(* This file was automatically generated: do not edit *********************)
-include "Basic-1/ty3/pr3_props.ma".
+include "basic_1/ty3/pr3_props.ma".
-include "Basic-1/arity/pr3.ma".
+include "basic_1/arity/pr3.ma".
-include "Basic-1/asucc/fwd.ma".
+include "basic_1/asucc/fwd.ma".
-theorem ty3_arity:
+lemma ty3_arity:
\forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (t2: T).((ty3 g c
t1 t2) \to (ex2 A (\lambda (a1: A).(arity g c t1 a1)) (\lambda (a1: A).(arity
g c t2 (asucc g a1))))))))
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 (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)
+(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))
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))))).
-(* COMMENTS
-Initial nodes: 3761
-END *)
projects / helm.git / blobdiff