X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Fty3%2Farity.ma;h=4f6b4cf133c7e44961efe8ac45720d263a898753;hb=20377cd037f6cc5eb9c6a5664354a8a0189d3f4f;hp=5f63defc6b253a9ab84ba9f3be717fe50ce7199d;hpb=e92710b1d9774a6491122668c8463b8658114610;p=helm.git

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/arity.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/arity.ma
index 5f63defc6..4f6b4cf13 100644
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/arity.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/arity.ma
@@ -77,91 +77,91 @@ c0 (TLRef n) a1)) (\lambda (a1: A).(arity g c0 (lift (S n) O u) (asucc g
 a1)))) (\lambda (x0: A).(\lambda (H7: (leq g x (asucc g x0))).(ex_intro2 A 
 (\lambda (a1: A).(arity g c0 (TLRef n) a1)) (\lambda (a1: A).(arity g c0 
 (lift (S n) O u) (asucc g a1))) x0 (arity_abst g c0 d u n H0 x0 (arity_repl g 
-d u x H4 (asucc g x0) H7)) (arity_lift g d u (asucc g x0) (arity_repl g d u x 
-H4 (asucc g x0) H7) c0 (S n) O (getl_drop Abst c0 d u n H0))))) H6)))))) 
-H3)))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (t: T).(\lambda (_: 
-(ty3 g c0 u t)).(\lambda (H1: (ex2 A (\lambda (a1: A).(arity g c0 u a1)) 
-(\lambda (a1: A).(arity g c0 t (asucc g a1))))).(\lambda (b: B).(\lambda (t3: 
-T).(\lambda (t4: T).(\lambda (_: (ty3 g (CHead c0 (Bind b) u) t3 
-t4)).(\lambda (H3: (ex2 A (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t3 
-a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t4 (asucc g a1))))).(let 
-H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: 
-A).(arity g c0 t (asucc g a1))) (ex2 A (\lambda (a1: A).(arity g c0 (THead 
-(Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b) u t4) (asucc 
-g a1)))) (\lambda (x: A).(\lambda (H5: (arity g c0 u x)).(\lambda (_: (arity 
-g c0 t (asucc g x))).(let H7 \def H3 in (ex2_ind A (\lambda (a1: A).(arity g 
-(CHead c0 (Bind b) u) t3 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) 
-t4 (asucc g a1))) (ex2 A (\lambda (a1: A).(arity g c0 (THead (Bind b) u t3) 
-a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b) u t4) (asucc g a1)))) 
-(\lambda (x0: A).(\lambda (H8: (arity g (CHead c0 (Bind b) u) t3 
-x0)).(\lambda (H9: (arity g (CHead c0 (Bind b) u) t4 (asucc g x0))).(let H_x 
-\def (leq_asucc g x) in (let H10 \def H_x in (ex_ind A (\lambda (a0: A).(leq 
-g x (asucc g a0))) (ex2 A (\lambda (a1: A).(arity g c0 (THead (Bind b) u t3) 
-a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b) u t4) (asucc g a1)))) 
-(\lambda (x1: A).(\lambda (H11: (leq g x (asucc g x1))).(B_ind (\lambda (b0: 
-B).((arity g (CHead c0 (Bind b0) u) t3 x0) \to ((arity g (CHead c0 (Bind b0) 
-u) t4 (asucc g x0)) \to (ex2 A (\lambda (a1: A).(arity g c0 (THead (Bind b0) 
-u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b0) u t4) (asucc g 
-a1))))))) (\lambda (H12: (arity g (CHead c0 (Bind Abbr) u) t3 x0)).(\lambda 
-(H13: (arity g (CHead c0 (Bind Abbr) u) t4 (asucc g x0))).(ex_intro2 A 
-(\lambda (a1: A).(arity g c0 (THead (Bind Abbr) u t3) a1)) (\lambda (a1: 
-A).(arity g c0 (THead (Bind Abbr) u t4) (asucc g a1))) x0 (arity_bind g Abbr 
-not_abbr_abst c0 u x H5 t3 x0 H12) (arity_bind g Abbr not_abbr_abst c0 u x H5 
-t4 (asucc g x0) H13)))) (\lambda (H12: (arity g (CHead c0 (Bind Abst) u) t3 
-x0)).(\lambda (H13: (arity g (CHead c0 (Bind Abst) u) t4 (asucc g 
-x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t3) a1)) 
-(\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t4) (asucc g a1))) (AHead 
-x1 x0) (arity_head g c0 u x1 (arity_repl g c0 u x H5 (asucc g x1) H11) t3 x0 
