u: T).(\lambda (H: 
-(clear (CHead e (Flat f) u) x)).(let H0 \def (match H in clear return 
-(\lambda (c: C).(\lambda (c0: C).(\lambda (_: (clear c c0)).((eq C c (CHead e 
-(Flat f) u)) \to ((eq C c0 x) \to (clear e x)))))) with [(clear_bind b e0 u0) 
-\Rightarrow (\lambda (H0: (eq C (CHead e0 (Bind b) u0) (CHead e (Flat f) 
-u))).(\lambda (H1: (eq C (CHead e0 (Bind b) u0) x)).((let H2 \def (eq_ind C 
-(CHead e0 (Bind b) u0) (\lambda (e1: C).(match e1 in C return (\lambda (_: 
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match 
-k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat 
-_) \Rightarrow False])])) I (CHead e (Flat f) u) H0) in (False_ind ((eq C 
-(CHead e0 (Bind b) u0) x) \to (clear e x)) H2)) H1))) | (clear_flat e0 c H0 
-f0 u0) \Rightarrow (\lambda (H1: (eq C (CHead e0 (Flat f0) u0) (CHead e (Flat 
-f) u))).(\lambda (H2: (eq C c x)).((let H3 \def (f_equal C T (\lambda (e1: 
+(clear (CHead e (Flat f) u) x)).(insert_eq C (CHead e (Flat f) u) (\lambda 
+(c: C).(clear c x)) (\lambda (_: C).(clear e x)) (\lambda (y: C).(\lambda 
+(H0: (clear y x)).(clear_ind (\lambda (c: C).(\lambda (c0: C).((eq C c (CHead 
+e (Flat f) u)) \to (clear e c0)))) (\lambda (b: B).(\lambda (e0: C).(\lambda 
+(u0: T).(\lambda (H1: (eq C (CHead e0 (Bind b) u0) (CHead e (Flat f) 
+u))).(let H2 \def (eq_ind C (CHead e0 (Bind b) u0) (\lambda (ee: C).(match ee 
+in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead 
+_ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _) 
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e (Flat f) u) H1) 
+in (False_ind (clear e (CHead e0 (Bind b) u0)) H2)))))) (\lambda (e0: 
+C).(\lambda (c: C).(\lambda (H1: (clear e0 c)).(\lambda (H2: (((eq C e0 
+(CHead e (Flat f) u)) \to (clear e c)))).(\lambda (f0: F).(\lambda (u0: 
+T).(\lambda (H3: (eq C (CHead e0 (Flat f0) u0) (CHead e (Flat f) u))).(let H4 
+\def (f_equal C C (\lambda (e1: C).(match e1 in C return (\lambda (_: C).C) 
+with [(CSort _) \Rightarrow e0 | (CHead c0 _ _) \Rightarrow c0])) (CHead e0 
+(Flat f0) u0) (CHead e (Flat f) u) H3) in ((let H5 \def (f_equal C F (\lambda 
+(e1: C).(match e1 in C return (\lambda (_: C).F) with [(CSort _) \Rightarrow 
+f0 | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).F) with 
+[(Bind _) \Rightarrow f0 | (Flat f1) \Rightarrow f1])])) (CHead e0 (Flat f0) 
+u0) (CHead e (Flat f) u) H3) in ((let H6 \def (f_equal C T (\lambda (e1: 
 C).(match e1 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | 
 (CHead _ _ t) \Rightarrow t])) (CHead e0 (Flat f0) u0) (CHead e (Flat f) u) 
-H1) in ((let H4 \def (f_equal C F (\lambda (e1: C).(match e1 in C return 
-(\lambda (_: C).F) with [(CSort _) \Rightarrow f0 | (CHead _ k _) \Rightarrow 
-(match k in K return (\lambda (_: K).F) with [(Bind _) \Rightarrow f0 | (Flat 
-f1) \Rightarrow f1])])) (CHead e0 (Flat f0) u0) (CHead e (Flat f) u) H1) in 
-((let H5 \def (f_equal C C (\lambda (e1: C).(match e1 in C return (\lambda 
-(_: C).C) with [(CSort _) \Rightarrow e0 | (CHead c0 _ _) \Rightarrow c0])) 
-(CHead e0 (Flat f0) u0) (CHead e (Flat f) u) H1) in (eq_ind C e (\lambda (c0: 
-C).((eq F f0 f) \to ((eq T u0 u) \to ((eq C c x) \to ((clear c0 c) \to (clear 
-e x)))))) (\lambda (H6: (eq F f0 f)).(eq_ind F f (\lambda (_: F).((eq T u0 u) 
-\to ((eq C c x) \to ((clear e c) \to (clear e x))))) (\lambda (H7: (eq T u0 
-u)).(eq_ind T u (\lambda (_: T).((eq C c x) \to ((clear e c) \to (clear e 
-x)))) (\lambda (H8: (eq C c x)).(eq_ind C x (\lambda (c0: C).((clear e c0) 
-\to (clear e x))) (\lambda (H9: (clear e x)).H9) c (sym_eq C c x H8))) u0 
-(sym_eq T u0 u H7))) f0 (sym_eq F f0 f H6))) e0 (sym_eq C e0 e H5))) H4)) 
-H3)) H2 H0)))]) in (H0 (refl_equal C (CHead e (Flat f) u)) (refl_equal C 
-x))))))).
+H3) in (\lambda (_: (eq F f0 f)).(\lambda (H8: (eq C e0 e)).(let H9 \def 
+(eq_ind C e0 (\lambda (c0: C).((eq C c0 (CHead e (Flat f) u)) \to (clear e 
+c))) H2 e H8) in (let H10 \def (eq_ind C e0 (\lambda (c0: C).(clear c0 c)) H1 
+e H8) in H10))))) H5)) H4))))))))) y x H0))) H))))).
 
 theorem clear_gen_flat_r:
  \forall (f: F).(\forall (x: C).(\forall (e: C).(\forall (u: T).((clear x