(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/props.ma".
+include "basic_1/arity/props.ma".
-include "Basic-1/arity/cimp.ma".
+include "basic_1/arity/cimp.ma".
-include "Basic-1/aprem/props.ma".
+include "basic_1/aprem/props.ma".
theorem arity_aprem:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((arity g c t
b)))))))))))))
\def
\lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c t a)).(arity_ind g (\lambda (c0: C).(\lambda (_: T).(\lambda (a0:
-A).(\forall (i: nat).(\forall (b: A).((aprem i a0 b) \to (ex2_3 C T nat
-(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0))))
-(\lambda (d: C).(\lambda (u: T).(\lambda (_: nat).(arity g d u (asucc g
-b)))))))))))) (\lambda (c0: C).(\lambda (n: nat).(\lambda (i: nat).(\lambda
-(b: A).(\lambda (H0: (aprem i (ASort O n) b)).(let H_x \def (aprem_gen_sort b
-i O n H0) in (let H1 \def H_x in (False_ind (ex2_3 C T nat (\lambda (d:
-C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d:
-C).(\lambda (u: T).(\lambda (_: nat).(arity g d u (asucc g b)))))) H1))))))))
-(\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda
-(H0: (getl i c0 (CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (_:
-(arity g d u a0)).(\lambda (H2: ((\forall (i0: nat).(\forall (b: A).((aprem
-i0 a0 b) \to (ex2_3 C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i0 j) O d0 d)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d0 u0 (asucc g b))))))))))).(\lambda (i0: nat).(\lambda (b:
-A).(\lambda (H3: (aprem i0 a0 b)).(let H_x \def (H2 i0 b H3) in (let H4 \def
-H_x in (ex2_3_ind C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i0 j) O d0 d)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d0 u0 (asucc g b))))) (ex2_3 C T nat (\lambda (d0:
-C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i0 j) O d0 c0)))) (\lambda
-(d0: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0 (asucc g b))))))
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: nat).(\lambda (H5: (drop
-(plus i0 x2) O x0 d)).(\lambda (H6: (arity g x0 x1 (asucc g b))).(let H_x0
-\def (getl_drop_conf_rev (plus i0 x2) x0 d H5 Abbr c0 u i H0) in (let H7 \def
-H_x0 in (ex2_ind C (\lambda (c1: C).(drop (plus i0 x2) O c1 c0)) (\lambda
-(c1: C).(drop (S i) (plus i0 x2) c1 x0)) (ex2_3 C T nat (\lambda (d0:
-C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i0 j) O d0 c0)))) (\lambda
-(d0: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0 (asucc g b))))))
-(\lambda (x: C).(\lambda (H8: (drop (plus i0 x2) O x c0)).(\lambda (H9: (drop
-(S i) (plus i0 x2) x x0)).(ex2_3_intro C T nat (\lambda (d0: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus i0 j) O d0 c0)))) (\lambda (d0: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d0 u0 (asucc g b))))) x (lift (S i) (plus
-i0 x2) x1) x2 H8 (arity_lift g x0 x1 (asucc g b) H6 x (S i) (plus i0 x2)
-H9))))) H7)))))))) H4)))))))))))))) (\lambda (c0: C).(\lambda (d: C).(\lambda
-(u: T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d (Bind Abst)
-u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda (H2:
-((\forall (i0: nat).(\forall (b: A).((aprem i0 (asucc g a0) b) \to (ex2_3 C T
-nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i0 j) O d0
+(arity g c t a)).(let TMP_5 \def (\lambda (c0: C).(\lambda (_: T).(\lambda
+(a0: A).(\forall (i: nat).(\forall (b: A).((aprem i a0 b) \to (let TMP_2 \def
+(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_1 \def (plus i j)
+in (drop TMP_1 O d c0))))) in (let TMP_4 \def (\lambda (d: C).(\lambda (u:
+T).(\lambda (_: nat).(let TMP_3 \def (asucc g b) in (arity g d u TMP_3)))))
+in (ex2_3 C T nat TMP_2 TMP_4))))))))) in (let TMP_11 \def (\lambda (c0:
+C).(\lambda (n: nat).(\lambda (i: nat).(\lambda (b: A).(\lambda (H0: (aprem i
+(ASort O n) b)).(let H_x \def (aprem_gen_sort b i O n H0) in (let H1 \def H_x
+in (let TMP_7 \def (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let
+TMP_6 \def (plus i j) in (drop TMP_6 O d c0))))) in (let TMP_9 \def (\lambda
+(d: C).(\lambda (u: T).(\lambda (_: nat).(let TMP_8 \def (asucc g b) in
+(arity g d u TMP_8))))) in (let TMP_10 \def (ex2_3 C T nat TMP_7 TMP_9) in
+(False_ind TMP_10 H1))))))))))) in (let TMP_45 \def (\lambda (c0: C).(\lambda
+(d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d
+(Bind Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity g d u a0)).(\lambda
+(H2: ((\forall (i0: nat).(\forall (b: A).((aprem i0 a0 b) \to (ex2_3 C T nat
+(\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i0 j) O d0
d)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0
(asucc g b))))))))))).(\lambda (i0: nat).(\lambda (b: A).(\lambda (H3: (aprem
-i0 a0 b)).(let H4 \def (H2 i0 b (aprem_asucc g a0 b i0 H3)) in (ex2_3_ind C T
-nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i0 j) O d0
-d)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0
-(asucc g b))))) (ex2_3 C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i0 j) O d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d0 u0 (asucc g b)))))) (\lambda (x0: C).(\lambda (x1:
-T).(\lambda (x2: nat).(\lambda (H5: (drop (plus i0 x2) O x0 d)).(\lambda (H6:
-(arity g x0 x1 (asucc g b))).(let H_x \def (getl_drop_conf_rev (plus i0 x2)
-x0 d H5 Abst c0 u i H0) in (let H7 \def H_x in (ex2_ind C (\lambda (c1:
-C).(drop (plus i0 x2) O c1 c0)) (\lambda (c1: C).(drop (S i) (plus i0 x2) c1
-x0)) (ex2_3 C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(drop
-(plus i0 j) O d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda (_:
-nat).(arity g d0 u0 (asucc g b)))))) (\lambda (x: C).(\lambda (H8: (drop
-(plus i0 x2) O x c0)).(\lambda (H9: (drop (S i) (plus i0 x2) x
-x0)).(ex2_3_intro C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i0 j) O d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d0 u0 (asucc g b))))) x (lift (S i) (plus i0 x2) x1) x2 H8
-(arity_lift g x0 x1 (asucc g b) H6 x (S i) (plus i0 x2) H9))))) H7))))))))
-H4))))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda
-(c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u
-a1)).(\lambda (_: ((\forall (i: nat).(\forall (b0: A).((aprem i a1 b0) \to
+i0 a0 b)).(let H_x \def (H2 i0 b H3) in (let H4 \def H_x in (let TMP_13 \def
+(\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_12 \def (plus i0
+j) in (drop TMP_12 O d0 d))))) in (let TMP_15 \def (\lambda (d0: C).(\lambda
+(u0: T).(\lambda (_: nat).(let TMP_14 \def (asucc g b) in (arity g d0 u0
+TMP_14))))) in (let TMP_17 \def (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
+nat).(let TMP_16 \def (plus i0 j) in (drop TMP_16 O d0 c0))))) in (let TMP_19
+\def (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_18 \def
+(asucc g b) in (arity g d0 u0 TMP_18))))) in (let TMP_20 \def (ex2_3 C T nat
+TMP_17 TMP_19) in (let TMP_44 \def (\lambda (x0: C).(\lambda (x1: T).(\lambda
+(x2: nat).(\lambda (H5: (drop (plus i0 x2) O x0 d)).(\lambda (H6: (arity g x0
+x1 (asucc g b))).(let TMP_21 \def (plus i0 x2) in (let H_x0 \def
+(getl_drop_conf_rev TMP_21 x0 d H5 Abbr c0 u i H0) in (let H7 \def H_x0 in
+(let TMP_23 \def (\lambda (c1: C).(let TMP_22 \def (plus i0 x2) in (drop
+TMP_22 O c1 c0))) in (let TMP_26 \def (\lambda (c1: C).(let TMP_24 \def (S i)
+in (let TMP_25 \def (plus i0 x2) in (drop TMP_24 TMP_25 c1 x0)))) in (let
+TMP_28 \def (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_27
+\def (plus i0 j) in (drop TMP_27 O d0 c0))))) in (let TMP_30 \def (\lambda
+(d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_29 \def (asucc g b) in
+(arity g d0 u0 TMP_29))))) in (let TMP_31 \def (ex2_3 C T nat TMP_28 TMP_30)
+in (let TMP_43 \def (\lambda (x: C).(\lambda (H8: (drop (plus i0 x2) O x
+c0)).(\lambda (H9: (drop (S i) (plus i0 x2) x x0)).(let TMP_33 \def (\lambda
+(d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_32 \def (plus i0 j) in
+(drop TMP_32 O d0 c0))))) in (let TMP_35 \def (\lambda (d0: C).(\lambda (u0:
+T).(\lambda (_: nat).(let TMP_34 \def (asucc g b) in (arity g d0 u0
+TMP_34))))) in (let TMP_36 \def (S i) in (let TMP_37 \def (plus i0 x2) in
+(let TMP_38 \def (lift TMP_36 TMP_37 x1) in (let TMP_39 \def (asucc g b) in
+(let TMP_40 \def (S i) in (let TMP_41 \def (plus i0 x2) in (let TMP_42 \def
+(arity_lift g x0 x1 TMP_39 H6 x TMP_40 TMP_41 H9) in (ex2_3_intro C T nat
+TMP_33 TMP_35 x TMP_38 x2 H8 TMP_42))))))))))))) in (ex2_ind C TMP_23 TMP_26
+TMP_31 TMP_43 H7))))))))))))))) in (ex2_3_ind C T nat TMP_13 TMP_15 TMP_20
+TMP_44 H4)))))))))))))))))))) in (let TMP_80 \def (\lambda (c0: C).(\lambda
+(d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d
+(Bind Abst) u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g
+a0))).(\lambda (H2: ((\forall (i0: nat).(\forall (b: A).((aprem i0 (asucc g
+a0) b) \to (ex2_3 C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
+nat).(drop (plus i0 j) O d0 d)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
+(_: nat).(arity g d0 u0 (asucc g b))))))))))).(\lambda (i0: nat).(\lambda (b:
+A).(\lambda (H3: (aprem i0 a0 b)).(let H_y \def (H2 i0 b) in (let TMP_46 \def
+(aprem_asucc g a0 b i0 H3) in (let H4 \def (H_y TMP_46) in (let TMP_48 \def
+(\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_47 \def (plus i0
+j) in (drop TMP_47 O d0 d))))) in (let TMP_50 \def (\lambda (d0: C).(\lambda
+(u0: T).(\lambda (_: nat).(let TMP_49 \def (asucc g b) in (arity g d0 u0
+TMP_49))))) in (let TMP_52 \def (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
+nat).(let TMP_51 \def (plus i0 j) in (drop TMP_51 O d0 c0))))) in (let TMP_54
+\def (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_53 \def
+(asucc g b) in (arity g d0 u0 TMP_53))))) in (let TMP_55 \def (ex2_3 C T nat
+TMP_52 TMP_54) in (let TMP_79 \def (\lambda (x0: C).(\lambda (x1: T).(\lambda
+(x2: nat).(\lambda (H5: (drop (plus i0 x2) O x0 d)).(\lambda (H6: (arity g x0
+x1 (asucc g b))).(let TMP_56 \def (plus i0 x2) in (let H_x \def
+(getl_drop_conf_rev TMP_56 x0 d H5 Abst c0 u i H0) in (let H7 \def H_x in
+(let TMP_58 \def (\lambda (c1: C).(let TMP_57 \def (plus i0 x2) in (drop
+TMP_57 O c1 c0))) in (let TMP_61 \def (\lambda (c1: C).(let TMP_59 \def (S i)
+in (let TMP_60 \def (plus i0 x2) in (drop TMP_59 TMP_60 c1 x0)))) in (let
+TMP_63 \def (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_62
+\def (plus i0 j) in (drop TMP_62 O d0 c0))))) in (let TMP_65 \def (\lambda
+(d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_64 \def (asucc g b) in
+(arity g d0 u0 TMP_64))))) in (let TMP_66 \def (ex2_3 C T nat TMP_63 TMP_65)
+in (let TMP_78 \def (\lambda (x: C).(\lambda (H8: (drop (plus i0 x2) O x
+c0)).(\lambda (H9: (drop (S i) (plus i0 x2) x x0)).(let TMP_68 \def (\lambda
+(d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_67 \def (plus i0 j) in
+(drop TMP_67 O d0 c0))))) in (let TMP_70 \def (\lambda (d0: C).(\lambda (u0:
+T).(\lambda (_: nat).(let TMP_69 \def (asucc g b) in (arity g d0 u0
+TMP_69))))) in (let TMP_71 \def (S i) in (let TMP_72 \def (plus i0 x2) in
+(let TMP_73 \def (lift TMP_71 TMP_72 x1) in (let TMP_74 \def (asucc g b) in
+(let TMP_75 \def (S i) in (let TMP_76 \def (plus i0 x2) in (let TMP_77 \def
+(arity_lift g x0 x1 TMP_74 H6 x TMP_75 TMP_76 H9) in (ex2_3_intro C T nat
+TMP_68 TMP_70 x TMP_73 x2 H8 TMP_77))))))))))))) in (ex2_ind C TMP_58 TMP_61
+TMP_66 TMP_78 H7))))))))))))))) in (ex2_3_ind C T nat TMP_48 TMP_50 TMP_55
+TMP_79 H4))))))))))))))))))))) in (let TMP_106 \def (\lambda (b: B).(\lambda
+(_: (not (eq B b Abst))).(\lambda (c0: C).(\lambda (u: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 u a1)).(\lambda (_: ((\forall (i: nat).(\forall
+(b0: A).((aprem i a1 b0) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_:
+T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda
+(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b0))))))))))).(\lambda (t0:
+T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c0 (Bind b) u) t0
+a2)).(\lambda (H4: ((\forall (i: nat).(\forall (b0: A).((aprem i a2 b0) \to
(ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus
-i j) O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d
-u0 (asucc g b0))))))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_:
-(arity g (CHead c0 (Bind b) u) t0 a2)).(\lambda (H4: ((\forall (i:
-nat).(\forall (b0: A).((aprem i a2 b0) \to (ex2_3 C T nat (\lambda (d:
-C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d (CHead c0 (Bind b)
-u))))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g b0))))))))))).(\lambda (i: nat).(\lambda (b0: A).(\lambda (H5:
-(aprem i a2 b0)).(let H_x \def (H4 i b0 H5) in (let H6 \def H_x in (ex2_3_ind
-C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O
-d (CHead c0 (Bind b) u))))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_:
-nat).(arity g d u0 (asucc g b0))))) (ex2_3 C T nat (\lambda (d: C).(\lambda
-(_: T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b0)))))) (\lambda (x0:
-C).(\lambda (x1: T).(\lambda (x2: nat).(\lambda (H7: (drop (plus i x2) O x0
-(CHead c0 (Bind b) u))).(\lambda (H8: (arity g x0 x1 (asucc g b0))).(let H9
-\def (eq_ind nat (S (plus i x2)) (\lambda (n: nat).(drop n O x0 c0)) (drop_S
-b x0 c0 u (plus i x2) H7) (plus i (S x2)) (plus_n_Sm i x2)) in (ex2_3_intro C
-T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d
-c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g b0))))) x0 x1 (S x2) H9 H8))))))) H6))))))))))))))))) (\lambda (c0:
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (H0: (arity g c0 u (asucc g
-a1))).(\lambda (_: ((\forall (i: nat).(\forall (b: A).((aprem i (asucc g a1)
-b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop
-(plus i j) O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_:
-nat).(arity g d u0 (asucc g b))))))))))).(\lambda (t0: T).(\lambda (a2:
-A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t0 a2)).(\lambda (H3:
-((\forall (i: nat).(\forall (b: A).((aprem i a2 b) \to (ex2_3 C T nat
-(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d (CHead
-c0 (Bind Abst) u))))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_:
-nat).(arity g d u0 (asucc g b))))))))))).(\lambda (i: nat).(\lambda (b:
-A).(\lambda (H4: (aprem i (AHead a1 a2) b)).(nat_ind (\lambda (n:
-nat).((aprem n (AHead a1 a2) b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda
-(_: T).(\lambda (j: nat).(drop (plus n j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b)))))))) (\lambda (H5:
-(aprem O (AHead a1 a2) b)).(let H_y \def (aprem_gen_head_O a1 a2 b H5) in
-(eq_ind_r A a1 (\lambda (a0: A).(ex2_3 C T nat (\lambda (d: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus O j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g a0))))))) (ex2_3_intro C T
-nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus O j) O d
-c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g a1))))) c0 u O (drop_refl c0) H0) b H_y))) (\lambda (i0:
+i j) O d (CHead c0 (Bind b) u))))) (\lambda (d: C).(\lambda (u0: T).(\lambda
+(_: nat).(arity g d u0 (asucc g b0))))))))))).(\lambda (i: nat).(\lambda (b0:
+A).(\lambda (H5: (aprem i a2 b0)).(let H_x \def (H4 i b0 H5) in (let H6 \def
+H_x in (let TMP_84 \def (\lambda (d: C).(\lambda (_: T).(\lambda (j:
+nat).(let TMP_81 \def (plus i j) in (let TMP_82 \def (Bind b) in (let TMP_83
+\def (CHead c0 TMP_82 u) in (drop TMP_81 O d TMP_83))))))) in (let TMP_86
+\def (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_85 \def
+(asucc g b0) in (arity g d u0 TMP_85))))) in (let TMP_88 \def (\lambda (d:
+C).(\lambda (_: T).(\lambda (j: nat).(let TMP_87 \def (plus i j) in (drop
+TMP_87 O d c0))))) in (let TMP_90 \def (\lambda (d: C).(\lambda (u0:
+T).(\lambda (_: nat).(let TMP_89 \def (asucc g b0) in (arity g d u0
+TMP_89))))) in (let TMP_91 \def (ex2_3 C T nat TMP_88 TMP_90) in (let TMP_105
+\def (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: nat).(\lambda (H7: (drop
+(plus i x2) O x0 (CHead c0 (Bind b) u))).(\lambda (H8: (arity g x0 x1 (asucc
+g b0))).(let TMP_92 \def (plus i x2) in (let TMP_93 \def (S TMP_92) in (let
+TMP_94 \def (\lambda (n: nat).(drop n O x0 c0)) in (let TMP_95 \def (plus i
+x2) in (let TMP_96 \def (drop_S b x0 c0 u TMP_95 H7) in (let TMP_97 \def (S
+x2) in (let TMP_98 \def (plus i TMP_97) in (let TMP_99 \def (plus_n_Sm i x2)
+in (let H9 \def (eq_ind nat TMP_93 TMP_94 TMP_96 TMP_98 TMP_99) in (let
+TMP_101 \def (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_100
+\def (plus i j) in (drop TMP_100 O d c0))))) in (let TMP_103 \def (\lambda
+(d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_102 \def (asucc g b0) in
+(arity g d u0 TMP_102))))) in (let TMP_104 \def (S x2) in (ex2_3_intro C T
+nat TMP_101 TMP_103 x0 x1 TMP_104 H9 H8)))))))))))))))))) in (ex2_3_ind C T
+nat TMP_84 TMP_86 TMP_91 TMP_105 H6))))))))))))))))))))))) in (let TMP_145
+\def (\lambda (c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (H0: (arity g
+c0 u (asucc g a1))).(\lambda (_: ((\forall (i: nat).(\forall (b: A).((aprem i
+(asucc g a1) b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda
+(j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda (u0:
+T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))))))).(\lambda (t0:
+T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t0
+a2)).(\lambda (H3: ((\forall (i: nat).(\forall (b: A).((aprem i a2 b) \to
+(ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus
+i j) O d (CHead c0 (Bind Abst) u))))) (\lambda (d: C).(\lambda (u0:
+T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))))))).(\lambda (i:
+nat).(\lambda (b: A).(\lambda (H4: (aprem i (AHead a1 a2) b)).(let TMP_111
+\def (\lambda (n: nat).((aprem n (AHead a1 a2) b) \to (let TMP_108 \def
+(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_107 \def (plus n
+j) in (drop TMP_107 O d c0))))) in (let TMP_110 \def (\lambda (d: C).(\lambda
+(u0: T).(\lambda (_: nat).(let TMP_109 \def (asucc g b) in (arity g d u0
+TMP_109))))) in (ex2_3 C T nat TMP_108 TMP_110))))) in (let TMP_123 \def
+(\lambda (H5: (aprem O (AHead a1 a2) b)).(let H_y \def (aprem_gen_head_O a1
+a2 b H5) in (let TMP_116 \def (\lambda (a0: A).(let TMP_113 \def (\lambda (d:
+C).(\lambda (_: T).(\lambda (j: nat).(let TMP_112 \def (plus O j) in (drop
+TMP_112 O d c0))))) in (let TMP_115 \def (\lambda (d: C).(\lambda (u0:
+T).(\lambda (_: nat).(let TMP_114 \def (asucc g a0) in (arity g d u0
+TMP_114))))) in (ex2_3 C T nat TMP_113 TMP_115)))) in (let TMP_118 \def
+(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_117 \def (plus O
+j) in (drop TMP_117 O d c0))))) in (let TMP_120 \def (\lambda (d: C).(\lambda
+(u0: T).(\lambda (_: nat).(let TMP_119 \def (asucc g a1) in (arity g d u0
+TMP_119))))) in (let TMP_121 \def (drop_refl c0) in (let TMP_122 \def
+(ex2_3_intro C T nat TMP_118 TMP_120 c0 u O TMP_121 H0) in (eq_ind_r A a1
+TMP_116 TMP_122 b H_y)))))))) in (let TMP_144 \def (\lambda (i0:
nat).(\lambda (_: (((aprem i0 (AHead a1 a2) b) \to (ex2_3 C T nat (\lambda
(d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i0 j) O d c0))))
(\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0 (asucc g
b))))))))).(\lambda (H5: (aprem (S i0) (AHead a1 a2) b)).(let H_y \def
(aprem_gen_head_S a1 a2 b i0 H5) in (let H_x \def (H3 i0 b H_y) in (let H6
-\def H_x in (ex2_3_ind C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i0 j) O d (CHead c0 (Bind Abst) u))))) (\lambda (d:
-C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b))))) (ex2_3 C
-T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus (S i0) j)
-O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g b)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2:
-nat).(\lambda (H7: (drop (plus i0 x2) O x0 (CHead c0 (Bind Abst)
-u))).(\lambda (H8: (arity g x0 x1 (asucc g b))).(ex2_3_intro C T nat (\lambda
-(d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus (S i0) j) O d c0))))
+\def H_x in (let TMP_127 \def (\lambda (d: C).(\lambda (_: T).(\lambda (j:
+nat).(let TMP_124 \def (plus i0 j) in (let TMP_125 \def (Bind Abst) in (let
+TMP_126 \def (CHead c0 TMP_125 u) in (drop TMP_124 O d TMP_126))))))) in (let
+TMP_129 \def (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_128
+\def (asucc g b) in (arity g d u0 TMP_128))))) in (let TMP_132 \def (\lambda
+(d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_130 \def (S i0) in (let
+TMP_131 \def (plus TMP_130 j) in (drop TMP_131 O d c0)))))) in (let TMP_134
