include "LambdaDelta-1/csubst0/getl.ma".
-include "LambdaDelta-1/csubst0/props.ma".
-
include "LambdaDelta-1/subst0/dec.ma".
include "LambdaDelta-1/subst0/fwd.ma".
(v: T).((subst0 i0 w u v) \to (\forall (P: Prop).P)))))))))).(\lambda (d0:
C).(\lambda (u0: T).(\lambda (i0: nat).(\lambda (H3: (getl i0 c0 (CHead d0
(Bind Void) u0))).(\lambda (w: T).(\lambda (v: T).(\lambda (H4: (subst0 i0 w
-(TLRef i) v)).(\lambda (P: Prop).(and_ind (eq nat i i0) (eq T v (lift (S i) O
-w)) P (\lambda (H5: (eq nat i i0)).(\lambda (_: (eq T v (lift (S i) O
+(TLRef i) v)).(\lambda (P: Prop).(land_ind (eq nat i i0) (eq T v (lift (S i)
+O w)) P (\lambda (H5: (eq nat i i0)).(\lambda (_: (eq T v (lift (S i) O
w))).(let H7 \def (eq_ind_r nat i0 (\lambda (n: nat).(getl n c0 (CHead d0
(Bind Void) u0))) H3 i H5) in (let H8 \def (eq_ind C (CHead d (Bind Abbr) u)
(\lambda (c1: C).(getl i c0 c1)) H0 (CHead d0 (Bind Void) u0) (getl_mono c0
\to (\forall (P: Prop).P)))))))))).(\lambda (d0: C).(\lambda (u0: T).(\lambda
(i0: nat).(\lambda (H3: (getl i0 c0 (CHead d0 (Bind Void) u0))).(\lambda (w:
T).(\lambda (v: T).(\lambda (H4: (subst0 i0 w (TLRef i) v)).(\lambda (P:
-Prop).(and_ind (eq nat i i0) (eq T v (lift (S i) O w)) P (\lambda (H5: (eq
+Prop).(land_ind (eq nat i i0) (eq T v (lift (S i) O w)) P (\lambda (H5: (eq
nat i i0)).(\lambda (_: (eq T v (lift (S i) O w))).(let H7 \def (eq_ind_r nat
i0 (\lambda (n: nat).(getl n c0 (CHead d0 (Bind Void) u0))) H3 i H5) in (let
H8 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (c1: C).(getl i c0 c1)) H0
n) t2 u i H1) in (let H2 \def H_x in (or3_ind (land (eq C c c2) (subst0 i u
(TSort n) t2)) (land (eq T (TSort n) t2) (csubst0 i u c c2)) (land (subst0 i
u (TSort n) t2) (csubst0 i u c c2)) (arity g c2 t2 (ASort O n)) (\lambda (H3:
-(land (eq C c c2) (subst0 i u (TSort n) t2))).(and_ind (eq C c c2) (subst0 i
+(land (eq C c c2) (subst0 i u (TSort n) t2))).(land_ind (eq C c c2) (subst0 i
u (TSort n) t2) (arity g c2 t2 (ASort O n)) (\lambda (H4: (eq C c
c2)).(\lambda (H5: (subst0 i u (TSort n) t2)).(eq_ind C c (\lambda (c0:
C).(arity g c0 t2 (ASort O n))) (subst0_gen_sort u t2 i n H5 (arity g c t2
(ASort O n))) c2 H4))) H3)) (\lambda (H3: (land (eq T (TSort n) t2) (csubst0
-i u c c2))).(and_ind (eq T (TSort n) t2) (csubst0 i u c c2) (arity g c2 t2
+i u c c2))).(land_ind (eq T (TSort n) t2) (csubst0 i u c c2) (arity g c2 t2
(ASort O n)) (\lambda (H4: (eq T (TSort n) t2)).(\lambda (_: (csubst0 i u c
c2)).(eq_ind T (TSort n) (\lambda (t: T).(arity g c2 t (ASort O n)))
(arity_sort g c2 n) t2 H4))) H3)) (\lambda (H3: (land (subst0 i u (TSort n)
-t2) (csubst0 i u c c2))).(and_ind (subst0 i u (TSort n) t2) (csubst0 i u c
+t2) (csubst0 i u c c2))).(land_ind (subst0 i u (TSort n) t2) (csubst0 i u c
c2) (arity g c2 t2 (ASort O n)) (\lambda (H4: (subst0 i u (TSort n)
t2)).(\lambda (_: (csubst0 i u c c2)).(subst0_gen_sort u t2 i n H4 (arity g
c2 t2 (ASort O n))))) H3)) H2)))))))))))) (\lambda (c: C).(\lambda (d:
(let H5 \def H_x in (or3_ind (land (eq C c c2) (subst0 i0 u0 (TLRef i) t2))
(land (eq T (TLRef i) t2) (csubst0 i0 u0 c c2)) (land (subst0 i0 u0 (TLRef i)
t2) (csubst0 i0 u0 c c2)) (arity g c2 t2 a0) (\lambda (H6: (land (eq C c c2)
-(subst0 i0 u0 (TLRef i) t2))).(and_ind (eq C c c2) (subst0 i0 u0 (TLRef i)
+(subst0 i0 u0 (TLRef i) t2))).(land_ind (eq C c c2) (subst0 i0 u0 (TLRef i)
t2) (arity g c2 t2 a0) (\lambda (H7: (eq C c c2)).(\lambda (H8: (subst0 i0 u0
-(TLRef i) t2)).(eq_ind C c (\lambda (c0: C).(arity g c0 t2 a0)) (and_ind (eq
+(TLRef i) t2)).(eq_ind C c (\lambda (c0: C).(arity g c0 t2 a0)) (land_ind (eq
nat i i0) (eq T t2 (lift (S i) O u0)) (arity g c t2 a0) (\lambda (H9: (eq nat
