we removed about 100 match-with costruction turning them into applications

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / Level-1 / LambdaDelta / getl / dec.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/dec.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/dec.ma
index 59c3775bb633f14be40381a915e3258a88653eab..6d892bdae97f0aedcb131fee081b09e9e590c9ac 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/dec.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/dec.ma
@@ -34,19 +34,18 @@ Prop).(getl_gen_sort n i d H P))))))) (\lambda (c0: C).(\lambda (H: ((\forall
 (i: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
 T).(getl i c0 (CHead e (Bind b) v)))))) (\forall (d: C).((getl i c0 d) \to 
 (\forall (P: Prop).P))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (i: 
-nat).(match i in nat return (\lambda (n: nat).(or (ex_3 C B T (\lambda (e: 
-C).(\lambda (b: B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) 
-v)))))) (\forall (d: C).((getl n (CHead c0 k t) d) \to (\forall (P: 
-Prop).P))))) with [O \Rightarrow (match k in K return (\lambda (k0: K).(or 
-(ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 
-k0 t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O (CHead c0 k0 t) d) 
-\to (\forall (P: Prop).P))))) with [(Bind b) \Rightarrow (or_introl (ex_3 C B 
-T (\lambda (e: C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) 
-t) (CHead e (Bind b0) v)))))) (\forall (d: C).((getl O (CHead c0 (Bind b) t) 
-d) \to (\forall (P: Prop).P))) (ex_3_intro C B T (\lambda (e: C).(\lambda 
-(b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) t) (CHead e (Bind b0) 
-v))))) c0 b t (getl_refl b c0 t))) | (Flat f) \Rightarrow (let H_x \def (H O) 
-in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+nat).(nat_ind (\lambda (n: nat).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+B).(\lambda (v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall 
+(d: C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))) (K_ind 
+(\lambda (k0: K).(or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
+T).(getl O (CHead c0 k0 t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl O 
+(CHead c0 k0 t) d) \to (\forall (P: Prop).P))))) (\lambda (b: B).(or_introl 
+(ex_3 C B T (\lambda (e: C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead 
+c0 (Bind b) t) (CHead e (Bind b0) v)))))) (\forall (d: C).((getl O (CHead c0 
+(Bind b) t) d) \to (\forall (P: Prop).P))) (ex_3_intro C B T (\lambda (e: 
+C).(\lambda (b0: B).(\lambda (v: T).(getl O (CHead c0 (Bind b) t) (CHead e 
+(Bind b0) v))))) c0 b t (getl_refl b c0 t)))) (\lambda (f: F).(let H_x \def 
+(H O) in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: 
 B).(\lambda (v: T).(getl O c0 (CHead e (Bind b) v)))))) (\forall (d: 
 C).((getl O c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T (\lambda (e: 
 C).(\lambda (b: B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e 
@@ -69,29 +68,32 @@ B).(\lambda (v: T).(getl O (CHead c0 (Flat f) t) (CHead e (Bind b) v))))))
 (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P))) 
 (\lambda (d: C).(\lambda (H2: (getl O (CHead c0 (Flat f) t) d)).(\lambda (P: 
 Prop).(H1 d (getl_intro O c0 d c0 (drop_refl c0) (clear_gen_flat f c0 d t 
-(getl_gen_O (CHead c0 (Flat f) t) d H2))) P)))))) H0)))]) | (S n) \Rightarrow 
-(let H_x \def (H (r k n)) in (let H0 \def H_x in (or_ind (ex_3 C B T (\lambda 
-(e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) 
-v)))))) (\forall (d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))) (or 
-(ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) 
-(CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead 
-c0 k t) d) \to (\forall (P: Prop).P)))) (\lambda (H1: (ex_3 C B T (\lambda 
-(e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) 
-v))))))).(ex_3_ind C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
-T).(getl (r k n) c0 (CHead e (Bind b) v))))) (or (ex_3 C B T (\lambda (e: 
-C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind 
-b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: 
-Prop).P)))) (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: 
-(getl (r k n) c0 (CHead x0 (Bind x1) x2))).(or_introl (ex_3 C B T (\lambda 
-(e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e 
-(Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall 
-(P: Prop).P))) (ex_3_intro C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: 
-T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_head k 
-n c0 (CHead x0 (Bind x1) x2) H2 t))))))) H1)) (\lambda (H1: ((\forall (d: 
-C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))))).(or_intror (ex_3 C B T 
+(getl_gen_O (CHead c0 (Flat f) t) d H2))) P)))))) H0)))) k) (\lambda (n: 
+nat).(\lambda (_: (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda 
+(v: T).(getl n (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl n (CHead c0 k t) d) \to (\forall (P: Prop).P))))).(let H_x \def (H 
+(r k n)) in (let H1 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda 
+(b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v)))))) (\forall 
+(d: C).((getl (r k n) c0 d) \to (\forall (P: Prop).P))) (or (ex_3 C B T 
 (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) 
 (CHead e (Bind b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to 
-(\forall (P: Prop).P))) (\lambda (d: C).(\lambda (H2: (getl (S n) (CHead c0 k 
-t) d)).(\lambda (P: Prop).(H1 d (getl_gen_S k c0 d t n H2) P)))))) 
-H0)))])))))) c).
+(\forall (P: Prop).P)))) (\lambda (H2: (ex_3 C B T (\lambda (e: C).(\lambda 
+(b: B).(\lambda (v: T).(getl (r k n) c0 (CHead e (Bind b) v))))))).(ex_3_ind 
+C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (r k n) c0 (CHead 
+e (Bind b) v))))) (or (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda 
+(v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) (\forall (d: 
+C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P)))) (\lambda (x0: 
+C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H3: (getl (r k n) c0 (CHead x0 
+(Bind x1) x2))).(or_introl (ex_3 C B T (\lambda (e: C).(\lambda (b: 
+B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind b) v)))))) 
+(\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: Prop).P))) 
+(ex_3_intro C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl (S n) 
+(CHead c0 k t) (CHead e (Bind b) v))))) x0 x1 x2 (getl_head k n c0 (CHead x0 
+(Bind x1) x2) H3 t))))))) H2)) (\lambda (H2: ((\forall (d: C).((getl (r k n) 
+c0 d) \to (\forall (P: Prop).P))))).(or_intror (ex_3 C B T (\lambda (e: 
+C).(\lambda (b: B).(\lambda (v: T).(getl (S n) (CHead c0 k t) (CHead e (Bind 
+b) v)))))) (\forall (d: C).((getl (S n) (CHead c0 k t) d) \to (\forall (P: 
+Prop).P))) (\lambda (d: C).(\lambda (H3: (getl (S n) (CHead c0 k t) 
+d)).(\lambda (P: Prop).(H2 d (getl_gen_S k c0 d t n H3) P)))))) H1))))) 
+i)))))) c).