+\def (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_133 \def
+(asucc g b) in (arity g d u0 TMP_133))))) in (let TMP_135 \def (ex2_3 C T nat
+TMP_132 TMP_134) in (let TMP_143 \def (\lambda (x0: C).(\lambda (x1:
+T).(\lambda (x2: nat).(\lambda (H7: (drop (plus i0 x2) O x0 (CHead c0 (Bind
+Abst) u))).(\lambda (H8: (arity g x0 x1 (asucc g b))).(let TMP_138 \def
+(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_136 \def (S i0) in
+(let TMP_137 \def (plus TMP_136 j) in (drop TMP_137 O d c0)))))) in (let
+TMP_140 \def (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_139
+\def (asucc g b) in (arity g d u0 TMP_139))))) in (let TMP_141 \def (plus i0
+x2) in (let TMP_142 \def (drop_S Abst x0 c0 u TMP_141 H7) in (ex2_3_intro C T
+nat TMP_138 TMP_140 x0 x1 x2 TMP_142 H8)))))))))) in (ex2_3_ind C T nat
+TMP_127 TMP_129 TMP_135 TMP_143 H6))))))))))))) in (nat_ind TMP_111 TMP_123
+TMP_144 i H4)))))))))))))))) in (let TMP_236 \def (\lambda (c0: C).(\lambda
+(u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u a1)).(\lambda (_:
+((\forall (i: nat).(\forall (b: A).((aprem i a1 b) \to (ex2_3 C T nat
+(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0))))
(\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0 (asucc g
-b))))) x0 x1 x2 (drop_S Abst x0 c0 u (plus i0 x2) H7) H8)))))) H6))))))) i
-H4))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda
-(_: (arity g c0 u a1)).(\lambda (_: ((\forall (i: nat).(\forall (b:
-A).((aprem i a1 b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))))))).(\lambda (t0:
-T).(\lambda (a2: A).(\lambda (_: (arity g c0 t0 (AHead a1 a2))).(\lambda (H3:
-((\forall (i: nat).(\forall (b: A).((aprem i (AHead a1 a2) b) \to (ex2_3 C T
+b))))))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g c0 t0
+(AHead a1 a2))).(\lambda (H3: ((\forall (i: nat).(\forall (b: A).((aprem i
+(AHead a1 a2) b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda
+(j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda (u0:
+T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))))))).(\lambda (i:
+nat).(\lambda (b: A).(\lambda (H4: (aprem i a2 b)).(let TMP_146 \def (S i) in
+(let H_y \def (H3 TMP_146 b) in (let TMP_147 \def (aprem_succ a2 b i H4 a1)
+in (let H5 \def (H_y TMP_147) in (let TMP_150 \def (\lambda (d: C).(\lambda
+(_: T).(\lambda (j: nat).(let TMP_148 \def (plus i j) in (let TMP_149 \def (S
+TMP_148) in (drop TMP_149 O d c0)))))) in (let TMP_152 \def (\lambda (d:
+C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_151 \def (asucc g b) in (arity
+g d u0 TMP_151))))) in (let TMP_154 \def (\lambda (d: C).(\lambda (_:
+T).(\lambda (j: nat).(let TMP_153 \def (plus i j) in (drop TMP_153 O d
+c0))))) in (let TMP_156 \def (\lambda (d: C).(\lambda (u0: T).(\lambda (_:
+nat).(let TMP_155 \def (asucc g b) in (arity g d u0 TMP_155))))) in (let
+TMP_157 \def (ex2_3 C T nat TMP_154 TMP_156) in (let TMP_235 \def (\lambda
+(x0: C).(\lambda (x1: T).(\lambda (x2: nat).(\lambda (H6: (drop (S (plus i
+x2)) O x0 c0)).(\lambda (H7: (arity g x0 x1 (asucc g b))).(let TMP_162 \def
+(\lambda (c1: C).((drop (S (plus i x2)) O c1 c0) \to ((arity g c1 x1 (asucc g
+b)) \to (let TMP_159 \def (\lambda (d: C).(\lambda (_: T).(\lambda (j:
+nat).(let TMP_158 \def (plus i j) in (drop TMP_158 O d c0))))) in (let
+TMP_161 \def (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_160
+\def (asucc g b) in (arity g d u0 TMP_160))))) in (ex2_3 C T nat TMP_159
+TMP_161)))))) in (let TMP_186 \def (\lambda (n: nat).(\lambda (H8: (drop (S
+(plus i x2)) O (CSort n) c0)).(\lambda (_: (arity g (CSort n) x1 (asucc g
+b))).(let TMP_163 \def (CSort n) in (let TMP_164 \def (eq C c0 TMP_163) in
+(let TMP_165 \def (plus i x2) in (let TMP_166 \def (S TMP_165) in (let
+TMP_167 \def (eq nat TMP_166 O) in (let TMP_168 \def (eq nat O O) in (let
+TMP_170 \def (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_169
+\def (plus i j) in (drop TMP_169 O d c0))))) in (let TMP_172 \def (\lambda
+(d: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_171 \def (asucc g b) in
+(arity g d u0 TMP_171))))) in (let TMP_173 \def (ex2_3 C T nat TMP_170
+TMP_172) in (let TMP_182 \def (\lambda (_: (eq C c0 (CSort n))).(\lambda
+(H11: (eq nat (S (plus i x2)) O)).(\lambda (_: (eq nat O O)).(let TMP_174
+\def (plus i x2) in (let TMP_175 \def (S TMP_174) in (let TMP_176 \def
+(\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _) \Rightarrow
+True])) in (let H13 \def (eq_ind nat TMP_175 TMP_176 I O H11) in (let TMP_178
+\def (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_177 \def
+(plus i j) in (drop TMP_177 O d c0))))) in (let TMP_180 \def (\lambda (d:
+C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_179 \def (asucc g b) in (arity
+g d u0 TMP_179))))) in (let TMP_181 \def (ex2_3 C T nat TMP_178 TMP_180) in
+(False_ind TMP_181 H13))))))))))) in (let TMP_183 \def (plus i x2) in (let
+TMP_184 \def (S TMP_183) in (let TMP_185 \def (drop_gen_sort n TMP_184 O c0
+H8) in (and3_ind TMP_164 TMP_167 TMP_168 TMP_173 TMP_182
+TMP_185))))))))))))))))) in (let TMP_234 \def (\lambda (d: C).(\lambda (IHd:
+(((drop (S (plus i x2)) O d c0) \to ((arity g d x1 (asucc g b)) \to (ex2_3 C
+T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O
+d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0
+(asucc g b)))))))))).(\lambda (k: K).(\lambda (t1: T).(\lambda (H8: (drop (S
+(plus i x2)) O (CHead d k t1) c0)).(\lambda (H9: (arity g (CHead d k t1) x1
+(asucc g b))).(let TMP_191 \def (\lambda (k0: K).((arity g (CHead d k0 t1) x1
+(asucc g b)) \to ((drop (r k0 (plus i x2)) O d c0) \to (let TMP_188 \def
+(\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_187 \def (plus i
+j) in (drop TMP_187 O d0 c0))))) in (let TMP_190 \def (\lambda (d0:
+C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_189 \def (asucc g b) in (arity
+g d0 u0 TMP_189))))) in (ex2_3 C T nat TMP_188 TMP_190)))))) in (let TMP_211
+\def (\lambda (b0: B).(\lambda (H10: (arity g (CHead d (Bind b0) t1) x1
+(asucc g b))).(\lambda (H11: (drop (r (Bind b0) (plus i x2)) O d c0)).(let
+TMP_193 \def (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_192
+\def (plus i j) in (drop TMP_192 O d0 c0))))) in (let TMP_195 \def (\lambda
+(d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_194 \def (asucc g b) in
+(arity g d0 u0 TMP_194))))) in (let TMP_196 \def (Bind b0) in (let TMP_197
+\def (CHead d TMP_196 t1) in (let TMP_198 \def (S x2) in (let TMP_199 \def
+(plus i x2) in (let TMP_200 \def (S TMP_199) in (let TMP_203 \def (\lambda
+(n: nat).(let TMP_201 \def (Bind b0) in (let TMP_202 \def (CHead d TMP_201
+t1) in (drop n O TMP_202 c0)))) in (let TMP_204 \def (Bind b0) in (let
+TMP_205 \def (plus i x2) in (let TMP_206 \def (drop_drop TMP_204 TMP_205 d c0
+H11 t1) in (let TMP_207 \def (S x2) in (let TMP_208 \def (plus i TMP_207) in
+(let TMP_209 \def (plus_n_Sm i x2) in (let TMP_210 \def (eq_ind nat TMP_200
+TMP_203 TMP_206 TMP_208 TMP_209) in (ex2_3_intro C T nat TMP_193 TMP_195
+TMP_197 x1 TMP_198 TMP_210 H10))))))))))))))))))) in (let TMP_231 \def
+(\lambda (f: F).(\lambda (H10: (arity g (CHead d (Flat f) t1) x1 (asucc g
+b))).(\lambda (H11: (drop (r (Flat f) (plus i x2)) O d c0)).(let TMP_212 \def
+(Flat f) in (let TMP_213 \def (CHead d TMP_212 t1) in (let TMP_214 \def
+(asucc g b) in (let TMP_215 \def (cimp_flat_sx f d t1) in (let TMP_216 \def
+(arity_cimp_conf g TMP_213 x1 TMP_214 H10 d TMP_215) in (let H12 \def (IHd
+H11 TMP_216) in (let TMP_218 \def (\lambda (d0: C).(\lambda (_: T).(\lambda
+(j: nat).(let TMP_217 \def (plus i j) in (drop TMP_217 O d0 c0))))) in (let
+TMP_220 \def (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_219
+\def (asucc g b) in (arity g d0 u0 TMP_219))))) in (let TMP_222 \def (\lambda
+(d0: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_221 \def (plus i j) in
+(drop TMP_221 O d0 c0))))) in (let TMP_224 \def (\lambda (d0: C).(\lambda
+(u0: T).(\lambda (_: nat).(let TMP_223 \def (asucc g b) in (arity g d0 u0
+TMP_223))))) in (let TMP_225 \def (ex2_3 C T nat TMP_222 TMP_224) in (let
+TMP_230 \def (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: nat).(\lambda
+(H13: (drop (plus i x5) O x3 c0)).(\lambda (H14: (arity g x3 x4 (asucc g
+b))).(let TMP_227 \def (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
+nat).(let TMP_226 \def (plus i j) in (drop TMP_226 O d0 c0))))) in (let
+TMP_229 \def (\lambda (d0: C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_228
+\def (asucc g b) in (arity g d0 u0 TMP_228))))) in (ex2_3_intro C T nat
+TMP_227 TMP_229 x3 x4 x5 H13 H14)))))))) in (ex2_3_ind C T nat TMP_218
+TMP_220 TMP_225 TMP_230 H12)))))))))))))))) in (let TMP_232 \def (plus i x2)
+in (let TMP_233 \def (drop_gen_drop k d c0 t1 TMP_232 H8) in (K_ind TMP_191
+TMP_211 TMP_231 k H9 TMP_233)))))))))))) in (C_ind TMP_162 TMP_186 TMP_234 x0
+H6 H7))))))))) in (ex2_3_ind C T nat TMP_150 TMP_152 TMP_157 TMP_235
+H5))))))))))))))))))))))) in (let TMP_251 \def (\lambda (c0: C).(\lambda (u:
+T).(\lambda (a0: A).(\lambda (_: (arity g c0 u (asucc g a0))).(\lambda (_:
+((\forall (i: nat).(\forall (b: A).((aprem i (asucc g a0) b) \to (ex2_3 C T
nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d
c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g b))))))))))).(\lambda (i: nat).(\lambda (b: A).(\lambda (H4: (aprem
-i a2 b)).(let H5 \def (H3 (S i) b (aprem_succ a2 b i H4 a1)) in (ex2_3_ind C
-T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (S (plus i j))
-O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g b))))) (ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d u0 (asucc g b)))))) (\lambda (x0: C).(\lambda (x1:
-T).(\lambda (x2: nat).(\lambda (H6: (drop (S (plus i x2)) O x0 c0)).(\lambda
-(H7: (arity g x0 x1 (asucc g b))).(C_ind (\lambda (c1: C).((drop (S (plus i
-x2)) O c1 c0) \to ((arity g c1 x1 (asucc g b)) \to (ex2_3 C T nat (\lambda
-(d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda
-(d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b)))))))))
-(\lambda (n: nat).(\lambda (H8: (drop (S (plus i x2)) O (CSort n)
-c0)).(\lambda (_: (arity g (CSort n) x1 (asucc g b))).(and3_ind (eq C c0
-(CSort n)) (eq nat (S (plus i x2)) O) (eq nat O O) (ex2_3 C T nat (\lambda
-(d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda
-(d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))
-(\lambda (_: (eq C c0 (CSort n))).(\lambda (H11: (eq nat (S (plus i x2))
-O)).(\lambda (_: (eq nat O O)).(let H13 \def (eq_ind nat (S (plus i x2))
-(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H11) in (False_ind (ex2_3 C
-T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d
-c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0
-(asucc g b)))))) H13))))) (drop_gen_sort n (S (plus i x2)) O c0 H8)))))
-(\lambda (d: C).(\lambda (IHd: (((drop (S (plus i x2)) O d c0) \to ((arity g
-d x1 (asucc g b)) \to (ex2_3 C T nat (\lambda (d0: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus i j) O d0 c0)))) (\lambda (d0: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d0 u0 (asucc g b)))))))))).(\lambda (k:
-K).(\lambda (t1: T).(\lambda (H8: (drop (S (plus i x2)) O (CHead d k t1)
-c0)).(\lambda (H9: (arity g (CHead d k t1) x1 (asucc g b))).(K_ind (\lambda
-(k0: K).((arity g (CHead d k0 t1) x1 (asucc g b)) \to ((drop (r k0 (plus i
-x2)) O d c0) \to (ex2_3 C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i j) O d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d0 u0 (asucc g b))))))))) (\lambda (b0: B).(\lambda (H10:
-(arity g (CHead d (Bind b0) t1) x1 (asucc g b))).(\lambda (H11: (drop (r
-(Bind b0) (plus i x2)) O d c0)).(ex2_3_intro C T nat (\lambda (d0:
-C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d0 c0)))) (\lambda
-(d0: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0 (asucc g b)))))
-(CHead d (Bind b0) t1) x1 (S x2) (eq_ind nat (S (plus i x2)) (\lambda (n:
-nat).(drop n O (CHead d (Bind b0) t1) c0)) (drop_drop (Bind b0) (plus i x2) d
-c0 H11 t1) (plus i (S x2)) (plus_n_Sm i x2)) H10)))) (\lambda (f: F).(\lambda
-(H10: (arity g (CHead d (Flat f) t1) x1 (asucc g b))).(\lambda (H11: (drop (r
-(Flat f) (plus i x2)) O d c0)).(let H12 \def (IHd H11 (arity_cimp_conf g
-(CHead d (Flat f) t1) x1 (asucc g b) H10 d (cimp_flat_sx f d t1))) in
-(ex2_3_ind C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j: nat).(drop
-(plus i j) O d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda (_:
-nat).(arity g d0 u0 (asucc g b))))) (ex2_3 C T nat (\lambda (d0: C).(\lambda
-(_: T).(\lambda (j: nat).(drop (plus i j) O d0 c0)))) (\lambda (d0:
-C).(\lambda (u0: T).(\lambda (_: nat).(arity g d0 u0 (asucc g b))))))
-(\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: nat).(\lambda (H13: (drop
-(plus i x5) O x3 c0)).(\lambda (H14: (arity g x3 x4 (asucc g
-b))).(ex2_3_intro C T nat (\lambda (d0: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i j) O d0 c0)))) (\lambda (d0: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d0 u0 (asucc g b))))) x3 x4 x5 H13 H14)))))) H12))))) k H9
-(drop_gen_drop k d c0 t1 (plus i x2) H8)))))))) x0 H6 H7))))))
-H5)))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a0: A).(\lambda
-(_: (arity g c0 u (asucc g a0))).(\lambda (_: ((\forall (i: nat).(\forall (b:
-A).((aprem i (asucc g a0) b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))))))).(\lambda (t0:
-T).(\lambda (_: (arity g c0 t0 a0)).(\lambda (H3: ((\forall (i: nat).(\forall
-(b: A).((aprem i a0 b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b))))))))))).(\lambda (i:
-nat).(\lambda (b: A).(\lambda (H4: (aprem i a0 b)).(let H_x \def (H3 i b H4)
-in (let H5 \def H_x in (ex2_3_ind C T nat (\lambda (d: C).(\lambda (_:
-T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda
-(u0: T).(\lambda (_: nat).(arity g d u0 (asucc g b))))) (ex2_3 C T nat
-(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0))))
-(\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d u0 (asucc g
-b)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: nat).(\lambda (H6:
-(drop (plus i x2) O x0 c0)).(\lambda (H7: (arity g x0 x1 (asucc g
-b))).(ex2_3_intro C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j:
-nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda
-(_: nat).(arity g d u0 (asucc g b))))) x0 x1 x2 H6 H7)))))) H5))))))))))))))
-(\lambda (c0: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (_: (arity g c0
-t0 a1)).(\lambda (H1: ((\forall (i: nat).(\forall (b: A).((aprem i a1 b) \to
+(asucc g b))))))))))).(\lambda (t0: T).(\lambda (_: (arity g c0 t0
+a0)).(\lambda (H3: ((\forall (i: nat).(\forall (b: A).((aprem i a0 b) \to
(ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus
-i j) O d c0)))) (\lambda (d: C).(\lambda (u: T).(\lambda (_: nat).(arity g d
-u (asucc g b))))))))))).(\lambda (a2: A).(\lambda (H2: (leq g a1
-a2)).(\lambda (i: nat).(\lambda (b: A).(\lambda (H3: (aprem i a2 b)).(let H_x
-\def (aprem_repl g a1 a2 H2 i b H3) in (let H4 \def H_x in (ex2_ind A
-(\lambda (b1: A).(leq g b1 b)) (\lambda (b1: A).(aprem i a1 b1)) (ex2_3 C T
-nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d
-c0)))) (\lambda (d: C).(\lambda (u: T).(\lambda (_: nat).(arity g d u (asucc
-g b)))))) (\lambda (x: A).(\lambda (H5: (leq g x b)).(\lambda (H6: (aprem i
-a1 x)).(let H_x0 \def (H1 i x H6) in (let H7 \def H_x0 in (ex2_3_ind C T nat
-(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop (plus i j) O d c0))))
-(\lambda (d: C).(\lambda (u: T).(\lambda (_: nat).(arity g d u (asucc g
-x))))) (ex2_3 C T nat (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(drop
-(plus i j) O d c0)))) (\lambda (d: C).(\lambda (u: T).(\lambda (_:
-nat).(arity g d u (asucc g b)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda
-(x2: nat).(\lambda (H8: (drop (plus i x2) O x0 c0)).(\lambda (H9: (arity g x0
-x1 (asucc g x))).(ex2_3_intro C T nat (\lambda (d: C).(\lambda (_:
+i j) O d c0)))) (\lambda (d: C).(\lambda (u0: T).(\lambda (_: nat).(arity g d
+u0 (asucc g b))))))))))).(\lambda (i: nat).(\lambda (b: A).(\lambda (H4:
+(aprem i a0 b)).(let H_x \def (H3 i b H4) in (let H5 \def H_x in (let TMP_238
+\def (\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_237 \def
+(plus i j) in (drop TMP_237 O d c0))))) in (let TMP_240 \def (\lambda (d:
+C).(\lambda (u0: T).(\lambda (_: nat).(let TMP_239 \def (asucc g b) in (arity
+g d u0 TMP_239))))) in (let TMP_242 \def (\lambda (d: C).(\lambda (_:
+T).(\lambda (j: nat).(let TMP_241 \def (plus i j) in (drop TMP_241 O d
+c0))))) in (let TMP_244 \def (\lambda (d: C).(\lambda (u0: T).(\lambda (_:
+nat).(let TMP_243 \def (asucc g b) in (arity g d u0 TMP_243))))) in (let
+TMP_245 \def (ex2_3 C T nat TMP_242 TMP_244) in (let TMP_250 \def (\lambda
+(x0: C).(\lambda (x1: T).(\lambda (x2: nat).(\lambda (H6: (drop (plus i x2) O
+x0 c0)).(\lambda (H7: (arity g x0 x1 (asucc g b))).(let TMP_247 \def (\lambda
+(d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_246 \def (plus i j) in
+(drop TMP_246 O d c0))))) in (let TMP_249 \def (\lambda (d: C).(\lambda (u0:
+T).(\lambda (_: nat).(let TMP_248 \def (asucc g b) in (arity g d u0
+TMP_248))))) in (ex2_3_intro C T nat TMP_247 TMP_249 x0 x1 x2 H6 H7))))))))
+in (ex2_3_ind C T nat TMP_238 TMP_240 TMP_245 TMP_250 H5))))))))))))))))))))
+in (let TMP_278 \def (\lambda (c0: C).(\lambda (t0: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 t0 a1)).(\lambda (H1: ((\forall (i: nat).(\forall
+(b: A).((aprem i a1 b) \to (ex2_3 C T nat (\lambda (d: C).(\lambda (_:
T).(\lambda (j: nat).(drop (plus i j) O d c0)))) (\lambda (d: C).(\lambda (u:
-T).(\lambda (_: nat).(arity g d u (asucc g b))))) x0 x1 x2 H8 (arity_repl g
-x0 x1 (asucc g x) H9 (asucc g b) (asucc_repl g x b H5)))))))) H7))))))
-H4))))))))))))) c t a H))))).
-(* COMMENTS
-Initial nodes: 4526
-END *)
+T).(\lambda (_: nat).(arity g d u (asucc g b))))))))))).(\lambda (a2:
+A).(\lambda (H2: (leq g a1 a2)).(\lambda (i: nat).(\lambda (b: A).(\lambda
+(H3: (aprem i a2 b)).(let H_x \def (aprem_repl g a1 a2 H2 i b H3) in (let H4
+\def H_x in (let TMP_252 \def (\lambda (b1: A).(leq g b1 b)) in (let TMP_253
+\def (\lambda (b1: A).(aprem i a1 b1)) in (let TMP_255 \def (\lambda (d:
+C).(\lambda (_: T).(\lambda (j: nat).(let TMP_254 \def (plus i j) in (drop
+TMP_254 O d c0))))) in (let TMP_257 \def (\lambda (d: C).(\lambda (u:
+T).(\lambda (_: nat).(let TMP_256 \def (asucc g b) in (arity g d u
+TMP_256))))) in (let TMP_258 \def (ex2_3 C T nat TMP_255 TMP_257) in (let
+TMP_277 \def (\lambda (x: A).(\lambda (H5: (leq g x b)).(\lambda (H6: (aprem
+i a1 x)).(let H_x0 \def (H1 i x H6) in (let H7 \def H_x0 in (let TMP_260 \def
+(\lambda (d: C).(\lambda (_: T).(\lambda (j: nat).(let TMP_259 \def (plus i
+j) in (drop TMP_259 O d c0))))) in (let TMP_262 \def (\lambda (d: C).(\lambda
+(u: T).(\lambda (_: nat).(let TMP_261 \def (asucc g x) in (arity g d u
+TMP_261))))) in (let TMP_264 \def (\lambda (d: C).(\lambda (_: T).(\lambda
+(j: nat).(let TMP_263 \def (plus i j) in (drop TMP_263 O d c0))))) in (let
+TMP_266 \def (\lambda (d: C).(\lambda (u: T).(\lambda (_: nat).(let TMP_265
+\def (asucc g b) in (arity g d u TMP_265))))) in (let TMP_267 \def (ex2_3 C T
+nat TMP_264 TMP_266) in (let TMP_276 \def (\lambda (x0: C).(\lambda (x1:
+T).(\lambda (x2: nat).(\lambda (H8: (drop (plus i x2) O x0 c0)).(\lambda (H9:
+(arity g x0 x1 (asucc g x))).(let TMP_269 \def (\lambda (d: C).(\lambda (_:
+T).(\lambda (j: nat).(let TMP_268 \def (plus i j) in (drop TMP_268 O d
+c0))))) in (let TMP_271 \def (\lambda (d: C).(\lambda (u: T).(\lambda (_:
+nat).(let TMP_270 \def (asucc g b) in (arity g d u TMP_270))))) in (let
+TMP_272 \def (asucc g x) in (let TMP_273 \def (asucc g b) in (let TMP_274
+\def (asucc_repl g x b H5) in (let TMP_275 \def (arity_repl g x0 x1 TMP_272
+H9 TMP_273 TMP_274) in (ex2_3_intro C T nat TMP_269 TMP_271 x0 x1 x2 H8
+TMP_275)))))))))))) in (ex2_3_ind C T nat TMP_260 TMP_262 TMP_267 TMP_276
+H7)))))))))))) in (ex2_ind A TMP_252 TMP_253 TMP_258 TMP_277
+H4))))))))))))))))))) in (arity_ind g TMP_5 TMP_11 TMP_45 TMP_80 TMP_106
+TMP_145 TMP_236 TMP_251 TMP_278 c t a H)))))))))))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/defs.ma".
+include "basic_1/arity/fwd.ma".
-include "Basic-1/cimp/props.ma".