i i0)).(\lambda (H10: (eq T t2 (lift (S i) O u0))).(eq_ind_r T (lift (S i) O
u0) (\lambda (t: T).(arity g c t a0)) (let H11 \def (eq_ind_r nat i0 (\lambda
H17 \def (eq_ind_r C d1 (\lambda (c0: C).(getl i c (CHead c0 (Bind Abbr) u)))
H16 d H15) in (arity_lift g d u a0 H1 c (S i) O (getl_drop Abbr c d u i
H17))) u0 H14)))) H13)))) t2 H10))) (subst0_gen_lref u0 t2 i0 i H8)) c2 H7)))
-H6)) (\lambda (H6: (land (eq T (TLRef i) t2) (csubst0 i0 u0 c c2))).(and_ind
+H6)) (\lambda (H6: (land (eq T (TLRef i) t2) (csubst0 i0 u0 c c2))).(land_ind
(eq T (TLRef i) t2) (csubst0 i0 u0 c c2) (arity g c2 t2 a0) (\lambda (H7: (eq
T (TLRef i) t2)).(\lambda (H8: (csubst0 i0 u0 c c2)).(eq_ind T (TLRef i)
(\lambda (t: T).(arity g c2 t a0)) (lt_le_e i i0 (arity g c2 (TLRef i) a0)
d u x4 H22 x2 H23))))))))) H18)) H17)))))))))))) H11)) H10))) (\lambda (H9:
(le i0 i)).(arity_abbr g c2 d u i (csubst0_getl_ge i0 i H9 c c2 u0 H8 (CHead
d (Bind Abbr) u) H0) a0 H1))) t2 H7))) H6)) (\lambda (H6: (land (subst0 i0 u0
-(TLRef i) t2) (csubst0 i0 u0 c c2))).(and_ind (subst0 i0 u0 (TLRef i) t2)
+(TLRef i) t2) (csubst0 i0 u0 c c2))).(land_ind (subst0 i0 u0 (TLRef i) t2)
(csubst0 i0 u0 c c2) (arity g c2 t2 a0) (\lambda (H7: (subst0 i0 u0 (TLRef i)
-t2)).(\lambda (H8: (csubst0 i0 u0 c c2)).(and_ind (eq nat i i0) (eq T t2
+t2)).(\lambda (H8: (csubst0 i0 u0 c c2)).(land_ind (eq nat i i0) (eq T t2
(lift (S i) O u0)) (arity g c2 t2 a0) (\lambda (H9: (eq nat i i0)).(\lambda
(H10: (eq T t2 (lift (S i) O u0))).(eq_ind_r T (lift (S i) O u0) (\lambda (t:
T).(arity g c2 t a0)) (let H11 \def (eq_ind_r nat i0 (\lambda (n:
(or3_ind (land (eq C c c2) (subst0 i0 u0 (TLRef i) t2)) (land (eq T (TLRef i)
t2) (csubst0 i0 u0 c c2)) (land (subst0 i0 u0 (TLRef i) t2) (csubst0 i0 u0 c
c2)) (arity g c2 t2 a0) (\lambda (H6: (land (eq C c c2) (subst0 i0 u0 (TLRef
-i) t2))).(and_ind (eq C c c2) (subst0 i0 u0 (TLRef i) t2) (arity g c2 t2 a0)
+i) t2))).(land_ind (eq C c c2) (subst0 i0 u0 (TLRef i) t2) (arity g c2 t2 a0)
(\lambda (H7: (eq C c c2)).(\lambda (H8: (subst0 i0 u0 (TLRef i) t2)).(eq_ind
-C c (\lambda (c0: C).(arity g c0 t2 a0)) (and_ind (eq nat i i0) (eq T t2
+C c (\lambda (c0: C).(arity g c0 t2 a0)) (land_ind (eq nat i i0) (eq T t2
(lift (S i) O u0)) (arity g c t2 a0) (\lambda (H9: (eq nat i i0)).(\lambda
(H10: (eq T t2 (lift (S i) O u0))).(eq_ind_r T (lift (S i) O u0) (\lambda (t:
T).(arity g c t a0)) (let H11 \def (eq_ind_r nat i0 (\lambda (n: nat).(getl n
(Bind Abst) u) i H0 (CHead d1 (Bind Abbr) u0) H11)) in (False_ind (arity g c
(lift (S i) O u0) a0) H13)))) t2 H10))) (subst0_gen_lref u0 t2 i0 i H8)) c2
H7))) H6)) (\lambda (H6: (land (eq T (TLRef i) t2) (csubst0 i0 u0 c
-c2))).(and_ind (eq T (TLRef i) t2) (csubst0 i0 u0 c c2) (arity g c2 t2 a0)
+c2))).(land_ind (eq T (TLRef i) t2) (csubst0 i0 u0 c c2) (arity g c2 t2 a0)
(\lambda (H7: (eq T (TLRef i) t2)).(\lambda (H8: (csubst0 i0 u0 c
c2)).(eq_ind T (TLRef i) (\lambda (t: T).(arity g c2 t a0)) (lt_le_e i i0
(arity g c2 (TLRef i) a0) (\lambda (H9: (lt i i0)).(let H10 \def
d u x4 H22 x2 H23))))))))) H18)) H17)))))))))))) H11)) H10))) (\lambda (H9:
(le i0 i)).(arity_abst g c2 d u i (csubst0_getl_ge i0 i H9 c c2 u0 H8 (CHead
d (Bind Abst) u) H0) a0 H1))) t2 H7))) H6)) (\lambda (H6: (land (subst0 i0 u0
-(TLRef i) t2) (csubst0 i0 u0 c c2))).(and_ind (subst0 i0 u0 (TLRef i) t2)
+(TLRef i) t2) (csubst0 i0 u0 c c2))).(land_ind (subst0 i0 u0 (TLRef i) t2)
(csubst0 i0 u0 c c2) (arity g c2 t2 a0) (\lambda (H7: (subst0 i0 u0 (TLRef i)
-t2)).(\lambda (H8: (csubst0 i0 u0 c c2)).(and_ind (eq nat i i0) (eq T t2
+t2)).(\lambda (H8: (csubst0 i0 u0 c c2)).(land_ind (eq nat i i0) (eq T t2
(lift (S i) O u0)) (arity g c2 t2 a0) (\lambda (H9: (eq nat i i0)).(\lambda
