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=5f63defc6b253a9ab84ba9f3be717fe50ce7199d;hb=076f639446efce8d8cf83dcf7ca40b4376fc8c36;hp=25d4ad924241ff62a8c9aaf0a376395ae5803bc6;hpb=fdda444a05fe4c68c925cd94e4e3a38c93d0c35f;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 25d4ad924..5f63defc6 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
@@ -14,13 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/arity".
+include "LambdaDelta-1/ty3/pr3_props.ma".
 
-include "ty3/pr3_props.ma".
+include "LambdaDelta-1/arity/pr3.ma".
 
-include "arity/pr3.ma".
-
-include "asucc/fwd.ma".
+include "LambdaDelta-1/asucc/fwd.ma".
 
 theorem ty3_arity:
  \forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c 
@@ -86,86 +84,72 @@ H3)))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (t: T).(\lambda (_:
 (\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))))).(\lambda (t0: T).(\lambda (H4: (ty3 g (CHead c0 (Bind b) u) t4 
-t0)).(\lambda (H5: (ex2 A (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t4 
-a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t0 (asucc g a1))))).(let 
-H6 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: 
+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 (H7: (arity g c0 u x)).(\lambda (_: (arity 
-g c0 t (asucc g x))).(let H9 \def H3 in (ex2_ind A (\lambda (a1: A).(arity g 
+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 (H10: (arity g (CHead c0 (Bind b) u) t3 
-x0)).(\lambda (H11: (arity g (CHead c0 (Bind b) u) t4 (asucc g x0))).(let H_x 
-\def (leq_asucc g x) in (let H12 \def H_x in (ex_ind A (\lambda (a0: A).(leq 
+(\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 (H13: (leq g x (asucc g x1))).(B_ind (\lambda (b0: 
-B).((ty3 g (CHead c0 (Bind b0) u) t4 t0) \to ((ex2 A (\lambda (a1: A).(arity 
-g (CHead c0 (Bind b0) u) t4 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind 
-b0) u) t0 (asucc g a1)))) \to ((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 (_: (ty3 g (CHead c0 
-(Bind Abbr) u) t4 t0)).(\lambda (_: (ex2 A (\lambda (a1: A).(arity g (CHead 
-c0 (Bind Abbr) u) t4 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind Abbr) u) 
-t0 (asucc g a1))))).(\lambda (H16: (arity g (CHead c0 (Bind Abbr) u) t3 
-x0)).(\lambda (H17: (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 H7 t3 x0 H16) (arity_bind g Abbr 
-not_abbr_abst c0 u x H7 t4 (asucc g x0) H17)))))) (\lambda (_: (ty3 g (CHead 
-c0 (Bind Abst) u) t4 t0)).(\lambda (_: (ex2 A (\lambda (a1: A).(arity g 
-(CHead c0 (Bind Abst) u) t4 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind 
-Abst) u) t0 (asucc g a1))))).(\lambda (H16: (arity g (CHead c0 (Bind Abst) u) 
-t3 x0)).(\lambda (H17: (arity g (CHead c0 (Bind Abst) u) t4 (asucc g 
+(\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 H7 (asucc g x1) H13) t3 x0 
-H16) (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 H7 (asucc g x1) H13) t4 (asucc g 
-x0) H17) (asucc g (AHead x1 x0)) (leq_refl g (asucc g (AHead x1 x0))))))))) 
-(\lambda (_: (ty3 g (CHead c0 (Bind Void) u) t4 t0)).(\lambda (_: (ex2 A 
-(\lambda (a1: A).(arity g (CHead c0 (Bind Void) u) t4 a1)) (\lambda (a1: 
-A).(arity g (CHead c0 (Bind Void) u) t0 (asucc g a1))))).(\lambda (H16: 
-(arity g (CHead c0 (Bind Void) u) t3 x0)).(\lambda (H17: (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 H7 t3 x0 H16) 
-(arity_bind g Void not_void_abst c0 u x H7 t4 (asucc g x0) H17)))))) b H4 H5 
-H10 H11))) H12)))))) H9))))) H6))))))))))))))) (\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) 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 
+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) 
+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 
@@ -178,13 +162,21 @@ 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 (_: (ex2 A 
+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)) 
 (\lambda (a1: A).(arity g c0 t4 (asucc g a1))) (ex2 A (\lambda (a1: A).(arity 
-g c0 (THead (Flat Cast) t4 t3) a1)) (\lambda (a1: A).(arity g c0 t4 (asucc g 
-a1)))) (\lambda (x: A).(\lambda (H5: (arity g c0 t3 x)).(\lambda (H6: (arity 
-g c0 t4 (asucc g x))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Flat 
-Cast) t4 t3) a1)) (\lambda (a1: A).(arity g c0 t4 (asucc g a1))) x 
-(arity_cast g c0 t4 x H6 t3 H5) H6)))) H4)))))))))) c t1 t2 H))))).
+g c0 (THead (Flat Cast) t4 t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat 
+Cast) t0 t4) (asucc g a1)))) (\lambda (x: A).(\lambda (H5: (arity g c0 t3 
+x)).(\lambda (H6: (arity g c0 t4 (asucc g x))).(let H7 \def H3 in (ex2_ind A 
+(\lambda (a1: A).(arity g c0 t4 a1)) (\lambda (a1: A).(arity g c0 t0 (asucc g 
+a1))) (ex2 A (\lambda (a1: A).(arity g c0 (THead (Flat Cast) t4 t3) a1)) 
+(\lambda (a1: A).(arity g c0 (THead (Flat Cast) t0 t4) (asucc g a1)))) 
+(\lambda (x0: A).(\lambda (H8: (arity g c0 t4 x0)).(\lambda (H9: (arity g c0 
+t0 (asucc g x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Flat 
+Cast) t4 t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat Cast) t0 t4) 
+(asucc g a1))) x (arity_cast g c0 t4 x H6 t3 H5) (arity_cast g c0 t0 (asucc g 
+x) (arity_repl g c0 t0 (asucc g x0) H9 (asucc g (asucc g x)) (asucc_repl g x0 
+(asucc g x) (arity_mono g c0 t4 x0 H8 (asucc g x) H6))) t4 H6))))) H7))))) 
+H4)))))))))) c t1 t2 H))))).