+include "basic_1/cimp/props.ma".
theorem arity_cimp_conf:
\forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1
t a) \to (\forall (c2: C).((cimp c1 c2) \to (arity g c2 t a)))))))
\def
\lambda (g: G).(\lambda (c1: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c1 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
-A).(\forall (c2: C).((cimp c c2) \to (arity g c2 t0 a0)))))) (\lambda (c:
-C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_: (cimp c c2)).(arity_sort g
-c2 n))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
-nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0:
-A).(\lambda (_: (arity g d u a0)).(\lambda (H2: ((\forall (c2: C).((cimp d
-c2) \to (arity g c2 u a0))))).(\lambda (c2: C).(\lambda (H3: (cimp c
-c2)).(let H_x \def (H3 Abbr d u i H0) in (let H4 \def H_x in (ex_ind C
-(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (arity g c2 (TLRef i)
-a0) (\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x (Bind Abbr) u))).(let
-H_x0 \def (cimp_getl_conf c c2 H3 Abbr d u i H0) in (let H6 \def H_x0 in
-(ex2_ind C (\lambda (d2: C).(cimp d d2)) (\lambda (d2: C).(getl i c2 (CHead
-d2 (Bind Abbr) u))) (arity g c2 (TLRef i) a0) (\lambda (x0: C).(\lambda (H7:
-(cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind Abbr) u))).(let H9 \def
-(eq_ind C (CHead x (Bind Abbr) u) (\lambda (c0: C).(getl i c2 c0)) H5 (CHead
-x0 (Bind Abbr) u) (getl_mono c2 (CHead x (Bind Abbr) u) i H5 (CHead x0 (Bind
-Abbr) u) H8)) in (let H10 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow x | (CHead c0 _ _)
-\Rightarrow c0])) (CHead x (Bind Abbr) u) (CHead x0 (Bind Abbr) u) (getl_mono
-c2 (CHead x (Bind Abbr) u) i H5 (CHead x0 (Bind Abbr) u) H8)) in (let H11
-\def (eq_ind_r C x0 (\lambda (c0: C).(getl i c2 (CHead c0 (Bind Abbr) u))) H9
-x H10) in (let H12 \def (eq_ind_r C x0 (\lambda (c0: C).(cimp d c0)) H7 x
-H10) in (arity_abbr g c2 x u i H11 a0 (H2 x H12))))))))) H6)))))
-H4))))))))))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
-nat).(\lambda (H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0:
-A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda (H2: ((\forall (c2:
-C).((cimp d c2) \to (arity g c2 u (asucc g a0)))))).(\lambda (c2: C).(\lambda
-(H3: (cimp c c2)).(let H_x \def (H3 Abst d u i H0) in (let H4 \def H_x in
-(ex_ind C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (arity g c2
-(TLRef i) a0) (\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x (Bind Abst)
-u))).(let H_x0 \def (cimp_getl_conf c c2 H3 Abst d u i H0) in (let H6 \def
-H_x0 in (ex2_ind C (\lambda (d2: C).(cimp d d2)) (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (arity g c2 (TLRef i) a0) (\lambda (x0:
-C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind Abst)
-u))).(let H9 \def (eq_ind C (CHead x (Bind Abst) u) (\lambda (c0: C).(getl i
-c2 c0)) H5 (CHead x0 (Bind Abst) u) (getl_mono c2 (CHead x (Bind Abst) u) i
-H5 (CHead x0 (Bind Abst) u) H8)) in (let H10 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow x |
-(CHead c0 _ _) \Rightarrow c0])) (CHead x (Bind Abst) u) (CHead x0 (Bind
-Abst) u) (getl_mono c2 (CHead x (Bind Abst) u) i H5 (CHead x0 (Bind Abst) u)
-H8)) in (let H11 \def (eq_ind_r C x0 (\lambda (c0: C).(getl i c2 (CHead c0
-(Bind Abst) u))) H9 x H10) in (let H12 \def (eq_ind_r C x0 (\lambda (c0:
-C).(cimp d c0)) H7 x H10) in (arity_abst g c2 x u i H11 a0 (H2 x H12)))))))))
-H6))))) H4))))))))))))) (\lambda (b: B).(\lambda (H0: (not (eq B b
-Abst))).(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity
-g c u a1)).(\lambda (H2: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u
-a1))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c
-(Bind b) u) t0 a2)).(\lambda (H4: ((\forall (c2: C).((cimp (CHead c (Bind b)
-u) c2) \to (arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda (H5: (cimp c
-c2)).(arity_bind g b H0 c2 u a1 (H2 c2 H5) t0 a2 (H4 (CHead c2 (Bind b) u)
-(cimp_bind c c2 H5 b u)))))))))))))))) (\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (_: (arity g c u (asucc g a1))).(\lambda (H1:
-((\forall (c2: C).((cimp c c2) \to (arity g c2 u (asucc g a1)))))).(\lambda
-(t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind Abst) u) t0
-a2)).(\lambda (H3: ((\forall (c2: C).((cimp (CHead c (Bind Abst) u) c2) \to
-(arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda (H4: (cimp c
-c2)).(arity_head g c2 u a1 (H1 c2 H4) t0 a2 (H3 (CHead c2 (Bind Abst) u)
-(cimp_bind c c2 H4 Abst u)))))))))))))) (\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H1: ((\forall
+(arity g c1 t a)).(let TMP_1 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
+(a0: A).(\forall (c2: C).((cimp c c2) \to (arity g c2 t0 a0)))))) in (let
+TMP_2 \def (\lambda (c: C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_:
+(cimp c c2)).(arity_sort g c2 n))))) in (let TMP_41 \def (\lambda (c:
+C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c
+(CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity g d u
+a0)).(\lambda (H2: ((\forall (c2: C).((cimp d c2) \to (arity g c2 u
+a0))))).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(let H_x \def (H3 Abbr d
+u i H0) in (let H4 \def H_x in (let TMP_5 \def (\lambda (d2: C).(let TMP_3
+\def (Bind Abbr) in (let TMP_4 \def (CHead d2 TMP_3 u) in (getl i c2
+TMP_4)))) in (let TMP_6 \def (TLRef i) in (let TMP_7 \def (arity g c2 TMP_6
+a0) in (let TMP_40 \def (\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x
+(Bind Abbr) u))).(let H_x0 \def (cimp_getl_conf c c2 H3 Abbr d u i H0) in
+(let H6 \def H_x0 in (let TMP_8 \def (\lambda (d2: C).(cimp d d2)) in (let
+TMP_11 \def (\lambda (d2: C).(let TMP_9 \def (Bind Abbr) in (let TMP_10 \def
+(CHead d2 TMP_9 u) in (getl i c2 TMP_10)))) in (let TMP_12 \def (TLRef i) in
+(let TMP_13 \def (arity g c2 TMP_12 a0) in (let TMP_39 \def (\lambda (x0:
+C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind Abbr)
+u))).(let TMP_14 \def (Bind Abbr) in (let TMP_15 \def (CHead x TMP_14 u) in
+(let TMP_16 \def (\lambda (c0: C).(getl i c2 c0)) in (let TMP_17 \def (Bind
+Abbr) in (let TMP_18 \def (CHead x0 TMP_17 u) in (let TMP_19 \def (Bind Abbr)
+in (let TMP_20 \def (CHead x TMP_19 u) in (let TMP_21 \def (Bind Abbr) in
+(let TMP_22 \def (CHead x0 TMP_21 u) in (let TMP_23 \def (getl_mono c2 TMP_20
+i H5 TMP_22 H8) in (let H9 \def (eq_ind C TMP_15 TMP_16 H5 TMP_18 TMP_23) in
+(let TMP_24 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow x |
+(CHead c0 _ _) \Rightarrow c0])) in (let TMP_25 \def (Bind Abbr) in (let
+TMP_26 \def (CHead x TMP_25 u) in (let TMP_27 \def (Bind Abbr) in (let TMP_28
+\def (CHead x0 TMP_27 u) in (let TMP_29 \def (Bind Abbr) in (let TMP_30 \def
+(CHead x TMP_29 u) in (let TMP_31 \def (Bind Abbr) in (let TMP_32 \def (CHead
+x0 TMP_31 u) in (let TMP_33 \def (getl_mono c2 TMP_30 i H5 TMP_32 H8) in (let
+H10 \def (f_equal C C TMP_24 TMP_26 TMP_28 TMP_33) in (let TMP_36 \def
+(\lambda (c0: C).(let TMP_34 \def (Bind Abbr) in (let TMP_35 \def (CHead c0
+TMP_34 u) in (getl i c2 TMP_35)))) in (let H11 \def (eq_ind_r C x0 TMP_36 H9
+x H10) in (let TMP_37 \def (\lambda (c0: C).(cimp d c0)) in (let H12 \def
+(eq_ind_r C x0 TMP_37 H7 x H10) in (let TMP_38 \def (H2 x H12) in (arity_abbr
+g c2 x u i H11 a0 TMP_38))))))))))))))))))))))))))))))) in (ex2_ind C TMP_8
+TMP_11 TMP_13 TMP_39 H6)))))))))) in (ex_ind C TMP_5 TMP_7 TMP_40
+H4))))))))))))))))) in (let TMP_80 \def (\lambda (c: C).(\lambda (d:
+C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind
+Abst) u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda
+(H2: ((\forall (c2: C).((cimp d c2) \to (arity g c2 u (asucc g
+a0)))))).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(let H_x \def (H3 Abst d
+u i H0) in (let H4 \def H_x in (let TMP_44 \def (\lambda (d2: C).(let TMP_42
+\def (Bind Abst) in (let TMP_43 \def (CHead d2 TMP_42 u) in (getl i c2
+TMP_43)))) in (let TMP_45 \def (TLRef i) in (let TMP_46 \def (arity g c2
+TMP_45 a0) in (let TMP_79 \def (\lambda (x: C).(\lambda (H5: (getl i c2
+(CHead x (Bind Abst) u))).(let H_x0 \def (cimp_getl_conf c c2 H3 Abst d u i
+H0) in (let H6 \def H_x0 in (let TMP_47 \def (\lambda (d2: C).(cimp d d2)) in
+(let TMP_50 \def (\lambda (d2: C).(let TMP_48 \def (Bind Abst) in (let TMP_49
+\def (CHead d2 TMP_48 u) in (getl i c2 TMP_49)))) in (let TMP_51 \def (TLRef
+i) in (let TMP_52 \def (arity g c2 TMP_51 a0) in (let TMP_78 \def (\lambda
+(x0: C).(\lambda (H7: (cimp d x0)).(\lambda (H8: (getl i c2 (CHead x0 (Bind
+Abst) u))).(let TMP_53 \def (Bind Abst) in (let TMP_54 \def (CHead x TMP_53
+u) in (let TMP_55 \def (\lambda (c0: C).(getl i c2 c0)) in (let TMP_56 \def
+(Bind Abst) in (let TMP_57 \def (CHead x0 TMP_56 u) in (let TMP_58 \def (Bind
+Abst) in (let TMP_59 \def (CHead x TMP_58 u) in (let TMP_60 \def (Bind Abst)
+in (let TMP_61 \def (CHead x0 TMP_60 u) in (let TMP_62 \def (getl_mono c2
+TMP_59 i H5 TMP_61 H8) in (let H9 \def (eq_ind C TMP_54 TMP_55 H5 TMP_57
+TMP_62) in (let TMP_63 \def (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow x | (CHead c0 _ _) \Rightarrow c0])) in (let TMP_64 \def (Bind
+Abst) in (let TMP_65 \def (CHead x TMP_64 u) in (let TMP_66 \def (Bind Abst)
+in (let TMP_67 \def (CHead x0 TMP_66 u) in (let TMP_68 \def (Bind Abst) in
+(let TMP_69 \def (CHead x TMP_68 u) in (let TMP_70 \def (Bind Abst) in (let
+TMP_71 \def (CHead x0 TMP_70 u) in (let TMP_72 \def (getl_mono c2 TMP_69 i H5
+TMP_71 H8) in (let H10 \def (f_equal C C TMP_63 TMP_65 TMP_67 TMP_72) in (let
+TMP_75 \def (\lambda (c0: C).(let TMP_73 \def (Bind Abst) in (let TMP_74 \def
+(CHead c0 TMP_73 u) in (getl i c2 TMP_74)))) in (let H11 \def (eq_ind_r C x0
+TMP_75 H9 x H10) in (let TMP_76 \def (\lambda (c0: C).(cimp d c0)) in (let
+H12 \def (eq_ind_r C x0 TMP_76 H7 x H10) in (let TMP_77 \def (H2 x H12) in
+(arity_abst g c2 x u i H11 a0 TMP_77))))))))))))))))))))))))))))))) in
+(ex2_ind C TMP_47 TMP_50 TMP_52 TMP_78 H6)))))))))) in (ex_ind C TMP_44
+TMP_46 TMP_79 H4))))))))))))))))) in (let TMP_86 \def (\lambda (b:
+B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda (u:
+T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2: ((\forall
(c2: C).((cimp c c2) \to (arity g c2 u a1))))).(\lambda (t0: T).(\lambda (a2:
-A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3: ((\forall (c2:
-C).((cimp c c2) \to (arity g c2 t0 (AHead a1 a2)))))).(\lambda (c2:
-C).(\lambda (H4: (cimp c c2)).(arity_appl g c2 u a1 (H1 c2 H4) t0 a2 (H3 c2
-H4))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_:
-(arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c2: C).((cimp c c2) \to
-(arity g c2 u (asucc g a0)))))).(\lambda (t0: T).(\lambda (_: (arity g c t0
-a0)).(\lambda (H3: ((\forall (c2: C).((cimp c c2) \to (arity g c2 t0
-a0))))).(\lambda (c2: C).(\lambda (H4: (cimp c c2)).(arity_cast g c2 u a0 (H1
-c2 H4) t0 (H3 c2 H4)))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda
-(a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall (c2:
-C).((cimp c c2) \to (arity g c2 t0 a1))))).(\lambda (a2: A).(\lambda (H2:
-(leq g a1 a2)).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(arity_repl g c2
-t0 a1 (H1 c2 H3) a2 H2)))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 1505
-END *)
+A).(\lambda (_: (arity g (CHead c (Bind b) u) t0 a2)).(\lambda (H4: ((\forall
+(c2: C).((cimp (CHead c (Bind b) u) c2) \to (arity g c2 t0 a2))))).(\lambda
+(c2: C).(\lambda (H5: (cimp c c2)).(let TMP_81 \def (H2 c2 H5) in (let TMP_82
+\def (Bind b) in (let TMP_83 \def (CHead c2 TMP_82 u) in (let TMP_84 \def
+(cimp_bind c c2 H5 b u) in (let TMP_85 \def (H4 TMP_83 TMP_84) in (arity_bind
+g b H0 c2 u a1 TMP_81 t0 a2 TMP_85))))))))))))))))))) in (let TMP_92 \def
+(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
+(asucc g a1))).(\lambda (H1: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u
+(asucc g a1)))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g
+(CHead c (Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (c2: C).((cimp (CHead
+c (Bind Abst) u) c2) \to (arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda
+(H4: (cimp c c2)).(let TMP_87 \def (H1 c2 H4) in (let TMP_88 \def (Bind Abst)
+in (let TMP_89 \def (CHead c2 TMP_88 u) in (let TMP_90 \def (cimp_bind c c2
+H4 Abst u) in (let TMP_91 \def (H3 TMP_89 TMP_90) in (arity_head g c2 u a1
+TMP_87 t0 a2 TMP_91))))))))))))))))) in (let TMP_95 \def (\lambda (c:
+C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda
+(H1: ((\forall (c2: C).((cimp c c2) \to (arity g c2 u a1))))).(\lambda (t0:
+T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3:
+((\forall (c2: C).((cimp c c2) \to (arity g c2 t0 (AHead a1 a2)))))).(\lambda
+(c2: C).(\lambda (H4: (cimp c c2)).(let TMP_93 \def (H1 c2 H4) in (let TMP_94
+\def (H3 c2 H4) in (arity_appl g c2 u a1 TMP_93 t0 a2 TMP_94)))))))))))))) in
+(let TMP_98 \def (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda
+(_: (arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c2: C).((cimp c c2)
+\to (arity g c2 u (asucc g a0)))))).(\lambda (t0: T).(\lambda (_: (arity g c
+t0 a0)).(\lambda (H3: ((\forall (c2: C).((cimp c c2) \to (arity g c2 t0
+a0))))).(\lambda (c2: C).(\lambda (H4: (cimp c c2)).(let TMP_96 \def (H1 c2
+H4) in (let TMP_97 \def (H3 c2 H4) in (arity_cast g c2 u a0 TMP_96 t0
+TMP_97))))))))))))) in (let TMP_100 \def (\lambda (c: C).(\lambda (t0:
+T).(\lambda (a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall
+(c2: C).((cimp c c2) \to (arity g c2 t0 a1))))).(\lambda (a2: A).(\lambda
+(H2: (leq g a1 a2)).(\lambda (c2: C).(\lambda (H3: (cimp c c2)).(let TMP_99
+\def (H1 c2 H3) in (arity_repl g c2 t0 a1 TMP_99 a2 H2))))))))))) in
+(arity_ind g TMP_1 TMP_2 TMP_41 TMP_80 TMP_86 TMP_92 TMP_95 TMP_98 TMP_100 c1
+t a H)))))))))))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/leq/defs.ma".
+include "basic_1/leq/defs.ma".
-include "Basic-1/getl/defs.ma".
+include "basic_1/getl/defs.ma".
inductive arity (g: G): C \to (T \to (A \to Prop)) \def
| arity_sort: \forall (c: C).(\forall (n: nat).(arity g c (TSort n) (ASort O
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/defs.ma".
+include "basic_1/arity/defs.ma".
-include "Basic-1/leq/asucc.ma".
+include "basic_1/leq/asucc.ma".
-include "Basic-1/getl/drop.ma".
+include "basic_1/getl/drop.ma".
+
+let rec arity_ind (g: G) (P: (C \to (T \to (A \to Prop)))) (f: (\forall (c:
+C).(\forall (n: nat).(P c (TSort n) (ASort O n))))) (f0: (\forall (c:
+C).(\forall (d: C).(\forall (u: T).(\forall (i: nat).((getl i c (CHead d
+(Bind Abbr) u)) \to (\forall (a: A).((arity g d u a) \to ((P d u a) \to (P c
+(TLRef i) a)))))))))) (f1: (\forall (c: C).(\forall (d: C).(\forall (u:
+T).(\forall (i: nat).((getl i c (CHead d (Bind Abst) u)) \to (\forall (a:
+A).((arity g d u (asucc g a)) \to ((P d u (asucc g a)) \to (P c (TLRef i)
+a)))))))))) (f2: (\forall (b: B).((not (eq B b Abst)) \to (\forall (c:
+C).(\forall (u: T).(\forall (a1: A).((arity g c u a1) \to ((P c u a1) \to
+(\forall (t: T).(\forall (a2: A).((arity g (CHead c (Bind b) u) t a2) \to ((P
+(CHead c (Bind b) u) t a2) \to (P c (THead (Bind b) u t) a2))))))))))))) (f3:
+(\forall (c: C).(\forall (u: T).(\forall (a1: A).((arity g c u (asucc g a1))
+\to ((P c u (asucc g a1)) \to (\forall (t: T).(\forall (a2: A).((arity g
+(CHead c (Bind Abst) u) t a2) \to ((P (CHead c (Bind Abst) u) t a2) \to (P c
+(THead (Bind Abst) u t) (AHead a1 a2)))))))))))) (f4: (\forall (c:
+C).(\forall (u: T).(\forall (a1: A).((arity g c u a1) \to ((P c u a1) \to
+(\forall (t: T).(\forall (a2: A).((arity g c t (AHead a1 a2)) \to ((P c t
+(AHead a1 a2)) \to (P c (THead (Flat Appl) u t) a2))))))))))) (f5: (\forall
+(c: C).(\forall (u: T).(\forall (a: A).((arity g c u (asucc g a)) \to ((P c u
+(asucc g a)) \to (\forall (t: T).((arity g c t a) \to ((P c t a) \to (P c
+(THead (Flat Cast) u t) a)))))))))) (f6: (\forall (c: C).(\forall (t:
+T).(\forall (a1: A).((arity g c t a1) \to ((P c t a1) \to (\forall (a2:
+A).((leq g a1 a2) \to (P c t a2))))))))) (c: C) (t: T) (a: A) (a0: arity g c
+t a) on a0: P c t a \def match a0 with [(arity_sort c0 n) \Rightarrow (f c0
+n) | (arity_abbr c0 d u i g0 a1 a2) \Rightarrow (f0 c0 d u i g0 a1 a2
+((arity_ind g P f f0 f1 f2 f3 f4 f5 f6) d u a1 a2)) | (arity_abst c0 d u i g0
+a1 a2) \Rightarrow (f1 c0 d u i g0 a1 a2 ((arity_ind g P f f0 f1 f2 f3 f4 f5
+f6) d u (asucc g a1) a2)) | (arity_bind b n c0 u a1 a2 t0 a3 a4) \Rightarrow
+(f2 b n c0 u a1 a2 ((arity_ind g P f f0 f1 f2 f3 f4 f5 f6) c0 u a1 a2) t0 a3
+a4 ((arity_ind g P f f0 f1 f2 f3 f4 f5 f6) (CHead c0 (Bind b) u) t0 a3 a4)) |
+(arity_head c0 u a1 a2 t0 a3 a4) \Rightarrow (f3 c0 u a1 a2 ((arity_ind g P f
+f0 f1 f2 f3 f4 f5 f6) c0 u (asucc g a1) a2) t0 a3 a4 ((arity_ind g P f f0 f1
+f2 f3 f4 f5 f6) (CHead c0 (Bind Abst) u) t0 a3 a4)) | (arity_appl c0 u a1 a2
+t0 a3 a4) \Rightarrow (f4 c0 u a1 a2 ((arity_ind g P f f0 f1 f2 f3 f4 f5 f6)
+c0 u a1 a2) t0 a3 a4 ((arity_ind g P f f0 f1 f2 f3 f4 f5 f6) c0 t0 (AHead a1
+a3) a4)) | (arity_cast c0 u a1 a2 t0 a3) \Rightarrow (f5 c0 u a1 a2
+((arity_ind g P f f0 f1 f2 f3 f4 f5 f6) c0 u (asucc g a1) a2) t0 a3
+((arity_ind g P f f0 f1 f2 f3 f4 f5 f6) c0 t0 a1 a3)) | (arity_repl c0 t0 a1
+a2 a3 l) \Rightarrow (f6 c0 t0 a1 a2 ((arity_ind g P f f0 f1 f2 f3 f4 f5 f6)
+c0 t0 a1 a2) a3 l)].
theorem arity_gen_sort:
\forall (g: G).(\forall (c: C).(\forall (n: nat).(\forall (a: A).((arity g c
(arity g c y a)).(arity_ind g (\lambda (_: C).(\lambda (t: T).(\lambda (a0:
A).((eq T t (TSort n)) \to (leq g a0 (ASort O n)))))) (\lambda (_:
C).(\lambda (n0: nat).(\lambda (H1: (eq T (TSort n0) (TSort n))).(let H2 \def
-(f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
-[(TSort n1) \Rightarrow n1 | (TLRef _) \Rightarrow n0 | (THead _ _ _)
-\Rightarrow n0])) (TSort n0) (TSort n) H1) in (eq_ind_r nat n (\lambda (n1:
-nat).(leq g (ASort O n1) (ASort O n))) (leq_refl g (ASort O n)) n0 H2)))))
-(\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda
-(_: (getl i c0 (CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity
-g d u a0)).(\lambda (_: (((eq T u (TSort n)) \to (leq g a0 (ASort O
-n))))).(\lambda (H4: (eq T (TLRef i) (TSort n))).(let H5 \def (eq_ind T
-(TLRef i) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with
+(f_equal T nat (\lambda (e: T).(match e with [(TSort n1) \Rightarrow n1 |
+(TLRef _) \Rightarrow n0 | (THead _ _ _) \Rightarrow n0])) (TSort n0) (TSort
+n) H1) in (eq_ind_r nat n (\lambda (n1: nat).(leq g (ASort O n1) (ASort O
+n))) (leq_refl g (ASort O n)) n0 H2))))) (\lambda (c0: C).(\lambda (d:
+C).(\lambda (u: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind
+Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity g d u a0)).(\lambda (_: (((eq
+T u (TSort n)) \to (leq g a0 (ASort O n))))).(\lambda (H4: (eq T (TLRef i)
+(TSort n))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee with
[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _)
\Rightarrow False])) I (TSort n) H4) in (False_ind (leq g a0 (ASort O n))
H5))))))))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
nat).(\lambda (_: (getl i c0 (CHead d (Bind Abst) u))).(\lambda (a0:
A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda (_: (((eq T u (TSort n))
\to (leq g (asucc g a0) (ASort O n))))).(\lambda (H4: (eq T (TLRef i) (TSort
-n))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (TSort n) H4) in
-(False_ind (leq g a0 (ASort O n)) H5))))))))))) (\lambda (b: B).(\lambda (_:
-(not (eq B b Abst))).(\lambda (c0: C).(\lambda (u: T).(\lambda (a1:
-A).(\lambda (_: (arity g c0 u a1)).(\lambda (_: (((eq T u (TSort n)) \to (leq
-g a1 (ASort O n))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_: (arity g
-(CHead c0 (Bind b) u) t a2)).(\lambda (_: (((eq T t (TSort n)) \to (leq g a2
-(ASort O n))))).(\lambda (H6: (eq T (THead (Bind b) u t) (TSort n))).(let H7
-\def (eq_ind T (THead (Bind b) u t) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort n) H6) in
-(False_ind (leq g a2 (ASort O n)) H7)))))))))))))) (\lambda (c0: C).(\lambda
-(u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u (asucc g a1))).(\lambda
-(_: (((eq T u (TSort n)) \to (leq g (asucc g a1) (ASort O n))))).(\lambda (t:
-T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t
-a2)).(\lambda (_: (((eq T t (TSort n)) \to (leq g a2 (ASort O n))))).(\lambda
-(H5: (eq T (THead (Bind Abst) u t) (TSort n))).(let H6 \def (eq_ind T (THead
-(Bind Abst) u t) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop)
-with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _
-_) \Rightarrow True])) I (TSort n) H5) in (False_ind (leq g (AHead a1 a2)
-(ASort O n)) H6)))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a1:
-A).(\lambda (_: (arity g c0 u a1)).(\lambda (_: (((eq T u (TSort n)) \to (leq
-g a1 (ASort O n))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_: (arity g
-c0 t (AHead a1 a2))).(\lambda (_: (((eq T t (TSort n)) \to (leq g (AHead a1
-a2) (ASort O n))))).(\lambda (H5: (eq T (THead (Flat Appl) u t) (TSort
-n))).(let H6 \def (eq_ind T (THead (Flat Appl) u t) (\lambda (ee: T).(match
-ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False |
+n))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee with [(TSort
+_) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
+False])) I (TSort n) H4) in (False_ind (leq g a0 (ASort O n)) H5)))))))))))
+(\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda (c0: C).(\lambda
+(u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u a1)).(\lambda (_: (((eq T
+u (TSort n)) \to (leq g a1 (ASort O n))))).(\lambda (t: T).(\lambda (a2:
+A).(\lambda (_: (arity g (CHead c0 (Bind b) u) t a2)).(\lambda (_: (((eq T t
+(TSort n)) \to (leq g a2 (ASort O n))))).(\lambda (H6: (eq T (THead (Bind b)
+u t) (TSort n))).(let H7 \def (eq_ind T (THead (Bind b) u t) (\lambda (ee:
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
+| (THead _ _ _) \Rightarrow True])) I (TSort n) H6) in (False_ind (leq g a2
+(ASort O n)) H7)))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 u (asucc g a1))).(\lambda (_: (((eq T u (TSort
+n)) \to (leq g (asucc g a1) (ASort O n))))).(\lambda (t: T).(\lambda (a2:
+A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t a2)).(\lambda (_: (((eq T
+t (TSort n)) \to (leq g a2 (ASort O n))))).(\lambda (H5: (eq T (THead (Bind
+Abst) u t) (TSort n))).(let H6 \def (eq_ind T (THead (Bind Abst) u t)
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort n) H5) in
+(False_ind (leq g (AHead a1 a2) (ASort O n)) H6)))))))))))) (\lambda (c0:
+C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u a1)).(\lambda
+(_: (((eq T u (TSort n)) \to (leq g a1 (ASort O n))))).(\lambda (t:
+T).(\lambda (a2: A).(\lambda (_: (arity g c0 t (AHead a1 a2))).(\lambda (_:
+(((eq T t (TSort n)) \to (leq g (AHead a1 a2) (ASort O n))))).(\lambda (H5:
+(eq T (THead (Flat Appl) u t) (TSort n))).(let H6 \def (eq_ind T (THead (Flat
+Appl) u t) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False |
(TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort n)
H5) in (False_ind (leq g a2 (ASort O n)) H6)))))))))))) (\lambda (c0:
C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_: (arity g c0 u (asucc g
n))))).(\lambda (t: T).(\lambda (_: (arity g c0 t a0)).(\lambda (_: (((eq T t
(TSort n)) \to (leq g a0 (ASort O n))))).(\lambda (H5: (eq T (THead (Flat
Cast) u t) (TSort n))).(let H6 \def (eq_ind T (THead (Flat Cast) u t)
-(\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
-True])) I (TSort n) H5) in (False_ind (leq g a0 (ASort O n)) H6)))))))))))
-(\lambda (c0: C).(\lambda (t: T).(\lambda (a1: A).(\lambda (H1: (arity g c0 t
-a1)).(\lambda (H2: (((eq T t (TSort n)) \to (leq g a1 (ASort O
-n))))).(\lambda (a2: A).(\lambda (H3: (leq g a1 a2)).(\lambda (H4: (eq T t
-(TSort n))).(let H5 \def (f_equal T T (\lambda (e: T).e) t (TSort n) H4) in
-(let H6 \def (eq_ind T t (\lambda (t0: T).((eq T t0 (TSort n)) \to (leq g a1
-(ASort O n)))) H2 (TSort n) H5) in (let H7 \def (eq_ind T t (\lambda (t0:
-T).(arity g c0 t0 a1)) H1 (TSort n) H5) in (leq_trans g a2 a1 (leq_sym g a1
-a2 H3) (ASort O n) (H6 (refl_equal T (TSort n))))))))))))))) c y a H0)))
-H))))).