(H10: (eq T t2 (lift (S i) O u0))).(eq_ind_r T (lift (S i) O u0) (\lambda (t:
T).(arity g c2 t a0)) (let H11 \def (eq_ind_r nat i0 (\lambda (n:
(THead (Bind b) u t) t2)) (land (eq T (THead (Bind b) u t) t2) (csubst0 i u0
c c2)) (land (subst0 i u0 (THead (Bind b) u t) t2) (csubst0 i u0 c c2))
(arity g c2 t2 a2) (\lambda (H8: (land (eq C c c2) (subst0 i u0 (THead (Bind
-b) u t) t2))).(and_ind (eq C c c2) (subst0 i u0 (THead (Bind b) u t) t2)
+b) u t) t2))).(land_ind (eq C c c2) (subst0 i u0 (THead (Bind b) u t) t2)
(arity g c2 t2 a2) (\lambda (H9: (eq C c c2)).(\lambda (H10: (subst0 i u0
(THead (Bind b) u t) t2)).(eq_ind C c (\lambda (c0: C).(arity g c0 t2 a2))
(or3_ind (ex2 T (\lambda (u2: T).(eq T t2 (THead (Bind b) u2 t))) (\lambda
(S i) u0 (CHead c (Bind b) u) t x1 H14 (CHead c (Bind b) x0)
(csubst0_snd_bind b i u0 u x0 H13 c)))) t2 H12)))))) H11)) (subst0_gen_head
(Bind b) u0 u t t2 i H10)) c2 H9))) H8)) (\lambda (H8: (land (eq T (THead
-(Bind b) u t) t2) (csubst0 i u0 c c2))).(and_ind (eq T (THead (Bind b) u t)
+(Bind b) u t) t2) (csubst0 i u0 c c2))).(land_ind (eq T (THead (Bind b) u t)
t2) (csubst0 i u0 c c2) (arity g c2 t2 a2) (\lambda (H9: (eq T (THead (Bind
b) u t) t2)).(\lambda (H10: (csubst0 i u0 c c2)).(eq_ind T (THead (Bind b) u
t) (\lambda (t0: T).(arity g c2 t0 a2)) (arity_bind g b H0 c2 u a1 (H2 d1 u0
(Bind Abbr) u0) i H5) (CHead c2 (Bind b) u) t (fsubst0_fst (S i) u0 (CHead c
(Bind b) u) t (CHead c2 (Bind b) u) (csubst0_fst_bind b i c c2 u0 H10 u))))
t2 H9))) H8)) (\lambda (H8: (land (subst0 i u0 (THead (Bind b) u t) t2)
-(csubst0 i u0 c c2))).(and_ind (subst0 i u0 (THead (Bind b) u t) t2) (csubst0
-i u0 c c2) (arity g c2 t2 a2) (\lambda (H9: (subst0 i u0 (THead (Bind b) u t)
-t2)).(\lambda (H10: (csubst0 i u0 c c2)).(or3_ind (ex2 T (\lambda (u2: T).(eq
-T t2 (THead (Bind b) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2))) (ex2 T
-(\lambda (t3: T).(eq T t2 (THead (Bind b) u t3))) (\lambda (t3: T).(subst0 (s
-(Bind b) i) u0 t t3))) (ex3_2 T T (\lambda (u2: T).(\lambda (t3: T).(eq T t2
-(THead (Bind b) u2 t3)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i u0 u
-u2))) (\lambda (_: T).(\lambda (t3: T).(subst0 (s (Bind b) i) u0 t t3))))
-(arity g c2 t2 a2) (\lambda (H11: (ex2 T (\lambda (u2: T).(eq T t2 (THead
-(Bind b) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2)))).(ex2_ind T (\lambda
-(u2: T).(eq T t2 (THead (Bind b) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2))
-(arity g c2 t2 a2) (\lambda (x: T).(\lambda (H12: (eq T t2 (THead (Bind b) x
-t))).(\lambda (H13: (subst0 i u0 u x)).(eq_ind_r T (THead (Bind b) x t)
-(\lambda (t0: T).(arity g c2 t0 a2)) (arity_bind g b H0 c2 x a1 (H2 d1 u0 i
-H5 c2 x (fsubst0_both i u0 c u x H13 c2 H10)) t a2 (H4 d1 u0 (S i)
-(getl_clear_bind b (CHead c (Bind b) u) c u (clear_bind b c u) (CHead d1
-(Bind Abbr) u0) i H5) (CHead c2 (Bind b) x) t (fsubst0_fst (S i) u0 (CHead c
-(Bind b) u) t (CHead c2 (Bind b) x) (csubst0_both_bind b i u0 u x H13 c c2
-H10)))) t2 H12)))) H11)) (\lambda (H11: (ex2 T (\lambda (t3: T).(eq T t2
-(THead (Bind b) u t3))) (\lambda (t3: T).(subst0 (s (Bind b) i) u0 t
-t3)))).(ex2_ind T (\lambda (t3: T).(eq T t2 (THead (Bind b) u t3))) (\lambda
-(t3: T).(subst0 (s (Bind b) i) u0 t t3)) (arity g c2 t2 a2) (\lambda (x:
-T).(\lambda (H12: (eq T t2 (THead (Bind b) u x))).(\lambda (H13: (subst0 (s
-(Bind b) i) u0 t x)).(eq_ind_r T (THead (Bind b) u x) (\lambda (t0: T).(arity
-g c2 t0 a2)) (arity_bind g b H0 c2 u a1 (H2 d1 u0 i H5 c2 u (fsubst0_fst i u0
-c u c2 H10)) x a2 (H4 d1 u0 (S i) (getl_clear_bind b (CHead c (Bind b) u) c u
-(clear_bind b c u) (CHead d1 (Bind Abbr) u0) i H5) (CHead c2 (Bind b) u) x