-H12) (arity_repl g c0 (THead (Bind Abst) u t4) (AHead x1 (asucc g x0)) 
-(arity_head g c0 u x1 (arity_repl g c0 u x H5 (asucc g x1) H11) t4 (asucc g 
-x0) H13) (asucc g (AHead x1 x0)) (leq_refl g (asucc g (AHead x1 x0))))))) 
-(\lambda (H12: (arity g (CHead c0 (Bind Void) u) t3 x0)).(\lambda (H13: 
-(arity g (CHead c0 (Bind Void) u) t4 (asucc g x0))).(ex_intro2 A (\lambda 
-(a1: A).(arity g c0 (THead (Bind Void) u t3) a1)) (\lambda (a1: A).(arity g 
-c0 (THead (Bind Void) u t4) (asucc g a1))) x0 (arity_bind g Void 
-not_void_abst c0 u x H5 t3 x0 H12) (arity_bind g Void not_void_abst c0 u x H5 
-t4 (asucc g x0) H13)))) b H8 H9))) H10)))))) H7))))) H4)))))))))))) (\lambda 
-(c0: C).(\lambda (w: T).(\lambda (u: T).(\lambda (_: (ty3 g c0 w u)).(\lambda 
-(H1: (ex2 A (\lambda (a1: A).(arity g c0 w a1)) (\lambda (a1: A).(arity g c0 
-u (asucc g a1))))).(\lambda (v: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 v 
-(THead (Bind Abst) u t))).(\lambda (H3: (ex2 A (\lambda (a1: A).(arity g c0 v 
-a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t) (asucc g 
-a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 w a1)) 
-(\lambda (a1: A).(arity g c0 u (asucc g a1))) (ex2 A (\lambda (a1: A).(arity 
-g c0 (THead (Flat Appl) w v) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat 
-Appl) w (THead (Bind Abst) u t)) (asucc g a1)))) (\lambda (x: A).(\lambda 
-(H5: (arity g c0 w x)).(\lambda (H6: (arity g c0 u (asucc g x))).(let H7 \def 
-H3 in (ex2_ind A (\lambda (a1: A).(arity g c0 v a1)) (\lambda (a1: A).(arity 
-g c0 (THead (Bind Abst) u t) (asucc g a1))) (ex2 A (\lambda (a1: A).(arity g 
-c0 (THead (Flat Appl) w v) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat 
-Appl) w (THead (Bind Abst) u t)) (asucc g a1)))) (\lambda (x0: A).(\lambda 
-(H8: (arity g c0 v x0)).(\lambda (H9: (arity g c0 (THead (Bind Abst) u t) 
-(asucc g x0))).(let H10 \def (arity_gen_abst g c0 u t (asucc g x0) H9) in 
-(ex3_2_ind A A (\lambda (a1: A).(\lambda (a2: A).(eq A (asucc g x0) (AHead a1 
-a2)))) (\lambda (a1: A).(\lambda (_: A).(arity g c0 u (asucc g a1)))) 
-(\lambda (_: A).(\lambda (a2: A).(arity g (CHead c0 (Bind Abst) u) t a2))) 
-(ex2 A (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) a1)) (\lambda 
-(a1: A).(arity g c0 (THead (Flat Appl) w (THead (Bind Abst) u t)) (asucc g 
-a1)))) (\lambda (x1: A).(\lambda (x2: A).(\lambda (H11: (eq A (asucc g x0) 
-(AHead x1 x2))).(\lambda (H12: (arity g c0 u (asucc g x1))).(\lambda (H13: 
-(arity g (CHead c0 (Bind Abst) u) t x2)).(let H14 \def (sym_eq A (asucc g x0) 
-(AHead x1 x2) H11) in (let H15 \def (asucc_gen_head g x1 x2 x0 H14) in 
-(ex2_ind A (\lambda (a0: A).(eq A x0 (AHead x1 a0))) (\lambda (a0: A).(eq A 
-x2 (asucc g a0))) (ex2 A (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) 
+d u x H4 (asucc g x0) H7)) (arity_repl g c0 (lift (S n) O u) x (arity_lift g 
+d u x H4 c0 (S n) O (getl_drop Abst c0 d u n H0)) (asucc g x0) H7)))) 
+H6)))))) H3)))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (t: 
+T).(\lambda (_: (ty3 g c0 u t)).(\lambda (H1: (ex2 A (\lambda (a1: A).(arity 
+g c0 u a1)) (\lambda (a1: A).(arity g c0 t (asucc g a1))))).(\lambda (b: 
+B).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (ty3 g (CHead c0 (Bind b) 
+u) t3 t4)).(\lambda (H3: (ex2 A (\lambda (a1: A).(arity g (CHead c0 (Bind b) 
+u) t3 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t4 (asucc g 
+a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 u a1)) 