-(* COMMENTS
-Initial nodes: 1235
-END *)
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort n) H5) in
+(False_ind (leq g a0 (ASort O n)) H6))))))))))) (\lambda (c0: C).(\lambda (t:
+T).(\lambda (a1: A).(\lambda (H1: (arity g c0 t a1)).(\lambda (H2: (((eq T t
+(TSort n)) \to (leq g a1 (ASort O n))))).(\lambda (a2: A).(\lambda (H3: (leq
+g a1 a2)).(\lambda (H4: (eq T t (TSort n))).(let H5 \def (f_equal T T
+(\lambda (e: T).e) t (TSort n) H4) in (let H6 \def (eq_ind T t (\lambda (t0:
+T).((eq T t0 (TSort n)) \to (leq g a1 (ASort O n)))) H2 (TSort n) H5) in (let
+H7 \def (eq_ind T t (\lambda (t0: T).(arity g c0 t0 a1)) H1 (TSort n) H5) in
+(leq_trans g a2 a1 (leq_sym g a1 a2 H3) (ASort O n) (H6 (refl_equal T (TSort
+n))))))))))))))) c y a H0))) H))))).
theorem arity_gen_lref:
\forall (g: G).(\forall (c: C).(\forall (i: nat).(\forall (a: A).((arity g c
C).(\lambda (u: T).(getl i c0 (CHead d (Bind Abst) u)))) (\lambda (d:
C).(\lambda (u: T).(arity g d u (asucc g a0)))))))))) (\lambda (c0:
C).(\lambda (n: nat).(\lambda (H1: (eq T (TSort n) (TLRef i))).(let H2 \def
-(eq_ind T (TSort n) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
-(THead _ _ _) \Rightarrow False])) I (TLRef i) H1) in (False_ind (or (ex2_2 C
-T (\lambda (d: C).(\lambda (u: T).(getl i c0 (CHead d (Bind Abbr) u))))
-(\lambda (d: C).(\lambda (u: T).(arity g d u (ASort O n))))) (ex2_2 C T
-(\lambda (d: C).(\lambda (u: T).(getl i c0 (CHead d (Bind Abst) u))))
-(\lambda (d: C).(\lambda (u: T).(arity g d u (asucc g (ASort O n)))))))
-H2))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i0:
-nat).(\lambda (H1: (getl i0 c0 (CHead d (Bind Abbr) u))).(\lambda (a0:
-A).(\lambda (H2: (arity g d u a0)).(\lambda (_: (((eq T u (TLRef i)) \to (or
-(ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i d (CHead d0 (Bind Abbr)
-u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a0)))) (ex2_2 C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i d (CHead d0 (Bind Abst) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g
-a0))))))))).(\lambda (H4: (eq T (TLRef i0) (TLRef i))).(let H5 \def (f_equal
-T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort
-_) \Rightarrow i0 | (TLRef n) \Rightarrow n | (THead _ _ _) \Rightarrow i0]))
-(TLRef i0) (TLRef i) H4) in (let H6 \def (eq_ind nat i0 (\lambda (n:
-nat).(getl n c0 (CHead d (Bind Abbr) u))) H1 i H5) in (or_introl (ex2_2 C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a0)))) (ex2_2 C T (\lambda
-(d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda
-(d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0))))) (ex2_2_intro C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a0))) d u H6 H2)))))))))))))
-(\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i0: nat).(\lambda
-(H1: (getl i0 c0 (CHead d (Bind Abst) u))).(\lambda (a0: A).(\lambda (H2:
-(arity g d u (asucc g a0))).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2
-C T (\lambda (d0: C).(\lambda (u0: T).(getl i d (CHead d0 (Bind Abbr) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0))))) (ex2_2 C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i d (CHead d0 (Bind Abst) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g (asucc g
-a0)))))))))).(\lambda (H4: (eq T (TLRef i0) (TLRef i))).(let H5 \def (f_equal
-T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort
-_) \Rightarrow i0 | (TLRef n) \Rightarrow n | (THead _ _ _) \Rightarrow i0]))
-(TLRef i0) (TLRef i) H4) in (let H6 \def (eq_ind nat i0 (\lambda (n:
-nat).(getl n c0 (CHead d (Bind Abst) u))) H1 i H5) in (or_intror (ex2_2 C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a0)))) (ex2_2 C T (\lambda
-(d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda
-(d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0))))) (ex2_2_intro C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0)))) d u H6
-H2))))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda
-(c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u
-a1)).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d:
+(eq_ind T (TSort n) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow
+True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I
+(TLRef i) H1) in (False_ind (or (ex2_2 C T (\lambda (d: C).(\lambda (u:
+T).(getl i c0 (CHead d (Bind Abbr) u)))) (\lambda (d: C).(\lambda (u:
+T).(arity g d u (ASort O n))))) (ex2_2 C T (\lambda (d: C).(\lambda (u:
+T).(getl i c0 (CHead d (Bind Abst) u)))) (\lambda (d: C).(\lambda (u:
+T).(arity g d u (asucc g (ASort O n))))))) H2))))) (\lambda (c0: C).(\lambda
+(d: C).(\lambda (u: T).(\lambda (i0: nat).(\lambda (H1: (getl i0 c0 (CHead d
+(Bind Abbr) u))).(\lambda (a0: A).(\lambda (H2: (arity g d u a0)).(\lambda
+(_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d0: C).(\lambda (u0:
+T).(getl i d (CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0:
+T).(arity g d0 u0 a0)))) (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i
+d (CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0
+u0 (asucc g a0))))))))).(\lambda (H4: (eq T (TLRef i0) (TLRef i))).(let H5
+\def (f_equal T nat (\lambda (e: T).(match e with [(TSort _) \Rightarrow i0 |
+(TLRef n) \Rightarrow n | (THead _ _ _) \Rightarrow i0])) (TLRef i0) (TLRef
+i) H4) in (let H6 \def (eq_ind nat i0 (\lambda (n: nat).(getl n c0 (CHead d
+(Bind Abbr) u))) H1 i H5) in (or_introl (ex2_2 C T (\lambda (d0: C).(\lambda
+(u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda
+(u0: T).(arity g d0 u0 a0)))) (ex2_2 C T (\lambda (d0: C).(\lambda (u0:
+T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0:
+T).(arity g d0 u0 (asucc g a0))))) (ex2_2_intro C T (\lambda (d0: C).(\lambda
+(u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda
+(u0: T).(arity g d0 u0 a0))) d u H6 H2))))))))))))) (\lambda (c0: C).(\lambda
+(d: C).(\lambda (u: T).(\lambda (i0: nat).(\lambda (H1: (getl i0 c0 (CHead d
+(Bind Abst) u))).(\lambda (a0: A).(\lambda (H2: (arity g d u (asucc g
+a0))).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i d (CHead d0 (Bind Abbr) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0))))) (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i d (CHead d0 (Bind Abst) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 (asucc g (asucc g a0)))))))))).(\lambda
+(H4: (eq T (TLRef i0) (TLRef i))).(let H5 \def (f_equal T nat (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow i0 | (TLRef n) \Rightarrow n | (THead
+_ _ _) \Rightarrow i0])) (TLRef i0) (TLRef i) H4) in (let H6 \def (eq_ind nat
+i0 (\lambda (n: nat).(getl n c0 (CHead d (Bind Abst) u))) H1 i H5) in
+(or_intror (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0
+(Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a0))))
+(ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst)
+u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0)))))
+(ex2_2_intro C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind
+Abst) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a0))))
+d u H6 H2))))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b
+Abst))).(\lambda (c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity
+g c0 u a1)).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d:
C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d:
C).(\lambda (u0: T).(arity g d u0 a1)))) (ex2_2 C T (\lambda (d: C).(\lambda
(u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0:
(CHead c0 (Bind b) u) (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda
(u0: T).(arity g d u0 (asucc g a2))))))))).(\lambda (H6: (eq T (THead (Bind
b) u t) (TLRef i))).(let H7 \def (eq_ind T (THead (Bind b) u t) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
-(TLRef i) H6) in (False_ind (or (ex2_2 C T (\lambda (d: C).(\lambda (u0:
-T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0:
-T).(arity g d u0 a2)))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i
-c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0
-(asucc g a2)))))) H7)))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda
-(a1: A).(\lambda (_: (arity g c0 u (asucc g a1))).(\lambda (_: (((eq T u
-(TLRef i)) \to (or (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0
-(CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0
-(asucc g a1))))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0
-(CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0
-(asucc g (asucc g a1)))))))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_:
-(arity g (CHead c0 (Bind Abst) u) t a2)).(\lambda (_: (((eq T t (TLRef i))
-\to (or (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i (CHead c0 (Bind
-Abst) u) (CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity
-g d u0 a2)))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i (CHead c0
-(Bind Abst) u) (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0:
-T).(arity g d u0 (asucc g a2))))))))).(\lambda (H5: (eq T (THead (Bind Abst)
-u t) (TLRef i))).(let H6 \def (eq_ind T (THead (Bind Abst) u t) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
-(TLRef i) H5) in (False_ind (or (ex2_2 C T (\lambda (d: C).(\lambda (u0:
-T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0:
-T).(arity g d u0 (AHead a1 a2))))) (ex2_2 C T (\lambda (d: C).(\lambda (u0:
-T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0:
-T).(arity g d u0 (asucc g (AHead a1 a2))))))) H6)))))))))))) (\lambda (c0:
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u a1)).(\lambda
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
+| (THead _ _ _) \Rightarrow True])) I (TLRef i) H6) in (False_ind (or (ex2_2
+C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0))))
+(\lambda (d: C).(\lambda (u0: T).(arity g d u0 a2)))) (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 (asucc g a2)))))) H7)))))))))))))) (\lambda
+(c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u (asucc g
+a1))).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 (asucc g a1))))) (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 (asucc g (asucc g a1)))))))))).(\lambda (t:
+T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t
+a2)).(\lambda (_: (((eq T t (TLRef i)) \to (or (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i (CHead c0 (Bind Abst) u) (CHead d (Bind Abbr)
+u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 a2)))) (ex2_2 C T
+(\lambda (d: C).(\lambda (u0: T).(getl i (CHead c0 (Bind Abst) u) (CHead d
+(Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g
+a2))))))))).(\lambda (H5: (eq T (THead (Bind Abst) u t) (TLRef i))).(let H6
+\def (eq_ind T (THead (Bind Abst) u t) (\lambda (ee: T).(match ee with
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
+\Rightarrow True])) I (TLRef i) H5) in (False_ind (or (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 (AHead a1 a2))))) (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 (asucc g (AHead a1 a2))))))) H6))))))))))))
+(\lambda (c0: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u
+a1)).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 a1)))) (ex2_2 C T (\lambda (d: C).(\lambda
+(u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0:
+T).(arity g d u0 (asucc g a1))))))))).(\lambda (t: T).(\lambda (a2:
+A).(\lambda (_: (arity g c0 t (AHead a1 a2))).(\lambda (_: (((eq T t (TLRef
+i)) \to (or (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d
+(Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 (AHead a1
+a2))))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind
+Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g (AHead
+a1 a2)))))))))).(\lambda (H5: (eq T (THead (Flat Appl) u t) (TLRef i))).(let
+H6 \def (eq_ind T (THead (Flat Appl) u t) (\lambda (ee: T).(match ee with
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
+\Rightarrow True])) I (TLRef i) H5) in (False_ind (or (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 a2)))) (ex2_2 C T (\lambda (d: C).(\lambda
+(u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0:
+T).(arity g d u0 (asucc g a2)))))) H6)))))))))))) (\lambda (c0: C).(\lambda
+(u: T).(\lambda (a0: A).(\lambda (_: (arity g c0 u (asucc g a0))).(\lambda
(_: (((eq T u (TLRef i)) \to (or (ex2_2 C T (\lambda (d: C).(\lambda (u0:
T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0:
-T).(arity g d u0 a1)))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i
-c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0
-(asucc g a1))))))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_: (arity g
-c0 t (AHead a1 a2))).(\lambda (_: (((eq T t (TLRef i)) \to (or (ex2_2 C T
+T).(arity g d u0 (asucc g a0))))) (ex2_2 C T (\lambda (d: C).(\lambda (u0:
+T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0:
+T).(arity g d u0 (asucc g (asucc g a0)))))))))).(\lambda (t: T).(\lambda (_:
+(arity g c0 t a0)).(\lambda (_: (((eq T t (TLRef i)) \to (or (ex2_2 C T
(\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0))))
-(\lambda (d: C).(\lambda (u0: T).(arity g d u0 (AHead a1 a2))))) (ex2_2 C T
-(\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst) u0))))
-(\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g (AHead a1
-a2)))))))))).(\lambda (H5: (eq T (THead (Flat Appl) u t) (TLRef i))).(let H6
-\def (eq_ind T (THead (Flat Appl) u t) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
+(\lambda (d: C).(\lambda (u0: T).(arity g d u0 a0)))) (ex2_2 C T (\lambda (d:
+C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst) u0)))) (\lambda (d:
+C).(\lambda (u0: T).(arity g d u0 (asucc g a0))))))))).(\lambda (H5: (eq T
+(THead (Flat Cast) u t) (TLRef i))).(let H6 \def (eq_ind T (THead (Flat Cast)
+u t) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef i) H5) in
(False_ind (or (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead
-d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 a2))))
+d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 a0))))
(ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst)
-u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g a2))))))
-H6)))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_:
-(arity g c0 u (asucc g a0))).(\lambda (_: (((eq T u (TLRef i)) \to (or (ex2_2
-C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abbr) u0))))
-(\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g a0))))) (ex2_2 C T
-(\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind Abst) u0))))
-(\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g (asucc g
-a0)))))))))).(\lambda (t: T).(\lambda (_: (arity g c0 t a0)).(\lambda (_:
-(((eq T t (TLRef i)) \to (or (ex2_2 C T (\lambda (d: C).(\lambda (u0:
-T).(getl i c0 (CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0:
-T).(arity g d u0 a0)))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i
-c0 (CHead d (Bind Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0
-(asucc g a0))))))))).(\lambda (H5: (eq T (THead (Flat Cast) u t) (TLRef
-i))).(let H6 \def (eq_ind T (THead (Flat Cast) u t) (\lambda (ee: T).(match
-ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False |
-(TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef i)
-H5) in (False_ind (or (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0
-(CHead d (Bind Abbr) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0
-a0)))) (ex2_2 C T (\lambda (d: C).(\lambda (u0: T).(getl i c0 (CHead d (Bind
-Abst) u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g a0))))))
+u0)))) (\lambda (d: C).(\lambda (u0: T).(arity g d u0 (asucc g a0))))))
H6))))))))))) (\lambda (c0: C).(\lambda (t: T).(\lambda (a1: A).(\lambda (H1:
(arity g c0 t a1)).(\lambda (H2: (((eq T t (TLRef i)) \to (or (ex2_2 C T
(\lambda (d: C).(\lambda (u: T).(getl i c0 (CHead d (Bind Abbr) u))))
(CHead d (Bind Abst) u)))) (\lambda (d: C).(\lambda (u: T).(arity g d u
(asucc g a2)))) x0 x1 H10 (arity_repl g x0 x1 (asucc g a1) H11 (asucc g a2)
(asucc_repl g a1 a2 H3)))))))) H9)) H8))))))))))))) c y a H0))) H))))).