-(fsubst0_both (S i) u0 (CHead c (Bind b) u) t x H13 (CHead c2 (Bind b) u)
-(csubst0_fst_bind b i c c2 u0 H10 u)))) t2 H12)))) H11)) (\lambda (H11:
-(ex3_2 T T (\lambda (u2: T).(\lambda (t3: T).(eq T t2 (THead (Bind b) u2
-t3)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i u0 u u2))) (\lambda (_:
-T).(\lambda (t3: T).(subst0 (s (Bind b) i) u0 t t3))))).(ex3_2_ind T T
-(\lambda (u2: T).(\lambda (t3: T).(eq T t2 (THead (Bind b) u2 t3)))) (\lambda
-(u2: T).(\lambda (_: T).(subst0 i u0 u u2))) (\lambda (_: T).(\lambda (t3:
-T).(subst0 (s (Bind b) i) u0 t t3))) (arity g c2 t2 a2) (\lambda (x0:
-T).(\lambda (x1: T).(\lambda (H12: (eq T t2 (THead (Bind b) x0 x1))).(\lambda
-(H13: (subst0 i u0 u x0)).(\lambda (H14: (subst0 (s (Bind b) i) u0 t
-x1)).(eq_ind_r T (THead (Bind b) x0 x1) (\lambda (t0: T).(arity g c2 t0 a2))
-(arity_bind g b H0 c2 x0 a1 (H2 d1 u0 i H5 c2 x0 (fsubst0_both i u0 c u x0
-H13 c2 H10)) x1 a2 (H4 d1 u0 (S i) (getl_clear_bind b (CHead c (Bind b) u) c
-u (clear_bind b c u) (CHead d1 (Bind Abbr) u0) i H5) (CHead c2 (Bind b) x0)
-x1 (fsubst0_both (S i) u0 (CHead c (Bind b) u) t x1 H14 (CHead c2 (Bind b)
-x0) (csubst0_both_bind b i u0 u x0 H13 c c2 H10)))) t2 H12)))))) H11))
-(subst0_gen_head (Bind b) u0 u t t2 i H9)))) H8)) H7)))))))))))))))))))))
-(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (H0: (arity g c u
-(asucc g a1))).(\lambda (H1: ((\forall (d1: C).(\forall (u0: T).(\forall (i:
-nat).((getl i c (CHead d1 (Bind Abbr) u0)) \to (\forall (c2: C).(\forall (t2:
-T).((fsubst0 i u0 c u c2 t2) \to (arity g c2 t2 (asucc g
-a1))))))))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c
-(Bind Abst) u) t a2)).(\lambda (H3: ((\forall (d1: C).(\forall (u0:
-T).(\forall (i: nat).((getl i (CHead c (Bind Abst) u) (CHead d1 (Bind Abbr)
-u0)) \to (\forall (c2: C).(\forall (t2: T).((fsubst0 i u0 (CHead c (Bind
-Abst) u) t c2 t2) \to (arity g c2 t2 a2)))))))))).(\lambda (d1: C).(\lambda
-(u0: T).(\lambda (i: nat).(\lambda (H4: (getl i c (CHead d1 (Bind Abbr)
-u0))).(\lambda (c2: C).(\lambda (t2: T).(\lambda (H5: (fsubst0 i u0 c (THead
-(Bind Abst) u t) c2 t2)).(let H_x \def (fsubst0_gen_base c c2 (THead (Bind
-Abst) u t) t2 u0 i H5) in (let H6 \def H_x in (or3_ind (land (eq C c c2)
-(subst0 i u0 (THead (Bind Abst) u t) t2)) (land (eq T (THead (Bind Abst) u t)
-t2) (csubst0 i u0 c c2)) (land (subst0 i u0 (THead (Bind Abst) u t) t2)
-(csubst0 i u0 c c2)) (arity g c2 t2 (AHead a1 a2)) (\lambda (H7: (land (eq C
-c c2) (subst0 i u0 (THead (Bind Abst) u t) t2))).(and_ind (eq C c c2) (subst0
-i u0 (THead (Bind Abst) u t) t2) (arity g c2 t2 (AHead a1 a2)) (\lambda (H8:
-(eq C c c2)).(\lambda (H9: (subst0 i u0 (THead (Bind Abst) u t) t2)).(eq_ind
-C c (\lambda (c0: C).(arity g c0 t2 (AHead a1 a2))) (or3_ind (ex2 T (\lambda
-(u2: T).(eq T t2 (THead (Bind Abst) u2 t))) (\lambda (u2: T).(subst0 i u0 u
-u2))) (ex2 T (\lambda (t3: T).(eq T t2 (THead (Bind Abst) u t3))) (\lambda
-(t3: T).(subst0 (s (Bind Abst) i) u0 t t3))) (ex3_2 T T (\lambda (u2:
-T).(\lambda (t3: T).(eq T t2 (THead (Bind Abst) u2 t3)))) (\lambda (u2:
+(csubst0 i u0 c c2))).(land_ind (subst0 i u0 (THead (Bind b) u t) t2)
+(csubst0 i u0 c c2) (arity g c2 t2 a2) (\lambda (H9: (subst0 i u0 (THead
+(Bind b) u t) t2)).(\lambda (H10: (csubst0 i u0 c c2)).(or3_ind (ex2 T
+(\lambda (u2: T).(eq T t2 (THead (Bind b) u2 t))) (\lambda (u2: T).(subst0 i
+u0 u u2))) (ex2 T (\lambda (t3: T).(eq T t2 (THead (Bind b) u t3))) (\lambda
+(t3: T).(subst0 (s (Bind b) i) u0 t t3))) (ex3_2 T T (\lambda (u2:
+T).(\lambda (t3: T).(eq T t2 (THead (Bind b) u2 t3)))) (\lambda (u2:
T).(\lambda (_: T).(subst0 i u0 u u2))) (\lambda (_: T).(\lambda (t3:
-T).(subst0 (s (Bind Abst) i) u0 t t3)))) (arity g c t2 (AHead a1 a2))
-(\lambda (H10: (ex2 T (\lambda (u2: T).(eq T t2 (THead (Bind Abst) u2 t)))
-(\lambda (u2: T).(subst0 i u0 u u2)))).(ex2_ind T (\lambda (u2: T).(eq T t2
-(THead (Bind Abst) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2)) (arity g c t2
-(AHead a1 a2)) (\lambda (x: T).(\lambda (H11: (eq T t2 (THead (Bind Abst) x
-t))).(\lambda (H12: (subst0 i u0 u x)).(eq_ind_r T (THead (Bind Abst) x t)
-(\lambda (t0: T).(arity g c t0 (AHead a1 a2))) (arity_head g c x a1 (H1 d1 u0
-i H4 c x (fsubst0_snd i u0 c u x H12)) t a2 (H3 d1 u0 (S i) (getl_clear_bind
-Abst (CHead c (Bind Abst) u) c u (clear_bind Abst c u) (CHead d1 (Bind Abbr)
-u0) i H4) (CHead c (Bind Abst) x) t (fsubst0_fst (S i) u0 (CHead c (Bind
-Abst) u) t (CHead c (Bind Abst) x) (csubst0_snd_bind Abst i u0 u x H12 c))))
-t2 H11)))) H10)) (\lambda (H10: (ex2 T (\lambda (t3: T).(eq T t2 (THead (Bind
-Abst) u t3))) (\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t t3)))).(ex2_ind
-T (\lambda (t3: T).(eq T t2 (THead (Bind Abst) u t3))) (\lambda (t3:
-T).(subst0 (s (Bind Abst) i) u0 t t3)) (arity g c t2 (AHead a1 a2)) (\lambda
-(x: T).(\lambda (H11: (eq T t2 (THead (Bind Abst) u x))).(\lambda (H12:
-(subst0 (s (Bind Abst) i) u0 t x)).(eq_ind_r T (THead (Bind Abst) u x)
-(\lambda (t0: T).(arity g c t0 (AHead a1 a2))) (arity_head g c u a1 H0 x a2
-(H3 d1 u0 (S i) (getl_clear_bind Abst (CHead c (Bind Abst) u) c u (clear_bind
-Abst c u) (CHead d1 (Bind Abbr) u0) i H4) (CHead c (Bind Abst) u) x
-(fsubst0_snd (S i) u0 (CHead c (Bind Abst) u) t x H12))) t2 H11)))) H10))
-(\lambda (H10: (ex3_2 T T (\lambda (u2: T).(\lambda (t3: T).(eq T t2 (THead
-(Bind Abst) u2 t3)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i u0 u u2)))
-(\lambda (_: T).(\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t
+T).(subst0 (s (Bind b) i) u0 t t3)))) (arity g c2 t2 a2) (\lambda (H11: (ex2
+T (\lambda (u2: T).(eq T t2 (THead (Bind b) u2 t))) (\lambda (u2: T).(subst0
+i u0 u u2)))).(ex2_ind T (\lambda (u2: T).(eq T t2 (THead (Bind b) u2 t)))
+(\lambda (u2: T).(subst0 i u0 u u2)) (arity g c2 t2 a2) (\lambda (x:
+T).(\lambda (H12: (eq T t2 (THead (Bind b) x t))).(\lambda (H13: (subst0 i u0
+u x)).(eq_ind_r T (THead (Bind b) x t) (\lambda (t0: T).(arity g c2 t0 a2))
+(arity_bind g b H0 c2 x a1 (H2 d1 u0 i H5 c2 x (fsubst0_both i u0 c u x H13
+c2 H10)) t a2 (H4 d1 u0 (S i) (getl_clear_bind b (CHead c (Bind b) u) c u
+(clear_bind b c u) (CHead d1 (Bind Abbr) u0) i H5) (CHead c2 (Bind b) x) t
+(fsubst0_fst (S i) u0 (CHead c (Bind b) u) t (CHead c2 (Bind b) x)
+(csubst0_both_bind b i u0 u x H13 c c2 H10)))) t2 H12)))) H11)) (\lambda
+(H11: (ex2 T (\lambda (t3: T).(eq T t2 (THead (Bind b) u t3))) (\lambda (t3:
+T).(subst0 (s (Bind b) i) u0 t t3)))).(ex2_ind T (\lambda (t3: T).(eq T t2
+(THead (Bind b) u t3))) (\lambda (t3: T).(subst0 (s (Bind b) i) u0 t t3))
+(arity g c2 t2 a2) (\lambda (x: T).(\lambda (H12: (eq T t2 (THead (Bind b) u
+x))).(\lambda (H13: (subst0 (s (Bind b) i) u0 t x)).(eq_ind_r T (THead (Bind
+b) u x) (\lambda (t0: T).(arity g c2 t0 a2)) (arity_bind g b H0 c2 u a1 (H2
+d1 u0 i H5 c2 u (fsubst0_fst i u0 c u c2 H10)) x a2 (H4 d1 u0 (S i)
+(getl_clear_bind b (CHead c (Bind b) u) c u (clear_bind b c u) (CHead d1
+(Bind Abbr) u0) i H5) (CHead c2 (Bind b) u) x (fsubst0_both (S i) u0 (CHead c
+(Bind b) u) t x H13 (CHead c2 (Bind b) u) (csubst0_fst_bind b i c c2 u0 H10
+u)))) t2 H12)))) H11)) (\lambda (H11: (ex3_2 T T (\lambda (u2: T).(\lambda
+(t3: T).(eq T t2 (THead (Bind b) u2 t3)))) (\lambda (u2: T).(\lambda (_:
+T).(subst0 i u0 u u2))) (\lambda (_: T).(\lambda (t3: T).(subst0 (s (Bind b)
