(* This file was automatically generated: do not edit *********************)
-include "ty3/pr3_props.ma".
+include "LambdaDelta-1/ty3/pr3_props.ma".
-include "arity/pr3.ma".
+include "LambdaDelta-1/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
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
+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 (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
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