-(* COMMENTS
-Initial nodes: 3853
-END *)
theorem arity_gen_bind:
\forall (b: B).((not (eq B b Abst)) \to (\forall (g: G).(\forall (c:
(a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t
a))))))) (\lambda (c0: C).(\lambda (n: nat).(\lambda (H2: (eq T (TSort n)
(THead (Bind b) u t))).(let H3 \def (eq_ind T (TSort n) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I
-(THead (Bind b) u t) H2) in (False_ind (ex2 A (\lambda (a1: A).(arity g c0 u
-a1)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t (ASort O n)))) H3)))))
-(\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda
-(_: (getl i c0 (CHead d (Bind Abbr) u0))).(\lambda (a: A).(\lambda (_: (arity
-g d u0 a)).(\lambda (_: (((eq T u0 (THead (Bind b) u t)) \to (ex2 A (\lambda
-(a1: A).(arity g d u a1)) (\lambda (_: A).(arity g (CHead d (Bind b) u) t
-a)))))).(\lambda (H5: (eq T (TLRef i) (THead (Bind b) u t))).(let H6 \def
-(eq_ind T (TLRef i) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
-(THead _ _ _) \Rightarrow False])) I (THead (Bind b) u t) H5) in (False_ind
+T).(match ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
+(THead _ _ _) \Rightarrow False])) I (THead (Bind b) u t) H2) in (False_ind
(ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity g (CHead c0
-(Bind b) u) t a))) H6))))))))))) (\lambda (c0: C).(\lambda (d: C).(\lambda
-(u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind Abst)
-u0))).(\lambda (a: A).(\lambda (_: (arity g d u0 (asucc g a))).(\lambda (_:
-(((eq T u0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a1: A).(arity g d u
+(Bind b) u) t (ASort O n)))) H3))))) (\lambda (c0: C).(\lambda (d:
+C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind
+Abbr) u0))).(\lambda (a: A).(\lambda (_: (arity g d u0 a)).(\lambda (_: (((eq
+T u0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a1: A).(arity g d u a1))
+(\lambda (_: A).(arity g (CHead d (Bind b) u) t a)))))).(\lambda (H5: (eq T
+(TLRef i) (THead (Bind b) u t))).(let H6 \def (eq_ind T (TLRef i) (\lambda
+(ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow
+True | (THead _ _ _) \Rightarrow False])) I (THead (Bind b) u t) H5) in
+(False_ind (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity
+g (CHead c0 (Bind b) u) t a))) H6))))))))))) (\lambda (c0: C).(\lambda (d:
+C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind
+Abst) u0))).(\lambda (a: A).(\lambda (_: (arity g d u0 (asucc g a))).(\lambda
+(_: (((eq T u0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a1: A).(arity g d u
a1)) (\lambda (_: A).(arity g (CHead d (Bind b) u) t (asucc g
a))))))).(\lambda (H5: (eq T (TLRef i) (THead (Bind b) u t))).(let H6 \def
-(eq_ind T (TLRef i) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
-(THead _ _ _) \Rightarrow False])) I (THead (Bind b) u t) H5) in (False_ind
-(ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity g (CHead c0
-(Bind b) u) t a))) H6))))))))))) (\lambda (b0: B).(\lambda (H2: (not (eq B b0
-Abst))).(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (H3:
-(arity g c0 u0 a1)).(\lambda (H4: (((eq T u0 (THead (Bind b) u t)) \to (ex2 A
-(\lambda (a3: A).(arity g c0 u a3)) (\lambda (_: A).(arity g (CHead c0 (Bind
-b) u) t a1)))))).(\lambda (t0: T).(\lambda (a0: A).(\lambda (H5: (arity g
-(CHead c0 (Bind b0) u0) t0 a0)).(\lambda (H6: (((eq T t0 (THead (Bind b) u
-t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind b0) u0) u a3))
-(\lambda (_: A).(arity g (CHead (CHead c0 (Bind b0) u0) (Bind b) u) t
-a0)))))).(\lambda (H7: (eq T (THead (Bind b0) u0 t0) (THead (Bind b) u
-t))).(let H8 \def (f_equal T B (\lambda (e: T).(match e in T return (\lambda
-(_: T).B) with [(TSort _) \Rightarrow b0 | (TLRef _) \Rightarrow b0 | (THead
-k _ _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b1)
+(eq_ind T (TLRef i) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow
+False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I
+(THead (Bind b) u t) H5) in (False_ind (ex2 A (\lambda (a1: A).(arity g c0 u
+a1)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a))) H6)))))))))))
+(\lambda (b0: B).(\lambda (H2: (not (eq B b0 Abst))).(\lambda (c0:
+C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (H3: (arity g c0 u0
+a1)).(\lambda (H4: (((eq T u0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3:
+A).(arity g c0 u a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t
+a1)))))).(\lambda (t0: T).(\lambda (a0: A).(\lambda (H5: (arity g (CHead c0
+(Bind b0) u0) t0 a0)).(\lambda (H6: (((eq T t0 (THead (Bind b) u t)) \to (ex2
+A (\lambda (a3: A).(arity g (CHead c0 (Bind b0) u0) u a3)) (\lambda (_:
+A).(arity g (CHead (CHead c0 (Bind b0) u0) (Bind b) u) t a0)))))).(\lambda
+(H7: (eq T (THead (Bind b0) u0 t0) (THead (Bind b) u t))).(let H8 \def
+(f_equal T B (\lambda (e: T).(match e with [(TSort _) \Rightarrow b0 | (TLRef
+_) \Rightarrow b0 | (THead k _ _) \Rightarrow (match k with [(Bind b1)
\Rightarrow b1 | (Flat _) \Rightarrow b0])])) (THead (Bind b0) u0 t0) (THead
-(Bind b) u t) H7) in ((let H9 \def (f_equal T T (\lambda (e: T).(match e in T
-return (\lambda (_: T).T) with [(TSort _) \Rightarrow u0 | (TLRef _)
-\Rightarrow u0 | (THead _ t1 _) \Rightarrow t1])) (THead (Bind b0) u0 t0)
-(THead (Bind b) u t) H7) in ((let H10 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t0 |
-(TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow t1])) (THead (Bind b0)
-u0 t0) (THead (Bind b) u t) H7) in (\lambda (H11: (eq T u0 u)).(\lambda (H12:
-(eq B b0 b)).(let H13 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead
-(Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind b0) u0) u
-a3)) (\lambda (_: A).(arity g (CHead (CHead c0 (Bind b0) u0) (Bind b) u) t
-a0))))) H6 t H10) in (let H14 \def (eq_ind T t0 (\lambda (t1: T).(arity g
-(CHead c0 (Bind b0) u0) t1 a0)) H5 t H10) in (let H15 \def (eq_ind T u0
-(\lambda (t1: T).((eq T t (THead (Bind b) u t)) \to (ex2 A (\lambda (a3:
-A).(arity g (CHead c0 (Bind b0) t1) u a3)) (\lambda (_: A).(arity g (CHead
-(CHead c0 (Bind b0) t1) (Bind b) u) t a0))))) H13 u H11) in (let H16 \def
-(eq_ind T u0 (\lambda (t1: T).(arity g (CHead c0 (Bind b0) t1) t a0)) H14 u
-H11) in (let H17 \def (eq_ind T u0 (\lambda (t1: T).((eq T t1 (THead (Bind b)
-u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (_: A).(arity g
-(CHead c0 (Bind b) u) t a1))))) H4 u H11) in (let H18 \def (eq_ind T u0
-(\lambda (t1: T).(arity g c0 t1 a1)) H3 u H11) in (let H19 \def (eq_ind B b0
-(\lambda (b1: B).((eq T t (THead (Bind b) u t)) \to (ex2 A (\lambda (a3:
-A).(arity g (CHead c0 (Bind b1) u) u a3)) (\lambda (_: A).(arity g (CHead
-(CHead c0 (Bind b1) u) (Bind b) u) t a0))))) H15 b H12) in (let H20 \def
-(eq_ind B b0 (\lambda (b1: B).(arity g (CHead c0 (Bind b1) u) t a0)) H16 b
-H12) in (let H21 \def (eq_ind B b0 (\lambda (b1: B).(not (eq B b1 Abst))) H2
-b H12) in (ex_intro2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (_:
-A).(arity g (CHead c0 (Bind b) u) t a0)) a1 H18 H20))))))))))))) H9))
-H8)))))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a1: A).(\lambda
-(H2: (arity g c0 u0 (asucc g a1))).(\lambda (H3: (((eq T u0 (THead (Bind b) u
-t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (_: A).(arity g
-(CHead c0 (Bind b) u) t (asucc g a1))))))).(\lambda (t0: T).(\lambda (a0:
-A).(\lambda (H4: (arity g (CHead c0 (Bind Abst) u0) t0 a0)).(\lambda (H5:
-(((eq T t0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead
-c0 (Bind Abst) u0) u a3)) (\lambda (_: A).(arity g (CHead (CHead c0 (Bind
-Abst) u0) (Bind b) u) t a0)))))).(\lambda (H6: (eq T (THead (Bind Abst) u0
-t0) (THead (Bind b) u t))).(let H7 \def (f_equal T B (\lambda (e: T).(match e
-in T return (\lambda (_: T).B) with [(TSort _) \Rightarrow Abst | (TLRef _)
-\Rightarrow Abst | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abst])]))
-(THead (Bind Abst) u0 t0) (THead (Bind b) u t) H6) in ((let H8 \def (f_equal
-T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
+(Bind b) u t) H7) in ((let H9 \def (f_equal T T (\lambda (e: T).(match e with
+[(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t1 _)
+\Rightarrow t1])) (THead (Bind b0) u0 t0) (THead (Bind b) u t) H7) in ((let
+H10 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0
+| (TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow t1])) (THead (Bind
+b0) u0 t0) (THead (Bind b) u t) H7) in (\lambda (H11: (eq T u0 u)).(\lambda
+(H12: (eq B b0 b)).(let H13 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1
+(THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind
+b0) u0) u a3)) (\lambda (_: A).(arity g (CHead (CHead c0 (Bind b0) u0) (Bind
+b) u) t a0))))) H6 t H10) in (let H14 \def (eq_ind T t0 (\lambda (t1:
+T).(arity g (CHead c0 (Bind b0) u0) t1 a0)) H5 t H10) in (let H15 \def
+(eq_ind T u0 (\lambda (t1: T).((eq T t (THead (Bind b) u t)) \to (ex2 A
+(\lambda (a3: A).(arity g (CHead c0 (Bind b0) t1) u a3)) (\lambda (_:
+A).(arity g (CHead (CHead c0 (Bind b0) t1) (Bind b) u) t a0))))) H13 u H11)
+in (let H16 \def (eq_ind T u0 (\lambda (t1: T).(arity g (CHead c0 (Bind b0)
+t1) t a0)) H14 u H11) in (let H17 \def (eq_ind T u0 (\lambda (t1: T).((eq T
+t1 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3))
+(\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a1))))) H4 u H11) in (let
+H18 \def (eq_ind T u0 (\lambda (t1: T).(arity g c0 t1 a1)) H3 u H11) in (let
+H19 \def (eq_ind B b0 (\lambda (b1: B).((eq T t (THead (Bind b) u t)) \to
+(ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind b1) u) u a3)) (\lambda (_:
+A).(arity g (CHead (CHead c0 (Bind b1) u) (Bind b) u) t a0))))) H15 b H12) in
+(let H20 \def (eq_ind B b0 (\lambda (b1: B).(arity g (CHead c0 (Bind b1) u) t
+a0)) H16 b H12) in (let H21 \def (eq_ind B b0 (\lambda (b1: B).(not (eq B b1
+Abst))) H2 b H12) in (ex_intro2 A (\lambda (a3: A).(arity g c0 u a3))
+(\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a0)) a1 H18 H20)))))))))))))
+H9)) H8)))))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
+A).(\lambda (H2: (arity g c0 u0 (asucc g a1))).(\lambda (H3: (((eq T u0
+(THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda
+(_: A).(arity g (CHead c0 (Bind b) u) t (asucc g a1))))))).(\lambda (t0:
+T).(\lambda (a0: A).(\lambda (H4: (arity g (CHead c0 (Bind Abst) u0) t0
+a0)).(\lambda (H5: (((eq T t0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3:
+A).(arity g (CHead c0 (Bind Abst) u0) u a3)) (\lambda (_: A).(arity g (CHead
+(CHead c0 (Bind Abst) u0) (Bind b) u) t a0)))))).(\lambda (H6: (eq T (THead
+(Bind Abst) u0 t0) (THead (Bind b) u t))).(let H7 \def (f_equal T B (\lambda
+(e: T).(match e with [(TSort _) \Rightarrow Abst | (TLRef _) \Rightarrow Abst
+| (THead k _ _) \Rightarrow (match k with [(Bind b0) \Rightarrow b0 | (Flat
+_) \Rightarrow Abst])])) (THead (Bind Abst) u0 t0) (THead (Bind b) u t) H6)
+in ((let H8 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
\Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t1 _) \Rightarrow t1]))
(THead (Bind Abst) u0 t0) (THead (Bind b) u t) H6) in ((let H9 \def (f_equal
-T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow t1]))
-(THead (Bind Abst) u0 t0) (THead (Bind b) u t) H6) in (\lambda (H10: (eq T u0
-u)).(\lambda (H11: (eq B Abst b)).(let H12 \def (eq_ind T t0 (\lambda (t1:
-T).((eq T t1 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g
-(CHead c0 (Bind Abst) u0) u a3)) (\lambda (_: A).(arity g (CHead (CHead c0
-(Bind Abst) u0) (Bind b) u) t a0))))) H5 t H9) in (let H13 \def (eq_ind T t0
-(\lambda (t1: T).(arity g (CHead c0 (Bind Abst) u0) t1 a0)) H4 t H9) in (let
-H14 \def (eq_ind T u0 (\lambda (t1: T).((eq T t (THead (Bind b) u t)) \to
-(ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind Abst) t1) u a3)) (\lambda
-(_: A).(arity g (CHead (CHead c0 (Bind Abst) t1) (Bind b) u) t a0))))) H12 u
-H10) in (let H15 \def (eq_ind T u0 (\lambda (t1: T).(arity g (CHead c0 (Bind
-Abst) t1) t a0)) H13 u H10) in (let H16 \def (eq_ind T u0 (\lambda (t1:
-T).((eq T t1 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u
-a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t (asucc g a1)))))) H3 u
-H10) in (let H17 \def (eq_ind T u0 (\lambda (t1: T).(arity g c0 t1 (asucc g
-a1))) H2 u H10) in (let H18 \def (eq_ind_r B b (\lambda (b0: B).((eq T t
-(THead (Bind b0) u t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind
-Abst) u) u a3)) (\lambda (_: A).(arity g (CHead (CHead c0 (Bind Abst) u)
-(Bind b0) u) t a0))))) H14 Abst H11) in (let H19 \def (eq_ind_r B b (\lambda
-(b0: B).((eq T u (THead (Bind b0) u t)) \to (ex2 A (\lambda (a3: A).(arity g
-c0 u a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b0) u) t (asucc g a1))))))
-H16 Abst H11) in (let H20 \def (eq_ind_r B b (\lambda (b0: B).(not (eq B b0
-Abst))) H Abst H11) in (eq_ind B Abst (\lambda (b0: B).(ex2 A (\lambda (a3:
-A).(arity g c0 u a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b0) u) t
-(AHead a1 a0))))) (let H21 \def (match (H20 (refl_equal B Abst)) in False
-return (\lambda (_: False).(ex2 A (\lambda (a3: A).(arity g c0 u a3))
-(\lambda (_: A).(arity g (CHead c0 (Bind Abst) u) t (AHead a1 a0))))) with
-[]) in H21) b H11))))))))))))) H8)) H7)))))))))))) (\lambda (c0: C).(\lambda
-(u0: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u0 a1)).(\lambda (_: (((eq
-T u0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3))
-(\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a1)))))).(\lambda (t0:
-T).(\lambda (a0: A).(\lambda (_: (arity g c0 t0 (AHead a1 a0))).(\lambda (_:
-(((eq T t0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u
-a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t (AHead a1
-a0))))))).(\lambda (H6: (eq T (THead (Flat Appl) u0 t0) (THead (Bind b) u
-t))).(let H7 \def (eq_ind T (THead (Flat Appl) u0 t0) (\lambda (ee: T).(match
-ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False |
-(TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
-True])])) I (THead (Bind b) u t) H6) in (False_ind (ex2 A (\lambda (a3:
-A).(arity g c0 u a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a0)))
-H7)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a: A).(\lambda (_:
-(arity g c0 u0 (asucc g a))).(\lambda (_: (((eq T u0 (THead (Bind b) u t))
-\to (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity g
-(CHead c0 (Bind b) u) t (asucc g a))))))).(\lambda (t0: T).(\lambda (_:
-(arity g c0 t0 a)).(\lambda (_: (((eq T t0 (THead (Bind b) u t)) \to (ex2 A
+T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef _)
+\Rightarrow t0 | (THead _ _ t1) \Rightarrow t1])) (THead (Bind Abst) u0 t0)
+(THead (Bind b) u t) H6) in (\lambda (H10: (eq T u0 u)).(\lambda (H11: (eq B
+Abst b)).(let H12 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead (Bind
+b) u t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u0) u
+a3)) (\lambda (_: A).(arity g (CHead (CHead c0 (Bind Abst) u0) (Bind b) u) t
+a0))))) H5 t H9) in (let H13 \def (eq_ind T t0 (\lambda (t1: T).(arity g
+(CHead c0 (Bind Abst) u0) t1 a0)) H4 t H9) in (let H14 \def (eq_ind T u0
+(\lambda (t1: T).((eq T t (THead (Bind b) u t)) \to (ex2 A (\lambda (a3:
+A).(arity g (CHead c0 (Bind Abst) t1) u a3)) (\lambda (_: A).(arity g (CHead
+(CHead c0 (Bind Abst) t1) (Bind b) u) t a0))))) H12 u H10) in (let H15 \def
+(eq_ind T u0 (\lambda (t1: T).(arity g (CHead c0 (Bind Abst) t1) t a0)) H13 u
+H10) in (let H16 \def (eq_ind T u0 (\lambda (t1: T).((eq T t1 (THead (Bind b)
+u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (_: A).(arity g
+(CHead c0 (Bind b) u) t (asucc g a1)))))) H3 u H10) in (let H17 \def (eq_ind
+T u0 (\lambda (t1: T).(arity g c0 t1 (asucc g a1))) H2 u H10) in (let H18
+\def (eq_ind_r B b (\lambda (b0: B).((eq T t (THead (Bind b0) u t)) \to (ex2
+A (\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u) u a3)) (\lambda (_:
+A).(arity g (CHead (CHead c0 (Bind Abst) u) (Bind b0) u) t a0))))) H14 Abst
+H11) in (let H19 \def (eq_ind_r B b (\lambda (b0: B).((eq T u (THead (Bind
+b0) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (_:
+A).(arity g (CHead c0 (Bind b0) u) t (asucc g a1)))))) H16 Abst H11) in (let
+H20 \def (eq_ind_r B b (\lambda (b0: B).(not (eq B b0 Abst))) H Abst H11) in
+(eq_ind B Abst (\lambda (b0: B).(ex2 A (\lambda (a3: A).(arity g c0 u a3))
+(\lambda (_: A).(arity g (CHead c0 (Bind b0) u) t (AHead a1 a0))))) (let H21
+\def (match (H20 (refl_equal B Abst)) in False with []) in H21) b
+H11))))))))))))) H8)) H7)))))))))))) (\lambda (c0: C).(\lambda (u0:
+T).(\lambda (a1: A).(\lambda (_: (arity g c0 u0 a1)).(\lambda (_: (((eq T u0
+(THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda
+(_: A).(arity g (CHead c0 (Bind b) u) t a1)))))).(\lambda (t0: T).(\lambda
+(a0: A).(\lambda (_: (arity g c0 t0 (AHead a1 a0))).(\lambda (_: (((eq T t0
+(THead (Bind b) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda
+(_: A).(arity g (CHead c0 (Bind b) u) t (AHead a1 a0))))))).(\lambda (H6: (eq
+T (THead (Flat Appl) u0 t0) (THead (Bind b) u t))).(let H7 \def (eq_ind T
+(THead (Flat Appl) u0 t0) (\lambda (ee: T).(match ee with [(TSort _)
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
+(match k with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I
+(THead (Bind b) u t) H6) in (False_ind (ex2 A (\lambda (a3: A).(arity g c0 u
+a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a0))) H7))))))))))))
+(\lambda (c0: C).(\lambda (u0: T).(\lambda (a: A).(\lambda (_: (arity g c0 u0
+(asucc g a))).(\lambda (_: (((eq T u0 (THead (Bind b) u t)) \to (ex2 A
(\lambda (a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity g (CHead c0 (Bind
-b) u) t a)))))).(\lambda (H6: (eq T (THead (Flat Cast) u0 t0) (THead (Bind b)
-u t))).(let H7 \def (eq_ind T (THead (Flat Cast) u0 t0) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K
-return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _)
+b) u) t (asucc g a))))))).(\lambda (t0: T).(\lambda (_: (arity g c0 t0
+a)).(\lambda (_: (((eq T t0 (THead (Bind b) u t)) \to (ex2 A (\lambda (a1:
+A).(arity g c0 u a1)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t
+a)))))).(\lambda (H6: (eq T (THead (Flat Cast) u0 t0) (THead (Bind b) u
+t))).(let H7 \def (eq_ind T (THead (Flat Cast) u0 t0) (\lambda (ee: T).(match
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k
+_ _) \Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat _)
\Rightarrow True])])) I (THead (Bind b) u t) H6) in (False_ind (ex2 A
(\lambda (a1: A).(arity g c0 u a1)) (\lambda (_: A).(arity g (CHead c0 (Bind
b) u) t a))) H7))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda (a1:
c0 u a3)) (\lambda (_: A).(arity g (CHead c0 (Bind b) u) t a0)) x H10
(arity_repl g (CHead c0 (Bind b) u) t a1 H11 a0 H4))))) H9))))))))))))) c y
a2 H1))) H0)))))))).
-(* COMMENTS
-Initial nodes: 3365
-END *)
theorem arity_gen_abst:
\forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (a:
A).(arity g c0 u (asucc g a1)))) (\lambda (_: A).(\lambda (a2: A).(arity g
(CHead c0 (Bind Abst) u) t a2)))))))) (\lambda (c0: C).(\lambda (n:
nat).(\lambda (H1: (eq T (TSort n) (THead (Bind Abst) u t))).(let H2 \def
-(eq_ind T (TSort n) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
-(THead _ _ _) \Rightarrow False])) I (THead (Bind Abst) u t) H1) in
-(False_ind (ex3_2 A A (\lambda (a1: A).(\lambda (a2: A).(eq A (ASort O n)
-(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)))) H2))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i:
-nat).(\lambda (_: (getl i c0 (CHead d (Bind Abbr) u0))).(\lambda (a0:
-A).(\lambda (_: (arity g d u0 a0)).(\lambda (_: (((eq T u0 (THead (Bind Abst)
-u t)) \to (ex3_2 A A (\lambda (a1: A).(\lambda (a2: A).(eq A a0 (AHead a1
-a2)))) (\lambda (a1: A).(\lambda (_: A).(arity g d u (asucc g a1)))) (\lambda
-(_: A).(\lambda (a2: A).(arity g (CHead d (Bind Abst) u) t a2))))))).(\lambda
-(H4: (eq T (TLRef i) (THead (Bind Abst) u t))).(let H5 \def (eq_ind T (TLRef
-i) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
-False])) I (THead (Bind Abst) u t) H4) in (False_ind (ex3_2 A A (\lambda (a1:
-A).(\lambda (a2: A).(eq A a0 (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)))) H5))))))))))) (\lambda (c0: C).(\lambda (d:
-C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind
-Abst) u0))).(\lambda (a0: A).(\lambda (_: (arity g d u0 (asucc g
-a0))).(\lambda (_: (((eq T u0 (THead (Bind Abst) u t)) \to (ex3_2 A A
-(\lambda (a1: A).(\lambda (a2: A).(eq A (asucc g a0) (AHead a1 a2))))
+(eq_ind T (TSort n) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow
+True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I
+(THead (Bind Abst) u t) H1) in (False_ind (ex3_2 A A (\lambda (a1:
+A).(\lambda (a2: A).(eq A (ASort O n) (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)))) H2))))) (\lambda (c0:
+C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0
+(CHead d (Bind Abbr) u0))).(\lambda (a0: A).(\lambda (_: (arity g d u0
+a0)).(\lambda (_: (((eq T u0 (THead (Bind Abst) u t)) \to (ex3_2 A A (\lambda
+(a1: A).(\lambda (a2: A).(eq A a0 (AHead a1 a2)))) (\lambda (a1: A).(\lambda
+(_: A).(arity g d u (asucc g a1)))) (\lambda (_: A).(\lambda (a2: A).(arity g
+(CHead d (Bind Abst) u) t a2))))))).(\lambda (H4: (eq T (TLRef i) (THead
+(Bind Abst) u t))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _
+_ _) \Rightarrow False])) I (THead (Bind Abst) u t) H4) in (False_ind (ex3_2
+A A (\lambda (a1: A).(\lambda (a2: A).(eq A a0 (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)))) H5))))))))))) (\lambda
+(c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl
+i c0 (CHead d (Bind Abst) u0))).(\lambda (a0: A).(\lambda (_: (arity g d u0
+(asucc g a0))).(\lambda (_: (((eq T u0 (THead (Bind Abst) u t)) \to (ex3_2 A
+A (\lambda (a1: A).(\lambda (a2: A).(eq A (asucc g a0) (AHead a1 a2))))
(\lambda (a1: A).(\lambda (_: A).(arity g d u (asucc g a1)))) (\lambda (_:
A).(\lambda (a2: A).(arity g (CHead d (Bind Abst) u) t a2))))))).(\lambda
(H4: (eq T (TLRef i) (THead (Bind Abst) u t))).(let H5 \def (eq_ind T (TLRef
-i) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
-False])) I (THead (Bind Abst) u t) H4) in (False_ind (ex3_2 A A (\lambda (a1:
-A).(\lambda (a2: A).(eq A a0 (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)))) H5))))))))))) (\lambda (b: B).(\lambda (H1:
-(not (eq B b Abst))).(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
-A).(\lambda (H2: (arity g c0 u0 a1)).(\lambda (H3: (((eq T u0 (THead (Bind
-Abst) u t)) \to (ex3_2 A A (\lambda (a2: A).(\lambda (a3: A).(eq A a1 (AHead
-a2 a3)))) (\lambda (a2: A).(\lambda (_: A).(arity g c0 u (asucc g a2))))
-(\lambda (_: A).(\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u) t
-a3))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (H4: (arity g (CHead c0
-(Bind b) u0) t0 a2)).(\lambda (H5: (((eq T t0 (THead (Bind Abst) u t)) \to
-(ex3_2 A A (\lambda (a3: A).(\lambda (a4: A).(eq A a2 (AHead a3 a4))))
-(\lambda (a3: A).(\lambda (_: A).(arity g (CHead c0 (Bind b) u0) u (asucc g
-a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead (CHead c0 (Bind b)
-u0) (Bind Abst) u) t a4))))))).(\lambda (H6: (eq T (THead (Bind b) u0 t0)
-(THead (Bind Abst) u t))).(let H7 \def (f_equal T B (\lambda (e: T).(match e
-in T return (\lambda (_: T).B) with [(TSort _) \Rightarrow b | (TLRef _)
-\Rightarrow b | (THead k _ _) \Rightarrow (match k in K return (\lambda (_:
-K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow b])])) (THead
-(Bind b) u0 t0) (THead (Bind Abst) u t) H6) in ((let H8 \def (f_equal T T
-(\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t1 _) \Rightarrow t1]))
-(THead (Bind b) u0 t0) (THead (Bind Abst) u t) H6) in ((let H9 \def (f_equal
-T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
+i) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Bind Abst) u
+t) H4) in (False_ind (ex3_2 A A (\lambda (a1: A).(\lambda (a2: A).(eq A a0
+(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)))) H5))))))))))) (\lambda (b: B).(\lambda (H1: (not (eq B b
+Abst))).(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (H2:
+(arity g c0 u0 a1)).(\lambda (H3: (((eq T u0 (THead (Bind Abst) u t)) \to
+(ex3_2 A A (\lambda (a2: A).(\lambda (a3: A).(eq A a1 (AHead a2 a3))))
+(\lambda (a2: A).(\lambda (_: A).(arity g c0 u (asucc g a2)))) (\lambda (_:
+A).(\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u) t a3))))))).(\lambda
+(t0: T).(\lambda (a2: A).(\lambda (H4: (arity g (CHead c0 (Bind b) u0) t0
+a2)).(\lambda (H5: (((eq T t0 (THead (Bind Abst) u t)) \to (ex3_2 A A
+(\lambda (a3: A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (\lambda (a3:
+A).(\lambda (_: A).(arity g (CHead c0 (Bind b) u0) u (asucc g a3)))) (\lambda
+(_: A).(\lambda (a4: A).(arity g (CHead (CHead c0 (Bind b) u0) (Bind Abst) u)
+t a4))))))).(\lambda (H6: (eq T (THead (Bind b) u0 t0) (THead (Bind Abst) u
+t))).(let H7 \def (f_equal T B (\lambda (e: T).(match e with [(TSort _)
+\Rightarrow b | (TLRef _) \Rightarrow b | (THead k _ _) \Rightarrow (match k
+with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow b])])) (THead (Bind b)
+u0 t0) (THead (Bind Abst) u t) H6) in ((let H8 \def (f_equal T T (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 |
+(THead _ t1 _) \Rightarrow t1])) (THead (Bind b) u0 t0) (THead (Bind Abst) u
+t) H6) in ((let H9 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
\Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow t1]))
(THead (Bind b) u0 t0) (THead (Bind Abst) u t) H6) in (\lambda (H10: (eq T u0
u)).(\lambda (H11: (eq B b Abst)).(let H12 \def (eq_ind T t0 (\lambda (t1:
H19 \def (eq_ind B b (\lambda (b0: B).(arity g (CHead c0 (Bind b0) u) t a2))
H15 Abst H11) in (let H20 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0