+i) u0 t t3))))).(ex3_2_ind T T (\lambda (u2: T).(\lambda (t3: T).(eq T t2
+(THead (Bind b) u2 t3)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i u0 u
+u2))) (\lambda (_: T).(\lambda (t3: T).(subst0 (s (Bind b) i) u0 t t3)))
+(arity g c2 t2 a2) (\lambda (x0: T).(\lambda (x1: T).(\lambda (H12: (eq T t2
+(THead (Bind b) x0 x1))).(\lambda (H13: (subst0 i u0 u x0)).(\lambda (H14:
+(subst0 (s (Bind b) i) u0 t x1)).(eq_ind_r T (THead (Bind b) x0 x1) (\lambda
+(t0: T).(arity g c2 t0 a2)) (arity_bind g b H0 c2 x0 a1 (H2 d1 u0 i H5 c2 x0
+(fsubst0_both i u0 c u x0 H13 c2 H10)) x1 a2 (H4 d1 u0 (S i) (getl_clear_bind
+b (CHead c (Bind b) u) c u (clear_bind b c u) (CHead d1 (Bind Abbr) u0) i H5)
+(CHead c2 (Bind b) x0) x1 (fsubst0_both (S i) u0 (CHead c (Bind b) u) t x1
+H14 (CHead c2 (Bind b) x0) (csubst0_both_bind b i u0 u x0 H13 c c2 H10)))) t2
+H12)))))) H11)) (subst0_gen_head (Bind b) u0 u t t2 i H9)))) H8))
+H7))))))))))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a1:
+A).(\lambda (H0: (arity g c u (asucc g a1))).(\lambda (H1: ((\forall (d1:
+C).(\forall (u0: T).(\forall (i: nat).((getl i c (CHead d1 (Bind Abbr) u0))
+\to (\forall (c2: C).(\forall (t2: T).((fsubst0 i u0 c u c2 t2) \to (arity g
+c2 t2 (asucc g a1))))))))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_:
+(arity g (CHead c (Bind Abst) u) t a2)).(\lambda (H3: ((\forall (d1:
+C).(\forall (u0: T).(\forall (i: nat).((getl i (CHead c (Bind Abst) u) (CHead
+d1 (Bind Abbr) u0)) \to (\forall (c2: C).(\forall (t2: T).((fsubst0 i u0
+(CHead c (Bind Abst) u) t c2 t2) \to (arity g c2 t2 a2)))))))))).(\lambda
+(d1: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (H4: (getl i c (CHead d1
+(Bind Abbr) u0))).(\lambda (c2: C).(\lambda (t2: T).(\lambda (H5: (fsubst0 i
+u0 c (THead (Bind Abst) u t) c2 t2)).(let H_x \def (fsubst0_gen_base c c2
+(THead (Bind Abst) u t) t2 u0 i H5) in (let H6 \def H_x in (or3_ind (land (eq
+C c c2) (subst0 i u0 (THead (Bind Abst) u t) t2)) (land (eq T (THead (Bind
+Abst) u t) t2) (csubst0 i u0 c c2)) (land (subst0 i u0 (THead (Bind Abst) u
+t) t2) (csubst0 i u0 c c2)) (arity g c2 t2 (AHead a1 a2)) (\lambda (H7: (land
+(eq C c c2) (subst0 i u0 (THead (Bind Abst) u t) t2))).(land_ind (eq C c c2)
+(subst0 i u0 (THead (Bind Abst) u t) t2) (arity g c2 t2 (AHead a1 a2))
+(\lambda (H8: (eq C c c2)).(\lambda (H9: (subst0 i u0 (THead (Bind Abst) u t)
+t2)).(eq_ind C c (\lambda (c0: C).(arity g c0 t2 (AHead a1 a2))) (or3_ind
+(ex2 T (\lambda (u2: T).(eq T t2 (THead (Bind Abst) u2 t))) (\lambda (u2:
+T).(subst0 i u0 u u2))) (ex2 T (\lambda (t3: T).(eq T t2 (THead (Bind Abst) u
+t3))) (\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t t3))) (ex3_2 T T
+(\lambda (u2: T).(\lambda (t3: T).(eq T t2 (THead (Bind Abst) u2 t3))))
+(\lambda (u2: T).(\lambda (_: T).(subst0 i u0 u u2))) (\lambda (_:
+T).(\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t t3)))) (arity g c t2
+(AHead a1 a2)) (\lambda (H10: (ex2 T (\lambda (u2: T).(eq T t2 (THead (Bind
+Abst) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2)))).(ex2_ind T (\lambda (u2:
+T).(eq T t2 (THead (Bind Abst) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2))
+(arity g c t2 (AHead a1 a2)) (\lambda (x: T).(\lambda (H11: (eq T t2 (THead
+(Bind Abst) x t))).(\lambda (H12: (subst0 i u0 u x)).(eq_ind_r T (THead (Bind
+Abst) x t) (\lambda (t0: T).(arity g c t0 (AHead a1 a2))) (arity_head g c x
+a1 (H1 d1 u0 i H4 c x (fsubst0_snd i u0 c u x H12)) t a2 (H3 d1 u0 (S i)
+(getl_clear_bind Abst (CHead c (Bind Abst) u) c u (clear_bind Abst c u)
+(CHead d1 (Bind Abbr) u0) i H4) (CHead c (Bind Abst) x) t (fsubst0_fst (S i)
+u0 (CHead c (Bind Abst) u) t (CHead c (Bind Abst) x) (csubst0_snd_bind Abst i
