- some bugs fixed in the domain-based preorders on environments

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / ty3 / arity.ma

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 4f6b4cf133c7e44961efe8ac45720d263a898753..3be6c0d3b056d950b5e55d1cf896c37dfe70b660 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/arity.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/ty3/arity.ma
@@ -119,49 +119,50 @@ 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) 
+(arity_bind g Void (sym_not_eq B Abst Void not_abst_void) c0 u x H5 t3 x0 
+H12) (arity_bind g Void (sym_not_eq B Abst Void not_abst_void) 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 (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 
+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))