Abst))) H1 Abst H11) in (let H21 \def (match (H20 (refl_equal B Abst)) in
-False return (\lambda (_: False).(ex3_2 A A (\lambda (a3: A).(\lambda (a4:
-A).(eq A a2 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_: A).(arity g c0 u
-(asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead c0 (Bind
-Abst) u) t a4))))) with []) in H21))))))))))))) H8)) H7))))))))))))))
-(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (H1: (arity g c0
-u0 (asucc g a1))).(\lambda (H2: (((eq T u0 (THead (Bind Abst) u t)) \to
-(ex3_2 A A (\lambda (a2: A).(\lambda (a3: A).(eq A (asucc g a1) (AHead a2
-a3)))) (\lambda (a2: A).(\lambda (_: A).(arity g c0 u (asucc g a2))))
-(\lambda (_: A).(\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u) t
-a3))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (H3: (arity g (CHead c0
-(Bind Abst) u0) t0 a2)).(\lambda (H4: (((eq T t0 (THead (Bind Abst) u t)) \to
-(ex3_2 A A (\lambda (a3: A).(\lambda (a4: A).(eq A a2 (AHead a3 a4))))
-(\lambda (a3: A).(\lambda (_: A).(arity g (CHead c0 (Bind Abst) u0) u (asucc
-g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead (CHead c0 (Bind
-Abst) u0) (Bind Abst) u) t a4))))))).(\lambda (H5: (eq T (THead (Bind Abst)
-u0 t0) (THead (Bind Abst) u t))).(let H6 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow u0 |
-(TLRef _) \Rightarrow u0 | (THead _ t1 _) \Rightarrow t1])) (THead (Bind
-Abst) u0 t0) (THead (Bind Abst) u t) H5) in ((let H7 \def (f_equal T T
-(\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
+False with []) in H21))))))))))))) H8)) H7)))))))))))))) (\lambda (c0:
+C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (H1: (arity g c0 u0 (asucc g
+a1))).(\lambda (H2: (((eq T u0 (THead (Bind Abst) u t)) \to (ex3_2 A A
+(\lambda (a2: A).(\lambda (a3: A).(eq A (asucc g a1) (AHead a2 a3))))
+(\lambda (a2: A).(\lambda (_: A).(arity g c0 u (asucc g a2)))) (\lambda (_:
+A).(\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u) t a3))))))).(\lambda
+(t0: T).(\lambda (a2: A).(\lambda (H3: (arity g (CHead c0 (Bind Abst) u0) t0
+a2)).(\lambda (H4: (((eq T t0 (THead (Bind Abst) u t)) \to (ex3_2 A A
+(\lambda (a3: A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (\lambda (a3:
+A).(\lambda (_: A).(arity g (CHead c0 (Bind Abst) u0) u (asucc g a3))))
+(\lambda (_: A).(\lambda (a4: A).(arity g (CHead (CHead c0 (Bind Abst) u0)
+(Bind Abst) u) t a4))))))).(\lambda (H5: (eq T (THead (Bind Abst) u0 t0)
+(THead (Bind Abst) u t))).(let H6 \def (f_equal T T (\lambda (e: T).(match e
+with [(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t1 _)
+\Rightarrow t1])) (THead (Bind Abst) u0 t0) (THead (Bind Abst) u t) H5) in
+((let H7 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
\Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow t1]))
(THead (Bind Abst) u0 t0) (THead (Bind Abst) u t) H5) in (\lambda (H8: (eq T
u0 u)).(let H9 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead (Bind
A).(\lambda (_: A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda
(a4: A).(arity g (CHead c0 (Bind Abst) u) t a4))))))).(\lambda (H5: (eq T
(THead (Flat Appl) u0 t0) (THead (Bind Abst) u t))).(let H6 \def (eq_ind T
-(THead (Flat Appl) u0 t0) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind
-Abst) u t) H5) in (False_ind (ex3_2 A A (\lambda (a3: A).(\lambda (a4: A).(eq
-A a2 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_: A).(arity g c0 u (asucc g
-a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead c0 (Bind Abst) u) t
-a4)))) H6)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a0:
-A).(\lambda (_: (arity g c0 u0 (asucc g a0))).(\lambda (_: (((eq T u0 (THead
-(Bind Abst) u t)) \to (ex3_2 A A (\lambda (a1: A).(\lambda (a2: A).(eq A
-(asucc g a0) (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))))))).(\lambda (t0: T).(\lambda (_: (arity g c0 t0
-a0)).(\lambda (_: (((eq T t0 (THead (Bind Abst) u t)) \to (ex3_2 A A (\lambda
-(a1: A).(\lambda (a2: A).(eq A a0 (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))))))).(\lambda (H5: (eq T (THead (Flat Cast)
-u0 t0) (THead (Bind Abst) u t))).(let H6 \def (eq_ind T (THead (Flat Cast) u0
-t0) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
-\Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind Abst) u t)
-H5) in (False_ind (ex3_2 A A (\lambda (a1: A).(\lambda (a2: A).(eq A a0
-(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)))) H6))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda (a1:
-A).(\lambda (H1: (arity g c0 t0 a1)).(\lambda (H2: (((eq T t0 (THead (Bind
-Abst) u t)) \to (ex3_2 A A (\lambda (a2: A).(\lambda (a3: A).(eq A a1 (AHead
-a2 a3)))) (\lambda (a2: A).(\lambda (_: A).(arity g c0 u (asucc g a2))))
-(\lambda (_: A).(\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u) t
-a3))))))).(\lambda (a2: A).(\lambda (H3: (leq g a1 a2)).(\lambda (H4: (eq T
-t0 (THead (Bind Abst) u t))).(let H5 \def (f_equal T T (\lambda (e: T).e) t0
-(THead (Bind Abst) u t) H4) in (let H6 \def (eq_ind T t0 (\lambda (t1:
-T).((eq T t1 (THead (Bind Abst) u t)) \to (ex3_2 A A (\lambda (a3:
+(THead (Flat Appl) u0 t0) (\lambda (ee: T).(match ee with [(TSort _)
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
+(match k with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I
+(THead (Bind Abst) u t) H5) in (False_ind (ex3_2 A A (\lambda (a3:
+A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_:
+A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g
+(CHead c0 (Bind Abst) u) t a4)))) H6)))))))))))) (\lambda (c0: C).(\lambda
+(u0: T).(\lambda (a0: A).(\lambda (_: (arity g c0 u0 (asucc g a0))).(\lambda
+(_: (((eq T u0 (THead (Bind Abst) u t)) \to (ex3_2 A A (\lambda (a1:
+A).(\lambda (a2: A).(eq A (asucc g a0) (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))))))).(\lambda (t0:
+T).(\lambda (_: (arity g c0 t0 a0)).(\lambda (_: (((eq T t0 (THead (Bind
+Abst) u t)) \to (ex3_2 A A (\lambda (a1: A).(\lambda (a2: A).(eq A a0 (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))))))).(\lambda (H5: (eq T (THead (Flat Cast) u0 t0) (THead (Bind Abst) u
+t))).(let H6 \def (eq_ind T (THead (Flat Cast) u0 t0) (\lambda (ee: T).(match
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k
+_ _) \Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat _)
+\Rightarrow True])])) I (THead (Bind Abst) u t) H5) in (False_ind (ex3_2 A A
+(\lambda (a1: A).(\lambda (a2: A).(eq A a0 (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)))) H6))))))))))) (\lambda
+(c0: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (H1: (arity g c0 t0
+a1)).(\lambda (H2: (((eq T t0 (THead (Bind Abst) u t)) \to (ex3_2 A A
+(\lambda (a2: A).(\lambda (a3: A).(eq A a1 (AHead a2 a3)))) (\lambda (a2:
+A).(\lambda (_: A).(arity g c0 u (asucc g a2)))) (\lambda (_: A).(\lambda
+(a3: A).(arity g (CHead c0 (Bind Abst) u) t a3))))))).(\lambda (a2:
+A).(\lambda (H3: (leq g a1 a2)).(\lambda (H4: (eq T t0 (THead (Bind Abst) u
+t))).(let H5 \def (f_equal T T (\lambda (e: T).e) t0 (THead (Bind Abst) u t)
+H4) in (let H6 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead (Bind
+Abst) u t)) \to (ex3_2 A A (\lambda (a3: A).(\lambda (a4: A).(eq A a1 (AHead
+a3 a4)))) (\lambda (a3: A).(\lambda (_: A).(arity g c0 u (asucc g a3))))
+(\lambda (_: A).(\lambda (a4: A).(arity g (CHead c0 (Bind Abst) u) t a4))))))
+H2 (THead (Bind Abst) u t) H5) in (let H7 \def (eq_ind T t0 (\lambda (t1:
+T).(arity g c0 t1 a1)) H1 (THead (Bind Abst) u t) H5) in (let H8 \def (H6
+(refl_equal T (THead (Bind Abst) u t))) in (ex3_2_ind A A (\lambda (a3:
A).(\lambda (a4: A).(eq A a1 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_:
A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g
-(CHead c0 (Bind Abst) u) t a4)))))) H2 (THead (Bind Abst) u t) H5) in (let H7
-\def (eq_ind T t0 (\lambda (t1: T).(arity g c0 t1 a1)) H1 (THead (Bind Abst)
-u t) H5) in (let H8 \def (H6 (refl_equal T (THead (Bind Abst) u t))) in
-(ex3_2_ind A A (\lambda (a3: A).(\lambda (a4: A).(eq A a1 (AHead a3 a4))))
-(\lambda (a3: A).(\lambda (_: A).(arity g c0 u (asucc g a3)))) (\lambda (_:
-A).(\lambda (a4: A).(arity g (CHead c0 (Bind Abst) u) t a4))) (ex3_2 A A
-(\lambda (a3: A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (\lambda (a3:
-A).(\lambda (_: A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda
-(a4: A).(arity g (CHead c0 (Bind Abst) u) t a4)))) (\lambda (x0: A).(\lambda
-(x1: A).(\lambda (H9: (eq A a1 (AHead x0 x1))).(\lambda (H10: (arity g c0 u
-(asucc g x0))).(\lambda (H11: (arity g (CHead c0 (Bind Abst) u) t x1)).(let
-H12 \def (eq_ind A a1 (\lambda (a0: A).(leq g a0 a2)) H3 (AHead x0 x1) H9) in
-(let H13 \def (eq_ind A a1 (\lambda (a0: A).(arity g c0 (THead (Bind Abst) u
-t) a0)) H7 (AHead x0 x1) H9) in (let H_x \def (leq_gen_head1 g x0 x1 a2 H12)
-in (let H14 \def H_x in (ex3_2_ind A A (\lambda (a3: A).(\lambda (_: A).(leq
-g x0 a3))) (\lambda (_: A).(\lambda (a4: A).(leq g x1 a4))) (\lambda (a3:
-A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (ex3_2 A A (\lambda (a3:
-A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_:
+(CHead c0 (Bind Abst) u) t a4))) (ex3_2 A A (\lambda (a3: A).(\lambda (a4:
+A).(eq A a2 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_: A).(arity g c0 u
+(asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead c0 (Bind
+Abst) u) t a4)))) (\lambda (x0: A).(\lambda (x1: A).(\lambda (H9: (eq A a1
+(AHead x0 x1))).(\lambda (H10: (arity g c0 u (asucc g x0))).(\lambda (H11:
+(arity g (CHead c0 (Bind Abst) u) t x1)).(let H12 \def (eq_ind A a1 (\lambda
+(a0: A).(leq g a0 a2)) H3 (AHead x0 x1) H9) in (let H13 \def (eq_ind A a1
+(\lambda (a0: A).(arity g c0 (THead (Bind Abst) u t) a0)) H7 (AHead x0 x1)
+H9) in (let H_x \def (leq_gen_head1 g x0 x1 a2 H12) in (let H14 \def H_x in
+(ex3_2_ind A A (\lambda (a3: A).(\lambda (_: A).(leq g x0 a3))) (\lambda (_:
+A).(\lambda (a4: A).(leq g x1 a4))) (\lambda (a3: A).(\lambda (a4: A).(eq A
+a2 (AHead a3 a4)))) (ex3_2 A A (\lambda (a3: A).(\lambda (a4: A).(eq A a2
+(AHead a3 a4)))) (\lambda (a3: A).(\lambda (_: A).(arity g c0 u (asucc g
+a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead c0 (Bind Abst) u) t
+a4)))) (\lambda (x2: A).(\lambda (x3: A).(\lambda (H15: (leq g x0
+x2)).(\lambda (H16: (leq g x1 x3)).(\lambda (H17: (eq A a2 (AHead x2
+x3))).(let H18 \def (f_equal A A (\lambda (e: A).e) a2 (AHead x2 x3) H17) in
+(eq_ind_r A (AHead x2 x3) (\lambda (a0: A).(ex3_2 A A (\lambda (a3:
+A).(\lambda (a4: A).(eq A a0 (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_:
A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g
-(CHead c0 (Bind Abst) u) t a4)))) (\lambda (x2: A).(\lambda (x3: A).(\lambda
-(H15: (leq g x0 x2)).(\lambda (H16: (leq g x1 x3)).(\lambda (H17: (eq A a2
-(AHead x2 x3))).(let H18 \def (f_equal A A (\lambda (e: A).e) a2 (AHead x2
-x3) H17) in (eq_ind_r A (AHead x2 x3) (\lambda (a0: A).(ex3_2 A A (\lambda
-(a3: A).(\lambda (a4: A).(eq A a0 (AHead a3 a4)))) (\lambda (a3: A).(\lambda
-(_: A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity
-g (CHead c0 (Bind Abst) u) t a4))))) (ex3_2_intro A A (\lambda (a3:
-A).(\lambda (a4: A).(eq A (AHead x2 x3) (AHead a3 a4)))) (\lambda (a3:
-A).(\lambda (_: A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda
-(a4: A).(arity g (CHead c0 (Bind Abst) u) t a4))) x2 x3 (refl_equal A (AHead
-x2 x3)) (arity_repl g c0 u (asucc g x0) H10 (asucc g x2) (asucc_repl g x0 x2
-H15)) (arity_repl g (CHead c0 (Bind Abst) u) t x1 H11 x3 H16)) a2 H18)))))))
+(CHead c0 (Bind Abst) u) t a4))))) (ex3_2_intro A A (\lambda (a3: A).(\lambda
+(a4: A).(eq A (AHead x2 x3) (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_:
+A).(arity g c0 u (asucc g a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g
+(CHead c0 (Bind Abst) u) t a4))) x2 x3 (refl_equal A (AHead x2 x3))
+(arity_repl g c0 u (asucc g x0) H10 (asucc g x2) (asucc_repl g x0 x2 H15))
+(arity_repl g (CHead c0 (Bind Abst) u) t x1 H11 x3 H16)) a2 H18)))))))
H14)))))))))) H8))))))))))))) c y a H0))) H)))))).
-(* COMMENTS
-Initial nodes: 4265
-END *)
theorem arity_gen_appl:
\forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (a2:
\to (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t
(AHead a1 a)))))))) (\lambda (c0: C).(\lambda (n: nat).(\lambda (H1: (eq T
(TSort n) (THead (Flat Appl) u t))).(let H2 \def (eq_ind T (TSort n) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
-False])) I (THead (Flat Appl) u t) H1) in (False_ind (ex2 A (\lambda (a1:
-A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t (AHead a1 (ASort O
-n))))) H2))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i:
-nat).(\lambda (_: (getl i c0 (CHead d (Bind Abbr) u0))).(\lambda (a:
-A).(\lambda (_: (arity g d u0 a)).(\lambda (_: (((eq T u0 (THead (Flat Appl)
-u t)) \to (ex2 A (\lambda (a1: A).(arity g d u a1)) (\lambda (a1: A).(arity g
-d t (AHead a1 a))))))).(\lambda (H4: (eq T (TLRef i) (THead (Flat Appl) u
-t))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Appl) u
-t) H4) in (False_ind (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1:
-A).(arity g c0 t (AHead a1 a)))) H5))))))))))) (\lambda (c0: C).(\lambda (d:
+(ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow
+False | (THead _ _ _) \Rightarrow False])) I (THead (Flat Appl) u t) H1) in
+(False_ind (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity
+g c0 t (AHead a1 (ASort O n))))) H2))))) (\lambda (c0: C).(\lambda (d:
+C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind
+Abbr) u0))).(\lambda (a: A).(\lambda (_: (arity g d u0 a)).(\lambda (_: (((eq
+T u0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a1: A).(arity g d u a1))
+(\lambda (a1: A).(arity g d t (AHead a1 a))))))).(\lambda (H4: (eq T (TLRef
+i) (THead (Flat Appl) u t))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee:
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
+(THead _ _ _) \Rightarrow False])) I (THead (Flat Appl) u t) H4) in
+(False_ind (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity
+g c0 t (AHead a1 a)))) H5))))))))))) (\lambda (c0: C).(\lambda (d:
C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0 (CHead d (Bind
Abst) u0))).(\lambda (a: A).(\lambda (_: (arity g d u0 (asucc g a))).(\lambda
(_: (((eq T u0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a1: A).(arity g
d u a1)) (\lambda (a1: A).(arity g d t (AHead a1 (asucc g a)))))))).(\lambda
(H4: (eq T (TLRef i) (THead (Flat Appl) u t))).(let H5 \def (eq_ind T (TLRef
-i) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
-False])) I (THead (Flat Appl) u t) H4) in (False_ind (ex2 A (\lambda (a1:
-A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t (AHead a1 a))))
-H5))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda (c0:
-C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u0
-a1)).(\lambda (_: (((eq T u0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda
-(a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3
-a1))))))).(\lambda (t0: T).(\lambda (a0: A).(\lambda (_: (arity g (CHead c0
-(Bind b) u0) t0 a0)).(\lambda (_: (((eq T t0 (THead (Flat Appl) u t)) \to
-(ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind b) u0) u a3)) (\lambda (a3:
-A).(arity g (CHead c0 (Bind b) u0) t (AHead a3 a0))))))).(\lambda (H6: (eq T
-(THead (Bind b) u0 t0) (THead (Flat Appl) u t))).(let H7 \def (eq_ind T
-(THead (Bind b) u0 t0) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat
-Appl) u t) H6) in (False_ind (ex2 A (\lambda (a3: A).(arity g c0 u a3))
-(\lambda (a3: A).(arity g c0 t (AHead a3 a0)))) H7)))))))))))))) (\lambda
-(c0: C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u0 (asucc
-g a1))).(\lambda (_: (((eq T u0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda
-(a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 (asucc g
-a1)))))))).(\lambda (t0: T).(\lambda (a0: A).(\lambda (_: (arity g (CHead c0
-(Bind Abst) u0) t0 a0)).(\lambda (_: (((eq T t0 (THead (Flat Appl) u t)) \to
-(ex2 A (\lambda (a3: A).(arity g (CHead c0 (Bind Abst) u0) u a3)) (\lambda
-(a3: A).(arity g (CHead c0 (Bind Abst) u0) t (AHead a3 a0))))))).(\lambda
-(H5: (eq T (THead (Bind Abst) u0 t0) (THead (Flat Appl) u t))).(let H6 \def
-(eq_ind T (THead (Bind Abst) u0 t0) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow
-False])])) I (THead (Flat Appl) u t) H5) in (False_ind (ex2 A (\lambda (a3:
-A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 (AHead a1
-a0))))) H6)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
-A).(\lambda (H1: (arity g c0 u0 a1)).(\lambda (H2: (((eq T u0 (THead (Flat
+i) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Appl) u
+t) H4) in (False_ind (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1:
+A).(arity g c0 t (AHead a1 a)))) H5))))))))))) (\lambda (b: B).(\lambda (_:
+(not (eq B b Abst))).(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 u0 a1)).(\lambda (_: (((eq T u0 (THead (Flat
Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3:
A).(arity g c0 t (AHead a3 a1))))))).(\lambda (t0: T).(\lambda (a0:
-A).(\lambda (H3: (arity g c0 t0 (AHead a1 a0))).(\lambda (H4: (((eq T t0
-(THead (Flat Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3))
-(\lambda (a3: A).(arity g c0 t (AHead a3 (AHead a1 a0)))))))).(\lambda (H5:
-(eq T (THead (Flat Appl) u0 t0) (THead (Flat Appl) u t))).(let H6 \def
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
+A).(\lambda (_: (arity g (CHead c0 (Bind b) u0) t0 a0)).(\lambda (_: (((eq T
+t0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g (CHead c0
+(Bind b) u0) u a3)) (\lambda (a3: A).(arity g (CHead c0 (Bind b) u0) t (AHead
+a3 a0))))))).(\lambda (H6: (eq T (THead (Bind b) u0 t0) (THead (Flat Appl) u
+t))).(let H7 \def (eq_ind T (THead (Bind b) u0 t0) (\lambda (ee: T).(match ee
+with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _
+_) \Rightarrow (match k with [(Bind _) \Rightarrow True | (Flat _)
+\Rightarrow False])])) I (THead (Flat Appl) u t) H6) in (False_ind (ex2 A
+(\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3
+a0)))) H7)))))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 u0 (asucc g a1))).(\lambda (_: (((eq T u0 (THead
+(Flat Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda
+(a3: A).(arity g c0 t (AHead a3 (asucc g a1)))))))).(\lambda (t0: T).(\lambda
+(a0: A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u0) t0 a0)).(\lambda (_:
+(((eq T t0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g
+(CHead c0 (Bind Abst) u0) u a3)) (\lambda (a3: A).(arity g (CHead c0 (Bind
+Abst) u0) t (AHead a3 a0))))))).(\lambda (H5: (eq T (THead (Bind Abst) u0 t0)
+(THead (Flat Appl) u t))).(let H6 \def (eq_ind T (THead (Bind Abst) u0 t0)
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat Appl) u t)
+H5) in (False_ind (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3:
+A).(arity g c0 t (AHead a3 (AHead a1 a0))))) H6)))))))))))) (\lambda (c0:
+C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (H1: (arity g c0 u0
+a1)).(\lambda (H2: (((eq T u0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda
+(a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3
+a1))))))).(\lambda (t0: T).(\lambda (a0: A).(\lambda (H3: (arity g c0 t0
+(AHead a1 a0))).(\lambda (H4: (((eq T t0 (THead (Flat Appl) u t)) \to (ex2 A
+(\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3
+(AHead a1 a0)))))))).(\lambda (H5: (eq T (THead (Flat Appl) u0 t0) (THead
+(Flat Appl) u t))).(let H6 \def (f_equal T T (\lambda (e: T).(match e with
[(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t1 _)
\Rightarrow t1])) (THead (Flat Appl) u0 t0) (THead (Flat Appl) u t) H5) in
-((let H7 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_:
-T).T) with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _
-t1) \Rightarrow t1])) (THead (Flat Appl) u0 t0) (THead (Flat Appl) u t) H5)
-in (\lambda (H8: (eq T u0 u)).(let H9 \def (eq_ind T t0 (\lambda (t1: T).((eq
-T t1 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3))
-(\lambda (a3: A).(arity g c0 t (AHead a3 (AHead a1 a0))))))) H4 t H7) in (let
-H10 \def (eq_ind T t0 (\lambda (t1: T).(arity g c0 t1 (AHead a1 a0))) H3 t
-H7) in (let H11 \def (eq_ind T u0 (\lambda (t1: T).((eq T t1 (THead (Flat
+((let H7 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
+\Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow t1]))
+(THead (Flat Appl) u0 t0) (THead (Flat Appl) u t) H5) in (\lambda (H8: (eq T
+u0 u)).(let H9 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead (Flat
Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3:
-A).(arity g c0 t (AHead a3 a1)))))) H2 u H8) in (let H12 \def (eq_ind T u0
-(\lambda (t1: T).(arity g c0 t1 a1)) H1 u H8) in (ex_intro2 A (\lambda (a3:
-A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 a0))) a1 H12
-H10))))))) H6)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a:
-A).(\lambda (_: (arity g c0 u0 (asucc g a))).(\lambda (_: (((eq T u0 (THead
-(Flat Appl) u t)) \to (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda
-(a1: A).(arity g c0 t (AHead a1 (asucc g a)))))))).(\lambda (t0: T).(\lambda
-(_: (arity g c0 t0 a)).(\lambda (_: (((eq T t0 (THead (Flat Appl) u t)) \to
-(ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t
-(AHead a1 a))))))).(\lambda (H5: (eq T (THead (Flat Cast) u0 t0) (THead (Flat
-Appl) u t))).(let H6 \def (eq_ind T (THead (Flat Cast) u0 t0) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K
-return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat f)
-\Rightarrow (match f in F return (\lambda (_: F).Prop) with [Appl \Rightarrow
-False | Cast \Rightarrow True])])])) I (THead (Flat Appl) u t) H5) in
-(False_ind (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity
-g c0 t (AHead a1 a)))) H6))))))))))) (\lambda (c0: C).(\lambda (t0:
-T).(\lambda (a1: A).(\lambda (H1: (arity g c0 t0 a1)).(\lambda (H2: (((eq T
-t0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a3: A).(arity g c0 u a3))
-(\lambda (a3: A).(arity g c0 t (AHead a3 a1))))))).(\lambda (a0: A).(\lambda
-(H3: (leq g a1 a0)).(\lambda (H4: (eq T t0 (THead (Flat Appl) u t))).(let H5
-\def (f_equal T T (\lambda (e: T).e) t0 (THead (Flat Appl) u t) H4) in (let
-H6 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead (Flat Appl) u t)) \to
+A).(arity g c0 t (AHead a3 (AHead a1 a0))))))) H4 t H7) in (let H10 \def
+(eq_ind T t0 (\lambda (t1: T).(arity g c0 t1 (AHead a1 a0))) H3 t H7) in (let
+H11 \def (eq_ind T u0 (\lambda (t1: T).((eq T t1 (THead (Flat Appl) u t)) \to
(ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t
-(AHead a3 a1)))))) H2 (THead (Flat Appl) u t) H5) in (let H7 \def (eq_ind T
-t0 (\lambda (t1: T).(arity g c0 t1 a1)) H1 (THead (Flat Appl) u t) H5) in
-(let H8 \def (H6 (refl_equal T (THead (Flat Appl) u t))) in (ex2_ind A
-(\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3
-a1))) (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0
-t (AHead a3 a0)))) (\lambda (x: A).(\lambda (H9: (arity g c0 u x)).(\lambda
-(H10: (arity g c0 t (AHead x a1))).(ex_intro2 A (\lambda (a3: A).(arity g c0
-u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 a0))) x H9 (arity_repl g c0 t
-(AHead x a1) H10 (AHead x a0) (leq_head g x x (leq_refl g x) a1 a0 H3))))))
-H8))))))))))))) c y a2 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 2277
-END *)
+(AHead a3 a1)))))) H2 u H8) in (let H12 \def (eq_ind T u0 (\lambda (t1:
+T).(arity g c0 t1 a1)) H1 u H8) in (ex_intro2 A (\lambda (a3: A).(arity g c0
+u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 a0))) a1 H12 H10)))))))
+H6)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a: A).(\lambda (_:
+(arity g c0 u0 (asucc g a))).(\lambda (_: (((eq T u0 (THead (Flat Appl) u t))
+\to (ex2 A (\lambda (a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t
+(AHead a1 (asucc g a)))))))).(\lambda (t0: T).(\lambda (_: (arity g c0 t0
+a)).(\lambda (_: (((eq T t0 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a1:
+A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t (AHead a1
+a))))))).(\lambda (H5: (eq T (THead (Flat Cast) u0 t0) (THead (Flat Appl) u
+t))).(let H6 \def (eq_ind T (THead (Flat Cast) u0 t0) (\lambda (ee: T).(match
+ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k
+_ _) \Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat f)
+\Rightarrow (match f with [Appl \Rightarrow False | Cast \Rightarrow
+True])])])) I (THead (Flat Appl) u t) H5) in (False_ind (ex2 A (\lambda (a1:
+A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t (AHead a1 a))))
+H6))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda
+(H1: (arity g c0 t0 a1)).(\lambda (H2: (((eq T t0 (THead (Flat Appl) u t))
+\to (ex2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t
+(AHead a3 a1))))))).(\lambda (a0: A).(\lambda (H3: (leq g a1 a0)).(\lambda
+(H4: (eq T t0 (THead (Flat Appl) u t))).(let H5 \def (f_equal T T (\lambda
+(e: T).e) t0 (THead (Flat Appl) u t) H4) in (let H6 \def (eq_ind T t0
+(\lambda (t1: T).((eq T t1 (THead (Flat Appl) u t)) \to (ex2 A (\lambda (a3:
+A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 a1)))))) H2
+(THead (Flat Appl) u t) H5) in (let H7 \def (eq_ind T t0 (\lambda (t1:
+T).(arity g c0 t1 a1)) H1 (THead (Flat Appl) u t) H5) in (let H8 \def (H6
+(refl_equal T (THead (Flat Appl) u t))) in (ex2_ind A (\lambda (a3: A).(arity
+g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 a1))) (ex2 A (\lambda
+(a3: A).(arity g c0 u a3)) (\lambda (a3: A).(arity g c0 t (AHead a3 a0))))
+(\lambda (x: A).(\lambda (H9: (arity g c0 u x)).(\lambda (H10: (arity g c0 t
+(AHead x a1))).(ex_intro2 A (\lambda (a3: A).(arity g c0 u a3)) (\lambda (a3:
+A).(arity g c0 t (AHead a3 a0))) x H9 (arity_repl g c0 t (AHead x a1) H10
+(AHead x a0) (leq_head g x x (leq_refl g x) a1 a0 H3)))))) H8))))))))))))) c
+y a2 H0))) H)))))).