+u0 u x H12 c)))) t2 H11)))) H10)) (\lambda (H10: (ex2 T (\lambda (t3: T).(eq
+T t2 (THead (Bind Abst) u t3))) (\lambda (t3: T).(subst0 (s (Bind Abst) i) u0
+t t3)))).(ex2_ind T (\lambda (t3: T).(eq T t2 (THead (Bind Abst) u t3)))
+(\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t t3)) (arity g c t2 (AHead a1
+a2)) (\lambda (x: T).(\lambda (H11: (eq T t2 (THead (Bind Abst) u
+x))).(\lambda (H12: (subst0 (s (Bind Abst) i) u0 t x)).(eq_ind_r T (THead
+(Bind Abst) u x) (\lambda (t0: T).(arity g c t0 (AHead a1 a2))) (arity_head g
+c u a1 H0 x a2 (H3 d1 u0 (S i) (getl_clear_bind Abst (CHead c (Bind Abst) u)
+c u (clear_bind Abst c u) (CHead d1 (Bind Abbr) u0) i H4) (CHead c (Bind
+Abst) u) x (fsubst0_snd (S i) u0 (CHead c (Bind Abst) u) t x H12))) t2
+H11)))) H10)) (\lambda (H10: (ex3_2 T T (\lambda (u2: T).(\lambda (t3: T).(eq
+T t2 (THead (Bind Abst) u2 t3)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i
+u0 u u2))) (\lambda (_: T).(\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t
t3))))).(ex3_2_ind T T (\lambda (u2: T).(\lambda (t3: T).(eq T t2 (THead
(Bind Abst) u2 t3)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i u0 u u2)))
(\lambda (_: T).(\lambda (t3: T).(subst0 (s (Bind Abst) i) u0 t t3))) (arity
i) u0 (CHead c (Bind Abst) u) t x1 H13 (CHead c (Bind Abst) x0)
(csubst0_snd_bind Abst i u0 u x0 H12 c)))) t2 H11)))))) H10))
(subst0_gen_head (Bind Abst) u0 u t t2 i H9)) c2 H8))) H7)) (\lambda (H7:
-(land (eq T (THead (Bind Abst) u t) t2) (csubst0 i u0 c c2))).(and_ind (eq T
+(land (eq T (THead (Bind Abst) u t) t2) (csubst0 i u0 c c2))).(land_ind (eq T
(THead (Bind Abst) u t) t2) (csubst0 i u0 c c2) (arity g c2 t2 (AHead a1 a2))
(\lambda (H8: (eq T (THead (Bind Abst) u t) t2)).(\lambda (H9: (csubst0 i u0
c c2)).(eq_ind T (THead (Bind Abst) u t) (\lambda (t0: T).(arity g c2 t0
Abst) u) t (fsubst0_fst (S i) u0 (CHead c (Bind Abst) u) t (CHead c2 (Bind
Abst) u) (csubst0_fst_bind Abst i c c2 u0 H9 u)))) t2 H8))) H7)) (\lambda
(H7: (land (subst0 i u0 (THead (Bind Abst) u t) t2) (csubst0 i u0 c
-c2))).(and_ind (subst0 i u0 (THead (Bind Abst) u t) t2) (csubst0 i u0 c c2)
+c2))).(land_ind (subst0 i u0 (THead (Bind Abst) u t) t2) (csubst0 i u0 c c2)
(arity g c2 t2 (AHead a1 a2)) (\lambda (H8: (subst0 i u0 (THead (Bind Abst) u
t) t2)).(\lambda (H9: (csubst0 i u0 c c2)).(or3_ind (ex2 T (\lambda (u2:
T).(eq T t2 (THead (Bind Abst) u2 t))) (\lambda (u2: T).(subst0 i u0 u u2)))
(subst0 i u0 (THead (Flat Appl) u t) t2)) (land (eq T (THead (Flat Appl) u t)
t2) (csubst0 i u0 c c2)) (land (subst0 i u0 (THead (Flat Appl) u t) t2)
(csubst0 i u0 c c2)) (arity g c2 t2 a2) (\lambda (H7: (land (eq C c c2)
-(subst0 i u0 (THead (Flat Appl) u t) t2))).(and_ind (eq C c c2) (subst0 i u0
+(subst0 i u0 (THead (Flat Appl) u t) t2))).(land_ind (eq C c c2) (subst0 i u0
(THead (Flat Appl) u t) t2) (arity g c2 t2 a2) (\lambda (H8: (eq C c
c2)).(\lambda (H9: (subst0 i u0 (THead (Flat Appl) u t) t2)).(eq_ind C c
(\lambda (c0: C).(arity g c0 t2 a2)) (or3_ind (ex2 T (\lambda (u2: T).(eq T
(fsubst0_snd i u0 c u x0 H12)) x1 a2 (H3 d1 u0 i H4 c x1 (fsubst0_snd i u0 c
t x1 H13))) t2 H11)))))) H10)) (subst0_gen_head (Flat Appl) u0 u t t2 i H9))
c2 H8))) H7)) (\lambda (H7: (land (eq T (THead (Flat Appl) u t) t2) (csubst0
-i u0 c c2))).(and_ind (eq T (THead (Flat Appl) u t) t2) (csubst0 i u0 c c2)
+i u0 c c2))).(land_ind (eq T (THead (Flat Appl) u t) t2) (csubst0 i u0 c c2)
(arity g c2 t2 a2) (\lambda (H8: (eq T (THead (Flat Appl) u t) t2)).(\lambda
(H9: (csubst0 i u0 c c2)).(eq_ind T (THead (Flat Appl) u t) (\lambda (t0:
T).(arity g c2 t0 a2)) (arity_appl g c2 u a1 (H1 d1 u0 i H4 c2 u (fsubst0_fst
