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

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

diff --git a/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/flt.ma b/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/flt.ma
index 589f2dd50cb759458d00f86b2c82fd8405a294de..88150ce35edb69f6d0266aa762a3c277e1424b43 100644 (file)
--- a/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/flt.ma
+++ b/matita/contribs/LAMBDA-TYPES/Level-1/LambdaDelta/getl/flt.ma
@@ -34,33 +34,33 @@ u))).(getl_gen_sort n i (CHead e (Bind b) u) H (flt e u (CSort n) (TLRef
 i)))))))) (\lambda (c0: C).(\lambda (H: ((\forall (e: C).(\forall (u: 
 T).(\forall (i: nat).((getl i c0 (CHead e (Bind b) u)) \to (flt e u c0 (TLRef 
 i)))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e: C).(\lambda (u: 
-T).(\lambda (i: nat).(match i in nat return (\lambda (n: nat).((getl n (CHead 
-c0 k t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef n)))) with 
-[O \Rightarrow (\lambda (H0: (getl O (CHead c0 k t) (CHead e (Bind b) 
-u))).((match k in K return (\lambda (k0: K).((clear (CHead c0 k0 t) (CHead e 
-(Bind b) u)) \to (flt e u (CHead c0 k0 t) (TLRef O)))) with [(Bind b0) 
-\Rightarrow (\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e (Bind b) 
-u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 in C return 
-(\lambda (_: C).C) with [(CSort _) \Rightarrow e | (CHead c _ _) \Rightarrow 
-c])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead 
-e (Bind b) u) t H1)) in ((let H3 \def (f_equal C B (\lambda (e0: C).(match e0 
-in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | (CHead _ k _) 
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b) 
-\Rightarrow b | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u) (CHead c0 
-(Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in ((let H4 
-\def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T) 
-with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead e (Bind 
-b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t 
-H1)) in (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e c0)).(eq_ind_r T t 
-(\lambda (t0: T).(flt e t0 (CHead c0 (Bind b0) t) (TLRef O))) (eq_ind_r C c0 
-(\lambda (c1: C).(flt c1 t (CHead c0 (Bind b0) t) (TLRef O))) (eq_ind B b 
-(\lambda (b1: B).(flt c0 t (CHead c0 (Bind b1) t) (TLRef O))) (flt_arith0 
-(Bind b) c0 t O) b0 H5) e H6) u H4)))) H3)) H2))) | (Flat f) \Rightarrow 
-(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b) u))).(flt_arith1 
-(Bind b) e c0 u (clear_cle c0 (CHead e (Bind b) u) (clear_gen_flat f c0 
-(CHead e (Bind b) u) t H1)) (Flat f) t O))]) (getl_gen_O (CHead c0 k t) 
-(CHead e (Bind b) u) H0))) | (S n) \Rightarrow (\lambda (H0: (getl (S n) 
-(CHead c0 k t) (CHead e (Bind b) u))).(let H_y \def (H e u (r k n) 
-(getl_gen_S k c0 (CHead e (Bind b) u) t n H0)) in (flt_arith2 e c0 u (r k n) 
-H_y k t (S n))))])))))))) c)).
+T).(\lambda (i: nat).(nat_ind (\lambda (n: nat).((getl n (CHead c0 k t) 
+(CHead e (Bind b) u)) \to (flt e u (CHead c0 k t) (TLRef n)))) (\lambda (H0: 
+(getl O (CHead c0 k t) (CHead e (Bind b) u))).(K_ind (\lambda (k0: K).((clear 
+(CHead c0 k0 t) (CHead e (Bind b) u)) \to (flt e u (CHead c0 k0 t) (TLRef 
+O)))) (\lambda (b0: B).(\lambda (H1: (clear (CHead c0 (Bind b0) t) (CHead e 
+(Bind b) u))).(let H2 \def (f_equal C C (\lambda (e0: C).(match e0 in C 
+return (\lambda (_: C).C) with [(CSort _) \Rightarrow e | (CHead c1 _ _) 
+\Rightarrow c1])) (CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind 
+b0 c0 (CHead e (Bind b) u) t H1)) in ((let H3 \def (f_equal C B (\lambda (e0: 
+C).(match e0 in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | 
+(CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with 
+[(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead e (Bind b) u) 
+(CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e (Bind b) u) t H1)) in 
+((let H4 \def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda 
+(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) 
+(CHead e (Bind b) u) (CHead c0 (Bind b0) t) (clear_gen_bind b0 c0 (CHead e 
+(Bind b) u) t H1)) in (\lambda (H5: (eq B b b0)).(\lambda (H6: (eq C e 
+c0)).(eq_ind_r T t (\lambda (t0: T).(flt e t0 (CHead c0 (Bind b0) t) (TLRef 
+O))) (eq_ind_r C c0 (\lambda (c1: C).(flt c1 t (CHead c0 (Bind b0) t) (TLRef 
+O))) (eq_ind B b (\lambda (b1: B).(flt c0 t (CHead c0 (Bind b1) t) (TLRef 
+O))) (flt_arith0 (Bind b) c0 t O) b0 H5) e H6) u H4)))) H3)) H2)))) (\lambda 
+(f: F).(\lambda (H1: (clear (CHead c0 (Flat f) t) (CHead e (Bind b) 
+u))).(flt_arith1 (Bind b) e c0 u (clear_cle c0 (CHead e (Bind b) u) 
+(clear_gen_flat f c0 (CHead e (Bind b) u) t H1)) (Flat f) t O))) k 
+(getl_gen_O (CHead c0 k t) (CHead e (Bind b) u) H0))) (\lambda (n: 
+nat).(\lambda (_: (((getl n (CHead c0 k t) (CHead e (Bind b) u)) \to (flt e u 
+(CHead c0 k t) (TLRef n))))).(\lambda (H1: (getl (S n) (CHead c0 k t) (CHead 
+e (Bind b) u))).(let H_y \def (H e u (r k n) (getl_gen_S k c0 (CHead e (Bind 
+b) u) t n H1)) in (flt_arith2 e c0 u (r k n) H_y k t (S n)))))) i)))))))) c)).