theorem arity_gen_cast:
\forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (a:
A).((eq T t0 (THead (Flat Cast) u t)) \to (land (arity g c0 u (asucc g a0))
(arity g c0 t a0)))))) (\lambda (c0: C).(\lambda (n: nat).(\lambda (H1: (eq T
(TSort n) (THead (Flat Cast) u t))).(let H2 \def (eq_ind T (TSort n) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
-False])) I (THead (Flat Cast) u t) H1) in (False_ind (land (arity g c0 u
-(asucc g (ASort O n))) (arity g c0 t (ASort O n))) H2))))) (\lambda (c0:
-C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (_: (getl i c0
-(CHead d (Bind Abbr) u0))).(\lambda (a0: A).(\lambda (_: (arity g d u0
-a0)).(\lambda (_: (((eq T u0 (THead (Flat Cast) u t)) \to (land (arity g d u
-(asucc g a0)) (arity g d t a0))))).(\lambda (H4: (eq T (TLRef i) (THead (Flat
-Cast) u t))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee in T
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
+(ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow
+False | (THead _ _ _) \Rightarrow False])) I (THead (Flat Cast) u t) H1) in
+(False_ind (land (arity g c0 u (asucc g (ASort O n))) (arity g c0 t (ASort O
+n))) H2))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i:
+nat).(\lambda (_: (getl i c0 (CHead d (Bind Abbr) u0))).(\lambda (a0:
+A).(\lambda (_: (arity g d u0 a0)).(\lambda (_: (((eq T u0 (THead (Flat Cast)
+u t)) \to (land (arity g d u (asucc g a0)) (arity g d t a0))))).(\lambda (H4:
+(eq T (TLRef i) (THead (Flat Cast) u t))).(let H5 \def (eq_ind T (TLRef i)
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Cast) u
t) H4) in (False_ind (land (arity g c0 u (asucc g a0)) (arity g c0 t a0))
H5))))))))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i:
A).(\lambda (_: (arity g d u0 (asucc g a0))).(\lambda (_: (((eq T u0 (THead
(Flat Cast) u t)) \to (land (arity g d u (asucc g (asucc g a0))) (arity g d t
(asucc g a0)))))).(\lambda (H4: (eq T (TLRef i) (THead (Flat Cast) u
-t))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Cast) u
-t) H4) in (False_ind (land (arity g c0 u (asucc g a0)) (arity g c0 t a0))
-H5))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda (c0:
-C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u0
-a1)).(\lambda (_: (((eq T u0 (THead (Flat Cast) u t)) \to (land (arity g c0 u
-(asucc g a1)) (arity g c0 t a1))))).(\lambda (t0: T).(\lambda (a2:
-A).(\lambda (_: (arity g (CHead c0 (Bind b) u0) t0 a2)).(\lambda (_: (((eq T
-t0 (THead (Flat Cast) u t)) \to (land (arity g (CHead c0 (Bind b) u0) u
-(asucc g a2)) (arity g (CHead c0 (Bind b) u0) t a2))))).(\lambda (H6: (eq T
-(THead (Bind b) u0 t0) (THead (Flat Cast) u t))).(let H7 \def (eq_ind T
-(THead (Bind b) u0 t0) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat
-Cast) u t) H6) in (False_ind (land (arity g c0 u (asucc g a2)) (arity g c0 t
-a2)) H7)))))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
-A).(\lambda (_: (arity g c0 u0 (asucc g a1))).(\lambda (_: (((eq T u0 (THead
-(Flat Cast) u t)) \to (land (arity g c0 u (asucc g (asucc g a1))) (arity g c0
-t (asucc g a1)))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g
-(CHead c0 (Bind Abst) u0) t0 a2)).(\lambda (_: (((eq T t0 (THead (Flat Cast)
-u t)) \to (land (arity g (CHead c0 (Bind Abst) u0) u (asucc g a2)) (arity g
-(CHead c0 (Bind Abst) u0) t a2))))).(\lambda (H5: (eq T (THead (Bind Abst) u0
-t0) (THead (Flat Cast) u t))).(let H6 \def (eq_ind T (THead (Bind Abst) u0
-t0) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
+t))).(let H5 \def (eq_ind T (TLRef i) (\lambda (ee: T).(match ee with [(TSort
+_) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
+False])) I (THead (Flat Cast) u t) H4) in (False_ind (land (arity g c0 u
+(asucc g a0)) (arity g c0 t a0)) H5))))))))))) (\lambda (b: B).(\lambda (_:
+(not (eq B b Abst))).(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 u0 a1)).(\lambda (_: (((eq T u0 (THead (Flat
+Cast) u t)) \to (land (arity g c0 u (asucc g a1)) (arity g c0 t
+a1))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c0
+(Bind b) u0) t0 a2)).(\lambda (_: (((eq T t0 (THead (Flat Cast) u t)) \to
+(land (arity g (CHead c0 (Bind b) u0) u (asucc g a2)) (arity g (CHead c0
+(Bind b) u0) t a2))))).(\lambda (H6: (eq T (THead (Bind b) u0 t0) (THead
+(Flat Cast) u t))).(let H7 \def (eq_ind T (THead (Bind b) u0 t0) (\lambda
+(ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow
+False | (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow True |
+(Flat _) \Rightarrow False])])) I (THead (Flat Cast) u t) H6) in (False_ind
+(land (arity g c0 u (asucc g a2)) (arity g c0 t a2)) H7))))))))))))))
+(\lambda (c0: C).(\lambda (u0: T).(\lambda (a1: A).(\lambda (_: (arity g c0
+u0 (asucc g a1))).(\lambda (_: (((eq T u0 (THead (Flat Cast) u t)) \to (land
+(arity g c0 u (asucc g (asucc g a1))) (arity g c0 t (asucc g
+a1)))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c0
+(Bind Abst) u0) t0 a2)).(\lambda (_: (((eq T t0 (THead (Flat Cast) u t)) \to
+(land (arity g (CHead c0 (Bind Abst) u0) u (asucc g a2)) (arity g (CHead c0
+(Bind Abst) u0) t a2))))).(\lambda (H5: (eq T (THead (Bind Abst) u0 t0)
+(THead (Flat Cast) u t))).(let H6 \def (eq_ind T (THead (Bind Abst) u0 t0)
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _)
\Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat Cast) u t)
H5) in (False_ind (land (arity g c0 u (asucc g (AHead a1 a2))) (arity g c0 t
(AHead a1 a2))) H6)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda
a1 a2))).(\lambda (_: (((eq T t0 (THead (Flat Cast) u t)) \to (land (arity g
c0 u (asucc g (AHead a1 a2))) (arity g c0 t (AHead a1 a2)))))).(\lambda (H5:
(eq T (THead (Flat Appl) u0 t0) (THead (Flat Cast) u t))).(let H6 \def
-(eq_ind T (THead (Flat Appl) u0 t0) (\lambda (ee: T).(match ee in T return
-(\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat f) \Rightarrow (match f
-in F return (\lambda (_: F).Prop) with [Appl \Rightarrow True | Cast
-\Rightarrow False])])])) I (THead (Flat Cast) u t) H5) in (False_ind (land
-(arity g c0 u (asucc g a2)) (arity g c0 t a2)) H6)))))))))))) (\lambda (c0:
-C).(\lambda (u0: T).(\lambda (a0: A).(\lambda (H1: (arity g c0 u0 (asucc g
-a0))).(\lambda (H2: (((eq T u0 (THead (Flat Cast) u t)) \to (land (arity g c0
-u (asucc g (asucc g a0))) (arity g c0 t (asucc g a0)))))).(\lambda (t0:
-T).(\lambda (H3: (arity g c0 t0 a0)).(\lambda (H4: (((eq T t0 (THead (Flat
-Cast) u t)) \to (land (arity g c0 u (asucc g a0)) (arity g c0 t
-a0))))).(\lambda (H5: (eq T (THead (Flat Cast) u0 t0) (THead (Flat Cast) u
-t))).(let H6 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda
-(_: T).T) with [(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead
-_ t1 _) \Rightarrow t1])) (THead (Flat Cast) u0 t0) (THead (Flat Cast) u t)
-H5) in ((let H7 \def (f_equal T T (\lambda (e: T).(match e in T return
-(\lambda (_: T).T) with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0
-| (THead _ _ t1) \Rightarrow t1])) (THead (Flat Cast) u0 t0) (THead (Flat
-Cast) u t) H5) in (\lambda (H8: (eq T u0 u)).(let H9 \def (eq_ind T t0
-(\lambda (t1: T).((eq T t1 (THead (Flat Cast) u t)) \to (land (arity g c0 u
-(asucc g a0)) (arity g c0 t a0)))) H4 t H7) in (let H10 \def (eq_ind T t0
-(\lambda (t1: T).(arity g c0 t1 a0)) H3 t H7) in (let H11 \def (eq_ind T u0
+(eq_ind T (THead (Flat Appl) u0 t0) (\lambda (ee: T).(match ee with [(TSort
+_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
+\Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat f) \Rightarrow
+(match f with [Appl \Rightarrow True | Cast \Rightarrow False])])])) I (THead
+(Flat Cast) u t) H5) in (False_ind (land (arity g c0 u (asucc g a2)) (arity g
+c0 t a2)) H6)))))))))))) (\lambda (c0: C).(\lambda (u0: T).(\lambda (a0:
+A).(\lambda (H1: (arity g c0 u0 (asucc g a0))).(\lambda (H2: (((eq T u0
+(THead (Flat Cast) u t)) \to (land (arity g c0 u (asucc g (asucc g a0)))
+(arity g c0 t (asucc g a0)))))).(\lambda (t0: T).(\lambda (H3: (arity g c0 t0
+a0)).(\lambda (H4: (((eq T t0 (THead (Flat Cast) u t)) \to (land (arity g c0
+u (asucc g a0)) (arity g c0 t a0))))).(\lambda (H5: (eq T (THead (Flat Cast)
+u0 t0) (THead (Flat Cast) u t))).(let H6 \def (f_equal T T (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 |
+(THead _ t1 _) \Rightarrow t1])) (THead (Flat Cast) u0 t0) (THead (Flat Cast)
+u t) H5) in ((let H7 \def (f_equal T T (\lambda (e: T).(match e with [(TSort
+_) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t1) \Rightarrow
+t1])) (THead (Flat Cast) u0 t0) (THead (Flat Cast) u t) H5) in (\lambda (H8:
+(eq T u0 u)).(let H9 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead
+(Flat Cast) u t)) \to (land (arity g c0 u (asucc g a0)) (arity g c0 t a0))))
+H4 t H7) in (let H10 \def (eq_ind T t0 (\lambda (t1: T).(arity g c0 t1 a0))
+H3 t H7) in (let H11 \def (eq_ind T u0 (\lambda (t1: T).((eq T t1 (THead
+(Flat Cast) u t)) \to (land (arity g c0 u (asucc g (asucc g a0))) (arity g c0
+t (asucc g a0))))) H2 u H8) in (let H12 \def (eq_ind T u0 (\lambda (t1:
+T).(arity g c0 t1 (asucc g a0))) H1 u H8) in (conj (arity g c0 u (asucc g
+a0)) (arity g c0 t a0) H12 H10))))))) H6))))))))))) (\lambda (c0: C).(\lambda
+(t0: T).(\lambda (a1: A).(\lambda (H1: (arity g c0 t0 a1)).(\lambda (H2:
+(((eq T t0 (THead (Flat Cast) u t)) \to (land (arity g c0 u (asucc g a1))
+(arity g c0 t a1))))).(\lambda (a2: A).(\lambda (H3: (leq g a1 a2)).(\lambda
+(H4: (eq T t0 (THead (Flat Cast) u t))).(let H5 \def (f_equal T T (\lambda
+(e: T).e) t0 (THead (Flat Cast) u t) H4) in (let H6 \def (eq_ind T t0
(\lambda (t1: T).((eq T t1 (THead (Flat Cast) u t)) \to (land (arity g c0 u
-(asucc g (asucc g a0))) (arity g c0 t (asucc g a0))))) H2 u H8) in (let H12
-\def (eq_ind T u0 (\lambda (t1: T).(arity g c0 t1 (asucc g a0))) H1 u H8) in
-(conj (arity g c0 u (asucc g a0)) (arity g c0 t a0) H12 H10)))))))
-H6))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda
-(H1: (arity g c0 t0 a1)).(\lambda (H2: (((eq T t0 (THead (Flat Cast) u t))
-\to (land (arity g c0 u (asucc g a1)) (arity g c0 t a1))))).(\lambda (a2:
-A).(\lambda (H3: (leq g a1 a2)).(\lambda (H4: (eq T t0 (THead (Flat Cast) u
-t))).(let H5 \def (f_equal T T (\lambda (e: T).e) t0 (THead (Flat Cast) u t)
-H4) in (let H6 \def (eq_ind T t0 (\lambda (t1: T).((eq T t1 (THead (Flat
-Cast) u t)) \to (land (arity g c0 u (asucc g a1)) (arity g c0 t a1)))) H2
-(THead (Flat Cast) u t) H5) in (let H7 \def (eq_ind T t0 (\lambda (t1:
-T).(arity g c0 t1 a1)) H1 (THead (Flat Cast) u t) H5) in (let H8 \def (H6
-(refl_equal T (THead (Flat Cast) u t))) in (land_ind (arity g c0 u (asucc g
-a1)) (arity g c0 t a1) (land (arity g c0 u (asucc g a2)) (arity g c0 t a2))
-(\lambda (H9: (arity g c0 u (asucc g a1))).(\lambda (H10: (arity g c0 t
-a1)).(conj (arity g c0 u (asucc g a2)) (arity g c0 t a2) (arity_repl g c0 u
-(asucc g a1) H9 (asucc g a2) (asucc_repl g a1 a2 H3)) (arity_repl g c0 t a1
-H10 a2 H3)))) H8))))))))))))) c y a H0))) H)))))).
-(* COMMENTS
-Initial nodes: 2147
-END *)
+(asucc g a1)) (arity g c0 t a1)))) H2 (THead (Flat Cast) u t) H5) in (let H7
+\def (eq_ind T t0 (\lambda (t1: T).(arity g c0 t1 a1)) H1 (THead (Flat Cast)
+u t) H5) in (let H8 \def (H6 (refl_equal T (THead (Flat Cast) u t))) in
+(land_ind (arity g c0 u (asucc g a1)) (arity g c0 t a1) (land (arity g c0 u
+(asucc g a2)) (arity g c0 t a2)) (\lambda (H9: (arity g c0 u (asucc g
+a1))).(\lambda (H10: (arity g c0 t a1)).(conj (arity g c0 u (asucc g a2))
+(arity g c0 t a2) (arity_repl g c0 u (asucc g a1) H9 (asucc g a2) (asucc_repl
+g a1 a2 H3)) (arity_repl g c0 t a1 H10 a2 H3)))) H8))))))))))))) c y a H0)))
+H)))))).
theorem arity_gen_appls:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (vs: TList).(\forall
(\lambda (a: A).(arity g c t a)) (ex A (\lambda (a: A).(arity g c t a)))
(\lambda (x0: A).(\lambda (H5: (arity g c t x0)).(ex_intro A (\lambda (a:
A).(arity g c t a)) x0 H5))) H4)))))) H1))))))) vs)))).
-(* COMMENTS
-Initial nodes: 341
-END *)
theorem arity_gen_lift:
\forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).(\forall (h:
a2)).(\lambda (x: nat).(\lambda (x0: T).(\lambda (H4: (eq T t0 (lift h x
x0))).(\lambda (c2: C).(\lambda (H5: (drop h x c c2)).(arity_repl g c2 x0 a1
(H2 x x0 H4 c2 H5) a2 H3))))))))))))) c1 y a H0))))) H))))))).
-(* COMMENTS
-Initial nodes: 4693
-END *)
+
+theorem arity_mono:
+ \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a1: A).((arity g c
+t a1) \to (\forall (a2: A).((arity g c t a2) \to (leq g a1 a2)))))))
+\def
+ \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a1: A).(\lambda (H:
+(arity g c t a1)).(arity_ind g (\lambda (c0: C).(\lambda (t0: T).(\lambda (a:
+A).(\forall (a2: A).((arity g c0 t0 a2) \to (leq g a a2)))))) (\lambda (c0:
+C).(\lambda (n: nat).(\lambda (a2: A).(\lambda (H0: (arity g c0 (TSort n)
+a2)).(leq_sym g a2 (ASort O n) (arity_gen_sort g c0 n a2 H0)))))) (\lambda
+(c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl
+i c0 (CHead d (Bind Abbr) u))).(\lambda (a: A).(\lambda (_: (arity g d u
+a)).(\lambda (H2: ((\forall (a2: A).((arity g d u a2) \to (leq g a
+a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef i) a2)).(let H4
+\def (arity_gen_lref g c0 i a2 H3) in (or_ind (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 a2)))) (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2))))) (leq g a a2) (\lambda
+(H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind
+Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
+a2))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0
+(Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a2)))
+(leq g a a2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0
+(CHead x0 (Bind Abbr) x1))).(\lambda (H7: (arity g x0 x1 a2)).(let H8 \def
+(eq_ind C (CHead d (Bind Abbr) u) (\lambda (c1: C).(getl i c0 c1)) H0 (CHead
+x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abbr) u) i H0 (CHead x0 (Bind
+Abbr) x1) H6)) in (let H9 \def (f_equal C C (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) (CHead d (Bind
+Abbr) u) (CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abbr) u) i H0
+(CHead x0 (Bind Abbr) x1) H6)) in ((let H10 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0]))
+(CHead d (Bind Abbr) u) (CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d
+(Bind Abbr) u) i H0 (CHead x0 (Bind Abbr) x1) H6)) in (\lambda (H11: (eq C d
+x0)).(let H12 \def (eq_ind_r T x1 (\lambda (t0: T).(getl i c0 (CHead x0 (Bind
+Abbr) t0))) H8 u H10) in (let H13 \def (eq_ind_r T x1 (\lambda (t0: T).(arity
+g x0 t0 a2)) H7 u H10) in (let H14 \def (eq_ind_r C x0 (\lambda (c1: C).(getl
+i c0 (CHead c1 (Bind Abbr) u))) H12 d H11) in (let H15 \def (eq_ind_r C x0
+(\lambda (c1: C).(arity g c1 u a2)) H13 d H11) in (H2 a2 H15))))))) H9)))))))
+H5)) (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
+(CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
+(asucc g a2)))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
+(CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
+(asucc g a2)))) (leq g a a2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6:
+(getl i c0 (CHead x0 (Bind Abst) x1))).(\lambda (_: (arity g x0 x1 (asucc g
+a2))).(let H8 \def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (c1: C).(getl i
+c0 c1)) H0 (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind Abbr) u) i
+H0 (CHead x0 (Bind Abst) x1) H6)) in (let H9 \def (eq_ind C (CHead d (Bind
+Abbr) u) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False |
+(CHead _ k _) \Rightarrow (match k with [(Bind b) \Rightarrow (match b with
+[Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) |
+(Flat _) \Rightarrow False])])) I (CHead x0 (Bind Abst) x1) (getl_mono c0
+(CHead d (Bind Abbr) u) i H0 (CHead x0 (Bind Abst) x1) H6)) in (False_ind
+(leq g a a2) H9))))))) H5)) H4)))))))))))) (\lambda (c0: C).(\lambda (d:
+C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d (Bind
+Abst) u))).(\lambda (a: A).(\lambda (_: (arity g d u (asucc g a))).(\lambda
+(H2: ((\forall (a2: A).((arity g d u a2) \to (leq g (asucc g a)
+a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef i) a2)).(let H4
+\def (arity_gen_lref g c0 i a2 H3) in (or_ind (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 a2)))) (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2))))) (leq g a a2) (\lambda
+(H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind
+Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
+a2))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0
+(Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a2)))
+(leq g a a2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0
+(CHead x0 (Bind Abbr) x1))).(\lambda (_: (arity g x0 x1 a2)).(let H8 \def
+(eq_ind C (CHead d (Bind Abst) u) (\lambda (c1: C).(getl i c0 c1)) H0 (CHead
+x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead x0 (Bind
+Abbr) x1) H6)) in (let H9 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda
+(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) I (CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d
+(Bind Abst) u) i H0 (CHead x0 (Bind Abbr) x1) H6)) in (False_ind (leq g a a2)
+H9))))))) H5)) (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0:
+T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0:
+T).(arity g d0 u0 (asucc g a2)))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda
+(u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda
+(u0: T).(arity g d0 u0 (asucc g a2)))) (leq g a a2) (\lambda (x0: C).(\lambda
+(x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind Abst) x1))).(\lambda (H7:
+(arity g x0 x1 (asucc g a2))).(let H8 \def (eq_ind C (CHead d (Bind Abst) u)
+(\lambda (c1: C).(getl i c0 c1)) H0 (CHead x0 (Bind Abst) x1) (getl_mono c0
+(CHead d (Bind Abst) u) i H0 (CHead x0 (Bind Abst) x1) H6)) in (let H9 \def
+(f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow d | (CHead
+c1 _ _) \Rightarrow c1])) (CHead d (Bind Abst) u) (CHead x0 (Bind Abst) x1)
+(getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead x0 (Bind Abst) x1) H6)) in
+((let H10 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind Abst) u)
+(CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead
+x0 (Bind Abst) x1) H6)) in (\lambda (H11: (eq C d x0)).(let H12 \def
+(eq_ind_r T x1 (\lambda (t0: T).(getl i c0 (CHead x0 (Bind Abst) t0))) H8 u
+H10) in (let H13 \def (eq_ind_r T x1 (\lambda (t0: T).(arity g x0 t0 (asucc g
+a2))) H7 u H10) in (let H14 \def (eq_ind_r C x0 (\lambda (c1: C).(getl i c0
+(CHead c1 (Bind Abst) u))) H12 d H11) in (let H15 \def (eq_ind_r C x0
+(\lambda (c1: C).(arity g c1 u (asucc g a2))) H13 d H11) in (asucc_inj g a a2
+(H2 (asucc g a2) H15)))))))) H9))))))) H5)) H4)))))))))))) (\lambda (b:
+B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c0: C).(\lambda (u:
+T).(\lambda (a2: A).(\lambda (_: (arity g c0 u a2)).(\lambda (_: ((\forall
+(a3: A).((arity g c0 u a3) \to (leq g a2 a3))))).(\lambda (t0: T).(\lambda
+(a3: A).(\lambda (_: (arity g (CHead c0 (Bind b) u) t0 a3)).(\lambda (H4:
+((\forall (a4: A).((arity g (CHead c0 (Bind b) u) t0 a4) \to (leq g a3
+a4))))).(\lambda (a0: A).(\lambda (H5: (arity g c0 (THead (Bind b) u t0)
+a0)).(let H6 \def (arity_gen_bind b H0 g c0 u t0 a0 H5) in (ex2_ind A
+(\lambda (a4: A).(arity g c0 u a4)) (\lambda (_: A).(arity g (CHead c0 (Bind
+b) u) t0 a0)) (leq g a3 a0) (\lambda (x: A).(\lambda (_: (arity g c0 u
+x)).(\lambda (H8: (arity g (CHead c0 (Bind b) u) t0 a0)).(H4 a0 H8))))
+H6))))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a2: A).(\lambda
+(_: (arity g c0 u (asucc g a2))).(\lambda (H1: ((\forall (a3: A).((arity g c0
+u a3) \to (leq g (asucc g a2) a3))))).(\lambda (t0: T).(\lambda (a3:
+A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t0 a3)).(\lambda (H3:
+((\forall (a4: A).((arity g (CHead c0 (Bind Abst) u) t0 a4) \to (leq g a3
+a4))))).(\lambda (a0: A).(\lambda (H4: (arity g c0 (THead (Bind Abst) u t0)
+a0)).(let H5 \def (arity_gen_abst g c0 u t0 a0 H4) in (ex3_2_ind A A (\lambda
+(a4: A).(\lambda (a5: A).(eq A a0 (AHead a4 a5)))) (\lambda (a4: A).(\lambda
+(_: A).(arity g c0 u (asucc g a4)))) (\lambda (_: A).(\lambda (a5: A).(arity
+g (CHead c0 (Bind Abst) u) t0 a5))) (leq g (AHead a2 a3) a0) (\lambda (x0:
+A).(\lambda (x1: A).(\lambda (H6: (eq A a0 (AHead x0 x1))).(\lambda (H7:
+(arity g c0 u (asucc g x0))).(\lambda (H8: (arity g (CHead c0 (Bind Abst) u)
+t0 x1)).(eq_ind_r A (AHead x0 x1) (\lambda (a: A).(leq g (AHead a2 a3) a))
+(leq_head g a2 x0 (asucc_inj g a2 x0 (H1 (asucc g x0) H7)) a3 x1 (H3 x1 H8))
+a0 H6)))))) H5))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a2:
+A).(\lambda (_: (arity g c0 u a2)).(\lambda (_: ((\forall (a3: A).((arity g
+c0 u a3) \to (leq g a2 a3))))).(\lambda (t0: T).(\lambda (a3: A).(\lambda (_:
+(arity g c0 t0 (AHead a2 a3))).(\lambda (H3: ((\forall (a4: A).((arity g c0
+t0 a4) \to (leq g (AHead a2 a3) a4))))).(\lambda (a0: A).(\lambda (H4: (arity
+g c0 (THead (Flat Appl) u t0) a0)).(let H5 \def (arity_gen_appl g c0 u t0 a0
+H4) in (ex2_ind A (\lambda (a4: A).(arity g c0 u a4)) (\lambda (a4: A).(arity
+g c0 t0 (AHead a4 a0))) (leq g a3 a0) (\lambda (x: A).(\lambda (_: (arity g
+c0 u x)).(\lambda (H7: (arity g c0 t0 (AHead x a0))).(ahead_inj_snd g a2 a3 x
+a0 (H3 (AHead x a0) H7))))) H5))))))))))))) (\lambda (c0: C).(\lambda (u:
+T).(\lambda (a: A).(\lambda (_: (arity g c0 u (asucc g a))).(\lambda (_:
+((\forall (a2: A).((arity g c0 u a2) \to (leq g (asucc g a) a2))))).(\lambda
+(t0: T).(\lambda (_: (arity g c0 t0 a)).(\lambda (H3: ((\forall (a2:
+A).((arity g c0 t0 a2) \to (leq g a a2))))).(\lambda (a2: A).(\lambda (H4:
+(arity g c0 (THead (Flat Cast) u t0) a2)).(let H5 \def (arity_gen_cast g c0 u
+t0 a2 H4) in (land_ind (arity g c0 u (asucc g a2)) (arity g c0 t0 a2) (leq g
+a a2) (\lambda (_: (arity g c0 u (asucc g a2))).(\lambda (H7: (arity g c0 t0
+a2)).(H3 a2 H7))) H5)))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda
+(a2: A).(\lambda (_: (arity g c0 t0 a2)).(\lambda (H1: ((\forall (a3:
+A).((arity g c0 t0 a3) \to (leq g a2 a3))))).(\lambda (a3: A).(\lambda (H2:
+(leq g a2 a3)).(\lambda (a0: A).(\lambda (H3: (arity g c0 t0 a0)).(leq_trans
+g a3 a2 (leq_sym g a2 a3 H2) a0 (H1 a0 H3))))))))))) c t a1 H))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/props.ma".