i u0 c u c2 H9)) t a2 (H3 d1 u0 i H4 c2 t (fsubst0_fst i u0 c t c2 H9))) t2
H8))) H7)) (\lambda (H7: (land (subst0 i u0 (THead (Flat Appl) u t) t2)
-(csubst0 i u0 c c2))).(and_ind (subst0 i u0 (THead (Flat Appl) u t) t2)
+(csubst0 i u0 c c2))).(land_ind (subst0 i u0 (THead (Flat Appl) u t) t2)
(csubst0 i u0 c c2) (arity g c2 t2 a2) (\lambda (H8: (subst0 i u0 (THead
(Flat Appl) u t) t2)).(\lambda (H9: (csubst0 i u0 c c2)).(or3_ind (ex2 T
(\lambda (u2: T).(eq T t2 (THead (Flat Appl) u2 t))) (\lambda (u2: T).(subst0
(subst0 i u0 (THead (Flat Cast) u t) t2)) (land (eq T (THead (Flat Cast) u t)
t2) (csubst0 i u0 c c2)) (land (subst0 i u0 (THead (Flat Cast) u t) t2)
(csubst0 i u0 c c2)) (arity g c2 t2 a0) (\lambda (H7: (land (eq C c c2)
-(subst0 i u0 (THead (Flat Cast) u t) t2))).(and_ind (eq C c c2) (subst0 i u0
+(subst0 i u0 (THead (Flat Cast) u t) t2))).(land_ind (eq C c c2) (subst0 i u0
(THead (Flat Cast) u t) t2) (arity g c2 t2 a0) (\lambda (H8: (eq C c
c2)).(\lambda (H9: (subst0 i u0 (THead (Flat Cast) u t) t2)).(eq_ind C c
(\lambda (c0: C).(arity g c0 t2 a0)) (or3_ind (ex2 T (\lambda (u2: T).(eq T
(fsubst0_snd i u0 c u x0 H12)) x1 (H3 d1 u0 i H4 c x1 (fsubst0_snd i u0 c t
x1 H13))) t2 H11)))))) H10)) (subst0_gen_head (Flat Cast) u0 u t t2 i H9)) c2
H8))) H7)) (\lambda (H7: (land (eq T (THead (Flat Cast) u t) t2) (csubst0 i
-u0 c c2))).(and_ind (eq T (THead (Flat Cast) u t) t2) (csubst0 i u0 c c2)
+u0 c c2))).(land_ind (eq T (THead (Flat Cast) u t) t2) (csubst0 i u0 c c2)
(arity g c2 t2 a0) (\lambda (H8: (eq T (THead (Flat Cast) u t) t2)).(\lambda
(H9: (csubst0 i u0 c c2)).(eq_ind T (THead (Flat Cast) u t) (\lambda (t0:
T).(arity g c2 t0 a0)) (arity_cast g c2 u a0 (H1 d1 u0 i H4 c2 u (fsubst0_fst
i u0 c u c2 H9)) t (H3 d1 u0 i H4 c2 t (fsubst0_fst i u0 c t c2 H9))) t2
H8))) H7)) (\lambda (H7: (land (subst0 i u0 (THead (Flat Cast) u t) t2)
-(csubst0 i u0 c c2))).(and_ind (subst0 i u0 (THead (Flat Cast) u t) t2)
+(csubst0 i u0 c c2))).(land_ind (subst0 i u0 (THead (Flat Cast) u t) t2)
(csubst0 i u0 c c2) (arity g c2 t2 a0) (\lambda (H8: (subst0 i u0 (THead
(Flat Cast) u t) t2)).(\lambda (H9: (csubst0 i u0 c c2)).(or3_ind (ex2 T
(\lambda (u2: T).(eq T t2 (THead (Flat Cast) u2 t))) (\lambda (u2: T).(subst0
c t c2 t2)).(let H_x \def (fsubst0_gen_base c c2 t t2 u i H4) in (let H5 \def
H_x in (or3_ind (land (eq C c c2) (subst0 i u t t2)) (land (eq T t t2)
(csubst0 i u c c2)) (land (subst0 i u t t2) (csubst0 i u c c2)) (arity g c2
-t2 a2) (\lambda (H6: (land (eq C c c2) (subst0 i u t t2))).(and_ind (eq C c
+t2 a2) (\lambda (H6: (land (eq C c c2) (subst0 i u t t2))).(land_ind (eq C c
c2) (subst0 i u t t2) (arity g c2 t2 a2) (\lambda (H7: (eq C c c2)).(\lambda
(H8: (subst0 i u t t2)).(eq_ind C c (\lambda (c0: C).(arity g c0 t2 a2))
(arity_repl g c t2 a1 (H1 d1 u i H3 c t2 (fsubst0_snd i u c t t2 H8)) a2 H2)
-c2 H7))) H6)) (\lambda (H6: (land (eq T t t2) (csubst0 i u c c2))).(and_ind
+c2 H7))) H6)) (\lambda (H6: (land (eq T t t2) (csubst0 i u c c2))).(land_ind
(eq T t t2) (csubst0 i u c c2) (arity g c2 t2 a2) (\lambda (H7: (eq T t
t2)).(\lambda (H8: (csubst0 i u c c2)).(eq_ind T t (\lambda (t0: T).(arity g
c2 t0 a2)) (arity_repl g c2 t a1 (H1 d1 u i H3 c2 t (fsubst0_fst i u c t c2
H8)) a2 H2) t2 H7))) H6)) (\lambda (H6: (land (subst0 i u t t2) (csubst0 i u
-c c2))).(and_ind (subst0 i u t t2) (csubst0 i u c c2) (arity g c2 t2 a2)
+c c2))).(land_ind (subst0 i u t t2) (csubst0 i u c c2) (arity g c2 t2 a2)
(\lambda (H7: (subst0 i u t t2)).(\lambda (H8: (csubst0 i u c
c2)).(arity_repl g c2 t2 a1 (H1 d1 u i H3 c2 t2 (fsubst0_both i u c t t2 H7
c2 H8)) a2 H2))) H6)) H5))))))))))))))))) c1 t1 a H))))).
projects / helm.git / blobdiff