+(\lambda (a1: A).(arity g c0 t (asucc g a1))) (ex2 A (\lambda (a1: A).(arity 
+g c0 (THead (Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b) 
+u t4) (asucc g a1)))) (\lambda (x: A).(\lambda (H5: (arity g c0 u 
+x)).(\lambda (_: (arity g c0 t (asucc g x))).(let H7 \def H3 in (ex2_ind A 
+(\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t3 a1)) (\lambda (a1: 
+A).(arity g (CHead c0 (Bind b) u) t4 (asucc g a1))) (ex2 A (\lambda (a1: 
+A).(arity g c0 (THead (Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead 
+(Bind b) u t4) (asucc g a1)))) (\lambda (x0: A).(\lambda (H8: (arity g (CHead 
+c0 (Bind b) u) t3 x0)).(\lambda (H9: (arity g (CHead c0 (Bind b) u) t4 (asucc 
+g x0))).(let H_x \def (leq_asucc g x) in (let H10 \def H_x in (ex_ind A 
+(\lambda (a0: A).(leq g x (asucc g a0))) (ex2 A (\lambda (a1: A).(arity g c0 
+(THead (Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b) u t4) 
+(asucc g a1)))) (\lambda (x1: A).(\lambda (H11: (leq g x (asucc g 
+x1))).(B_ind (\lambda (b0: B).((arity g (CHead c0 (Bind b0) u) t3 x0) \to 
+((arity g (CHead c0 (Bind b0) u) t4 (asucc g x0)) \to (ex2 A (\lambda (a1: 
+A).(arity g c0 (THead (Bind b0) u t3) a1)) (\lambda (a1: A).(arity g c0 
+(THead (Bind b0) u t4) (asucc g a1))))))) (\lambda (H12: (arity g (CHead c0 
+(Bind Abbr) u) t3 x0)).(\lambda (H13: (arity g (CHead c0 (Bind Abbr) u) t4 
+(asucc g x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Bind Abbr) u 
+t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abbr) u t4) (asucc g a1))) 
+x0 (arity_bind g Abbr not_abbr_abst c0 u x H5 t3 x0 H12) (arity_bind g Abbr 
+not_abbr_abst c0 u x H5 t4 (asucc g x0) H13)))) (\lambda (H12: (arity g 
+(CHead c0 (Bind Abst) u) t3 x0)).(\lambda (H13: (arity g (CHead c0 (Bind 
+Abst) u) t4 (asucc g x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead 
+(Bind Abst) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t4) 
+(asucc g a1))) (AHead x1 x0) (arity_head g c0 u x1 (arity_repl g c0 u x H5 
+(asucc g x1) H11) t3 x0 H12) (arity_repl g c0 (THead (Bind Abst) u t4) (AHead 
+x1 (asucc g x0)) (arity_head g c0 u x1 (arity_repl g c0 u x H5 (asucc g x1) 
+H11) t4 (asucc g x0) H13) (asucc g (AHead x1 x0)) (leq_refl g (asucc g (AHead 
+x1 x0))))))) (\lambda (H12: (arity g (CHead c0 (Bind Void) u) t3 
+x0)).(\lambda (H13: (arity g (CHead c0 (Bind Void) u) t4 (asucc g 
+x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Bind Void) u t3) a1)) 
+(\lambda (a1: A).(arity g c0 (THead (Bind Void) u t4) (asucc g a1))) x0 
+(arity_bind g Void not_void_abst c0 u x H5 t3 x0 H12) (arity_bind g Void 
+not_void_abst c0 u x H5 t4 (asucc g x0) H13)))) b H8 H9))) H10)))))) H7))))) 
+H4)))))))))))) (\lambda (c0: C).(\lambda (w: T).(\lambda (u: T).(\lambda (_: 
+(ty3 g c0 w u)).(\lambda (H1: (ex2 A (\lambda (a1: A).(arity g c0 w a1)) 
+(\lambda (a1: A).(arity g c0 u (asucc g a1))))).(\lambda (v: T).(\lambda (t: 
+T).(\lambda (_: (ty3 g c0 v (THead (Bind Abst) u t))).(\lambda (H3: (ex2 A 
+(\lambda (a1: A).(arity g c0 v a1)) (\lambda (a1: A).(arity g c0 (THead (Bind 
+Abst) u t) (asucc g a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: 
+A).(arity g c0 w a1)) (\lambda (a1: A).(arity g c0 u (asucc g a1))) (ex2 A 
+(\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) a1)) (\lambda (a1: 
+A).(arity g c0 (THead (Flat Appl) w (THead (Bind Abst) u t)) (asucc g a1)))) 
+(\lambda (x: A).(\lambda (H5: (arity g c0 w x)).(\lambda (H6: (arity g c0 u 
+(asucc g x))).(let H7 \def H3 in (ex2_ind A (\lambda (a1: A).(arity g c0 v 
+a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t) (asucc g a1))) (ex2 
+A (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) a1)) (\lambda (a1: 
+A).(arity g c0 (THead (Flat Appl) w (THead (Bind Abst) u t)) (asucc g a1)))) 
+(\lambda (x0: A).(\lambda (H8: (arity g c0 v x0)).(\lambda (H9: (arity g c0 
+(THead (Bind Abst) u t) (asucc g x0))).(let H10 \def (arity_gen_abst g c0 u t 
+(asucc g x0) H9) in (ex3_2_ind A A (\lambda (a1: A).(\lambda (a2: A).(eq A 
+(asucc g x0) (AHead a1 a2)))) (\lambda (a1: A).(\lambda (_: A).(arity g c0 u 
+(asucc g a1)))) (\lambda (_: A).(\lambda (a2: A).(arity g (CHead c0 (Bind 
+Abst) u) t a2))) (ex2 A (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) 
 a1)) (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w (THead (Bind Abst) u 
-t)) (asucc g a1)))) (\lambda (x3: A).(\lambda (H16: (eq A x0 (AHead x1 
-x3))).(\lambda (H17: (eq A x2 (asucc g x3))).(let H18 \def (eq_ind A x2 
-(\lambda (a: A).(arity g (CHead c0 (Bind Abst) u) t a)) H13 (asucc g x3) H17) 
-in (let H19 \def (eq_ind A x0 (\lambda (a: A).(arity g c0 v a)) H8 (AHead x1 
-x3) H16) in (ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) 
-a1)) (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w (THead (Bind Abst) u 
-t)) (asucc g a1))) x3 (arity_appl g c0 w x1 (arity_repl g c0 w x H5 x1 
-(leq_sym g x1 x (asucc_inj g x1 x (arity_mono g c0 u (asucc g x1) H12 (asucc 
-g x) H6)))) v x3 H19) (arity_appl g c0 w x H5 (THead (Bind Abst) u t) (asucc 
-g x3) (arity_head g c0 u x H6 t (asucc g x3) H18)))))))) H15)))))))) H10))))) 
-H7))))) H4))))))))))) (\lambda (c0: C).(\lambda (t3: T).(\lambda (t4: 
-T).(\lambda (_: (ty3 g c0 t3 t4)).(\lambda (H1: (ex2 A (\lambda (a1: 
-A).(arity g c0 t3 a1)) (\lambda (a1: A).(arity g c0 t4 (asucc g 
+t)) (asucc g a1)))) (\lambda (x1: A).(\lambda (x2: A).(\lambda (H11: (eq A 
+(asucc g x0) (AHead x1 x2))).(\lambda (H12: (arity g c0 u (asucc g 
+x1))).(\lambda (H13: (arity g (CHead c0 (Bind Abst) u) t x2)).(let H14 \def 
+(sym_eq A (asucc g x0) (AHead x1 x2) H11) in (let H15 \def (asucc_gen_head g 
+x1 x2 x0 H14) in (ex2_ind A (\lambda (a0: A).(eq A x0 (AHead x1 a0))) 
+(\lambda (a0: A).(eq A x2 (asucc g a0))) (ex2 A (\lambda (a1: A).(arity g c0 
+(THead (Flat Appl) w v) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat Appl) 
+w (THead (Bind Abst) u t)) (asucc g a1)))) (\lambda (x3: A).(\lambda (H16: 
+(eq A x0 (AHead x1 x3))).(\lambda (H17: (eq A x2 (asucc g x3))).(let H18 \def 
+(eq_ind A x2 (\lambda (a: A).(arity g (CHead c0 (Bind Abst) u) t a)) H13 
+(asucc g x3) H17) in (let H19 \def (eq_ind A x0 (\lambda (a: A).(arity g c0 v 
+a)) H8 (AHead x1 x3) H16) in (ex_intro2 A (\lambda (a1: A).(arity g c0 (THead 
+(Flat Appl) w v) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w 
+(THead (Bind Abst) u t)) (asucc g a1))) x3 (arity_appl g c0 w x1 (arity_repl 
+g c0 w x H5 x1 (leq_sym g x1 x (asucc_inj g x1 x (arity_mono g c0 u (asucc g 
+x1) H12 (asucc g x) H6)))) v x3 H19) (arity_appl g c0 w x H5 (THead (Bind 
+Abst) u t) (asucc g x3) (arity_head g c0 u x H6 t (asucc g x3) H18)))))))) 
+H15)))))))) H10))))) H7))))) H4))))))))))) (\lambda (c0: C).(\lambda (t3: 
+T).(\lambda (t4: T).(\lambda (_: (ty3 g c0 t3 t4)).(\lambda (H1: (ex2 A 
+(\lambda (a1: A).(arity g c0 t3 a1)) (\lambda (a1: A).(arity g c0 t4 (asucc g 
 a1))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t4 t0)).(\lambda (H3: (ex2 A 
 (\lambda (a1: A).(arity g c0 t4 a1)) (\lambda (a1: A).(arity g c0 t0 (asucc g 
 a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 t3 a1))