+include "basic_1/arity/props.ma".
-include "Basic-1/drop1/fwd.ma".
+include "basic_1/drop1/fwd.ma".
theorem arity_lift1:
\forall (g: G).(\forall (a: A).(\forall (c2: C).(\forall (hds:
PList).(\forall (c1: C).(\forall (t: T).((drop1 hds c1 c2) \to ((arity g c2 t
a) \to (arity g c1 (lift1 hds t) a))))))))
\def
- \lambda (g: G).(\lambda (a: A).(\lambda (c2: C).(\lambda (hds:
-PList).(PList_ind (\lambda (p: PList).(\forall (c1: C).(\forall (t:
-T).((drop1 p c1 c2) \to ((arity g c2 t a) \to (arity g c1 (lift1 p t) a))))))
-(\lambda (c1: C).(\lambda (t: T).(\lambda (H: (drop1 PNil c1 c2)).(\lambda
-(H0: (arity g c2 t a)).(let H_y \def (drop1_gen_pnil c1 c2 H) in (eq_ind_r C
-c2 (\lambda (c: C).(arity g c t a)) H0 c1 H_y)))))) (\lambda (n:
+ \lambda (g: G).(\lambda (a: A).(\lambda (c2: C).(\lambda (hds: PList).(let
+TMP_2 \def (\lambda (p: PList).(\forall (c1: C).(\forall (t: T).((drop1 p c1
+c2) \to ((arity g c2 t a) \to (let TMP_1 \def (lift1 p t) in (arity g c1
+TMP_1 a))))))) in (let TMP_4 \def (\lambda (c1: C).(\lambda (t: T).(\lambda
+(H: (drop1 PNil c1 c2)).(\lambda (H0: (arity g c2 t a)).(let H_y \def
+(drop1_gen_pnil c1 c2 H) in (let TMP_3 \def (\lambda (c: C).(arity g c t a))
+in (eq_ind_r C c2 TMP_3 H0 c1 H_y))))))) in (let TMP_13 \def (\lambda (n:
nat).(\lambda (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c1:
C).(\forall (t: T).((drop1 p c1 c2) \to ((arity g c2 t a) \to (arity g c1
(lift1 p t) a))))))).(\lambda (c1: C).(\lambda (t: T).(\lambda (H0: (drop1
(PCons n n0 p) c1 c2)).(\lambda (H1: (arity g c2 t a)).(let H_x \def
-(drop1_gen_pcons c1 c2 p n n0 H0) in (let H2 \def H_x in (ex2_ind C (\lambda
-(c3: C).(drop n n0 c1 c3)) (\lambda (c3: C).(drop1 p c3 c2)) (arity g c1
-(lift n n0 (lift1 p t)) a) (\lambda (x: C).(\lambda (H3: (drop n n0 c1
-x)).(\lambda (H4: (drop1 p x c2)).(arity_lift g x (lift1 p t) a (H x t H4 H1)
-c1 n n0 H3)))) H2))))))))))) hds)))).
-(* COMMENTS
-Initial nodes: 289
-END *)
+(drop1_gen_pcons c1 c2 p n n0 H0) in (let H2 \def H_x in (let TMP_5 \def
+(\lambda (c3: C).(drop n n0 c1 c3)) in (let TMP_6 \def (\lambda (c3:
+C).(drop1 p c3 c2)) in (let TMP_7 \def (lift1 p t) in (let TMP_8 \def (lift n
+n0 TMP_7) in (let TMP_9 \def (arity g c1 TMP_8 a) in (let TMP_12 \def
+(\lambda (x: C).(\lambda (H3: (drop n n0 c1 x)).(\lambda (H4: (drop1 p x
+c2)).(let TMP_10 \def (lift1 p t) in (let TMP_11 \def (H x t H4 H1) in
+(arity_lift g x TMP_10 a TMP_11 c1 n n0 H3)))))) in (ex2_ind C TMP_5 TMP_6
+TMP_9 TMP_12 H2))))))))))))))))) in (PList_ind TMP_2 TMP_4 TMP_13 hds))))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/arity.ma".
+include "basic_1/csuba/arity.ma".
-include "Basic-1/pr3/defs.ma".
+include "basic_1/pr3/fwd.ma".
-include "Basic-1/pr1/defs.ma".
+include "basic_1/pr1/fwd.ma".
-include "Basic-1/wcpr0/getl.ma".
+include "basic_1/wcpr0/getl.ma".
-include "Basic-1/pr0/fwd.ma".
+include "basic_1/pr0/props.ma".
-include "Basic-1/arity/subst0.ma".
+include "basic_1/arity/subst0.ma".
theorem arity_sred_wcpr0_pr0:
\forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (a: A).((arity g
(t4: T).(\lambda (H10: (pr0 t3 t4)).(\lambda (H11: (((eq T t3 (THead (Bind b)
u t)) \to (arity g c2 t4 a2)))).(\lambda (k: K).(\lambda (H12: (eq T (THead k
u1 t3) (THead (Bind b) u t))).(let H13 \def (f_equal T K (\lambda (e:
-T).(match e in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k |
-(TLRef _) \Rightarrow k | (THead k0 _ _) \Rightarrow k0])) (THead k u1 t3)
-(THead (Bind b) u t) H12) in ((let H14 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow u1 |
-(TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0])) (THead k u1 t3)
+T).(match e with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead
+k0 _ _) \Rightarrow k0])) (THead k u1 t3) (THead (Bind b) u t) H12) in ((let
+H14 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow u1
+| (TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0])) (THead k u1 t3)
(THead (Bind b) u t) H12) in ((let H15 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t3 |
-(TLRef _) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0])) (THead k u1 t3)
-(THead (Bind b) u t) H12) in (\lambda (H16: (eq T u1 u)).(\lambda (H17: (eq K
-k (Bind b))).(eq_ind_r K (Bind b) (\lambda (k0: K).(arity g c2 (THead k0 u2
-t4) a2)) (let H18 \def (eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead (Bind
-b) u t)) \to (arity g c2 t4 a2))) H11 t H15) in (let H19 \def (eq_ind T t3
-(\lambda (t0: T).(pr0 t0 t4)) H10 t H15) in (let H20 \def (eq_ind T u1
+T).(match e with [(TSort _) \Rightarrow t3 | (TLRef _) \Rightarrow t3 |
+(THead _ _ t0) \Rightarrow t0])) (THead k u1 t3) (THead (Bind b) u t) H12) in
+(\lambda (H16: (eq T u1 u)).(\lambda (H17: (eq K k (Bind b))).(eq_ind_r K
+(Bind b) (\lambda (k0: K).(arity g c2 (THead k0 u2 t4) a2)) (let H18 \def
+(eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead (Bind b) u t)) \to (arity g c2
+t4 a2))) H11 t H15) in (let H19 \def (eq_ind T t3 (\lambda (t0: T).(pr0 t0
+t4)) H10 t H15) in (let H20 \def (eq_ind T u1 (\lambda (t0: T).((eq T t0
+(THead (Bind b) u t)) \to (arity g c2 u2 a2))) H9 u H16) in (let H21 \def
+(eq_ind T u1 (\lambda (t0: T).(pr0 t0 u2)) H8 u H16) in (arity_bind g b H0 c2
+u2 a1 (H2 c2 H5 u2 H21) t4 a2 (H4 (CHead c2 (Bind b) u2) (wcpr0_comp c c2 H5
+u u2 H21 (Bind b)) t4 H19)))))) k H17)))) H14)) H13)))))))))))) (\lambda (u0:
+T).(\lambda (v1: T).(\lambda (v2: T).(\lambda (_: (pr0 v1 v2)).(\lambda (_:
+(((eq T v1 (THead (Bind b) u t)) \to (arity g c2 v2 a2)))).(\lambda (t3:
+T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead
+(Bind b) u t)) \to (arity g c2 t4 a2)))).(\lambda (H12: (eq T (THead (Flat
+Appl) v1 (THead (Bind Abst) u0 t3)) (THead (Bind b) u t))).(let H13 \def
+(eq_ind T (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3)) (\lambda (ee:
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
+| (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat
+_) \Rightarrow True])])) I (THead (Bind b) u t) H12) in (False_ind (arity g
+c2 (THead (Bind Abbr) v2 t4) a2) H13)))))))))))) (\lambda (b0: B).(\lambda
+(_: (not (eq B b0 Abst))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (_: (pr0
+v1 v2)).(\lambda (_: (((eq T v1 (THead (Bind b) u t)) \to (arity g c2 v2
+a2)))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda
+(_: (((eq T u1 (THead (Bind b) u t)) \to (arity g c2 u2 a2)))).(\lambda (t3:
+T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead
+(Bind b) u t)) \to (arity g c2 t4 a2)))).(\lambda (H15: (eq T (THead (Flat
+Appl) v1 (THead (Bind b0) u1 t3)) (THead (Bind b) u t))).(let H16 \def
+(eq_ind T (THead (Flat Appl) v1 (THead (Bind b0) u1 t3)) (\lambda (ee:
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
+| (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat
+_) \Rightarrow True])])) I (THead (Bind b) u t) H15) in (False_ind (arity g
+c2 (THead (Bind b0) u2 (THead (Flat Appl) (lift (S O) O v2) t4)) a2)
+H16))))))))))))))))) (\lambda (u1: T).(\lambda (u2: T).(\lambda (H8: (pr0 u1
+u2)).(\lambda (H9: (((eq T u1 (THead (Bind b) u t)) \to (arity g c2 u2
+a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H10: (pr0 t3 t4)).(\lambda
+(H11: (((eq T t3 (THead (Bind b) u t)) \to (arity g c2 t4 a2)))).(\lambda (w:
+T).(\lambda (H12: (subst0 O u2 t4 w)).(\lambda (H13: (eq T (THead (Bind Abbr)
+u1 t3) (THead (Bind b) u t))).(let H14 \def (f_equal T B (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow Abbr | (TLRef _) \Rightarrow Abbr |
+(THead k _ _) \Rightarrow (match k with [(Bind b0) \Rightarrow b0 | (Flat _)
+\Rightarrow Abbr])])) (THead (Bind Abbr) u1 t3) (THead (Bind b) u t) H13) in
+((let H15 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
+\Rightarrow u1 | (TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0]))
+(THead (Bind Abbr) u1 t3) (THead (Bind b) u t) H13) in ((let H16 \def
+(f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow t3 | (TLRef
+_) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0])) (THead (Bind Abbr) u1
+t3) (THead (Bind b) u t) H13) in (\lambda (H17: (eq T u1 u)).(\lambda (H18:
+(eq B Abbr b)).(let H19 \def (eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead
+(Bind b) u t)) \to (arity g c2 t4 a2))) H11 t H16) in (let H20 \def (eq_ind T
+t3 (\lambda (t0: T).(pr0 t0 t4)) H10 t H16) in (let H21 \def (eq_ind T u1
(\lambda (t0: T).((eq T t0 (THead (Bind b) u t)) \to (arity g c2 u2 a2))) H9
-u H16) in (let H21 \def (eq_ind T u1 (\lambda (t0: T).(pr0 t0 u2)) H8 u H16)
-in (arity_bind g b H0 c2 u2 a1 (H2 c2 H5 u2 H21) t4 a2 (H4 (CHead c2 (Bind b)
-u2) (wcpr0_comp c c2 H5 u u2 H21 (Bind b)) t4 H19)))))) k H17)))) H14))
-H13)))))))))))) (\lambda (u0: T).(\lambda (v1: T).(\lambda (v2: T).(\lambda
-(_: (pr0 v1 v2)).(\lambda (_: (((eq T v1 (THead (Bind b) u t)) \to (arity g
-c2 v2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3
-t4)).(\lambda (_: (((eq T t3 (THead (Bind b) u t)) \to (arity g c2 t4
-a2)))).(\lambda (H12: (eq T (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3))
-(THead (Bind b) u t))).(let H13 \def (eq_ind T (THead (Flat Appl) v1 (THead
-(Bind Abst) u0 t3)) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind
-b) u t) H12) in (False_ind (arity g c2 (THead (Bind Abbr) v2 t4) a2)
-H13)))))))))))) (\lambda (b0: B).(\lambda (_: (not (eq B b0 Abst))).(\lambda
-(v1: T).(\lambda (v2: T).(\lambda (_: (pr0 v1 v2)).(\lambda (_: (((eq T v1
-(THead (Bind b) u t)) \to (arity g c2 v2 a2)))).(\lambda (u1: T).(\lambda
-(u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (_: (((eq T u1 (THead (Bind b) u
-t)) \to (arity g c2 u2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_:
-(pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Bind b) u t)) \to (arity g c2 t4
-a2)))).(\lambda (H15: (eq T (THead (Flat Appl) v1 (THead (Bind b0) u1 t3))
-(THead (Bind b) u t))).(let H16 \def (eq_ind T (THead (Flat Appl) v1 (THead
-(Bind b0) u1 t3)) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind
-b) u t) H15) in (False_ind (arity g c2 (THead (Bind b0) u2 (THead (Flat Appl)
-(lift (S O) O v2) t4)) a2) H16))))))))))))))))) (\lambda (u1: T).(\lambda
-(u2: T).(\lambda (H8: (pr0 u1 u2)).(\lambda (H9: (((eq T u1 (THead (Bind b) u
-t)) \to (arity g c2 u2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda
-(H10: (pr0 t3 t4)).(\lambda (H11: (((eq T t3 (THead (Bind b) u t)) \to (arity
-g c2 t4 a2)))).(\lambda (w: T).(\lambda (H12: (subst0 O u2 t4 w)).(\lambda
-(H13: (eq T (THead (Bind Abbr) u1 t3) (THead (Bind b) u t))).(let H14 \def
-(f_equal T B (\lambda (e: T).(match e in T return (\lambda (_: T).B) with
-[(TSort _) \Rightarrow Abbr | (TLRef _) \Rightarrow Abbr | (THead k _ _)
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b0)
-\Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (THead (Bind Abbr) u1 t3)
-(THead (Bind b) u t) H13) in ((let H15 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow u1 |
-(TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0])) (THead (Bind
-Abbr) u1 t3) (THead (Bind b) u t) H13) in ((let H16 \def (f_equal T T
-(\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow t3 | (TLRef _) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0]))
-(THead (Bind Abbr) u1 t3) (THead (Bind b) u t) H13) in (\lambda (H17: (eq T
-u1 u)).(\lambda (H18: (eq B Abbr b)).(let H19 \def (eq_ind T t3 (\lambda (t0:
-T).((eq T t0 (THead (Bind b) u t)) \to (arity g c2 t4 a2))) H11 t H16) in
-(let H20 \def (eq_ind T t3 (\lambda (t0: T).(pr0 t0 t4)) H10 t H16) in (let
-H21 \def (eq_ind T u1 (\lambda (t0: T).((eq T t0 (THead (Bind b) u t)) \to
-(arity g c2 u2 a2))) H9 u H17) in (let H22 \def (eq_ind T u1 (\lambda (t0:
-T).(pr0 t0 u2)) H8 u H17) in (let H23 \def (eq_ind_r B b (\lambda (b0:
-B).((eq T t (THead (Bind b0) u t)) \to (arity g c2 t4 a2))) H19 Abbr H18) in
-(let H24 \def (eq_ind_r B b (\lambda (b0: B).((eq T u (THead (Bind b0) u t))
-\to (arity g c2 u2 a2))) H21 Abbr H18) in (let H25 \def (eq_ind_r B b
-(\lambda (b0: B).(\forall (c3: C).((wcpr0 (CHead c (Bind b0) u) c3) \to
-(\forall (t5: T).((pr0 t t5) \to (arity g c3 t5 a2)))))) H4 Abbr H18) in (let
-H26 \def (eq_ind_r B b (\lambda (b0: B).(arity g (CHead c (Bind b0) u) t a2))
-H3 Abbr H18) in (let H27 \def (eq_ind_r B b (\lambda (b0: B).(not (eq B b0
-Abst))) H0 Abbr H18) in (arity_bind g Abbr H27 c2 u2 a1 (H2 c2 H5 u2 H22) w
-a2 (arity_subst0 g (CHead c2 (Bind Abbr) u2) t4 a2 (H25 (CHead c2 (Bind Abbr)
-u2) (wcpr0_comp c c2 H5 u u2 H22 (Bind Abbr)) t4 H20) c2 u2 O (getl_refl Abbr
-c2 u2) w H12)))))))))))))) H15)) H14))))))))))))) (\lambda (b0: B).(\lambda
-(H8: (not (eq B b0 Abst))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H9:
-(pr0 t3 t4)).(\lambda (H10: (((eq T t3 (THead (Bind b) u t)) \to (arity g c2
-t4 a2)))).(\lambda (u0: T).(\lambda (H11: (eq T (THead (Bind b0) u0 (lift (S
-O) O t3)) (THead (Bind b) u t))).(let H12 \def (f_equal T B (\lambda (e:
-T).(match e in T return (\lambda (_: T).B) with [(TSort _) \Rightarrow b0 |
-(TLRef _) \Rightarrow b0 | (THead k _ _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow
-b0])])) (THead (Bind b0) u0 (lift (S O) O t3)) (THead (Bind b) u t) H11) in
-((let H13 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_:
-T).T) with [(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t0
-_) \Rightarrow t0])) (THead (Bind b0) u0 (lift (S O) O t3)) (THead (Bind b) u
-t) H11) in ((let H14 \def (f_equal T T (\lambda (e: T).(match e in T return
-(\lambda (_: T).T) with [(TSort _) \Rightarrow ((let rec lref_map (f: ((nat
-\to nat))) (d: nat) (t0: T) on t0: T \def (match t0 with [(TSort n)
-\Rightarrow (TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i d) with
-[true \Rightarrow i | false \Rightarrow (f i)])) | (THead k u1 t5)
-\Rightarrow (THead k (lref_map f d u1) (lref_map f (s k d) t5))]) in
-lref_map) (\lambda (x: nat).(plus x (S O))) O t3) | (TLRef _) \Rightarrow
-((let rec lref_map (f: ((nat \to nat))) (d: nat) (t0: T) on t0: T \def (match
-t0 with [(TSort n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow (TLRef
-(match (blt i d) with [true \Rightarrow i | false \Rightarrow (f i)])) |
-(THead k u1 t5) \Rightarrow (THead k (lref_map f d u1) (lref_map f (s k d)
-t5))]) in lref_map) (\lambda (x: nat).(plus x (S O))) O t3) | (THead _ _ t0)
-\Rightarrow t0])) (THead (Bind b0) u0 (lift (S O) O t3)) (THead (Bind b) u t)
-H11) in (\lambda (_: (eq T u0 u)).(\lambda (H16: (eq B b0 b)).(let H17 \def
-(eq_ind B b0 (\lambda (b1: B).(not (eq B b1 Abst))) H8 b H16) in (let H18
-\def (eq_ind_r T t (\lambda (t0: T).((eq T t3 (THead (Bind b) u t0)) \to
+u H17) in (let H22 \def (eq_ind T u1 (\lambda (t0: T).(pr0 t0 u2)) H8 u H17)
+in (let H23 \def (eq_ind_r B b (\lambda (b0: B).((eq T t (THead (Bind b0) u
+t)) \to (arity g c2 t4 a2))) H19 Abbr H18) in (let H24 \def (eq_ind_r B b
+(\lambda (b0: B).((eq T u (THead (Bind b0) u t)) \to (arity g c2 u2 a2))) H21
+Abbr H18) in (let H25 \def (eq_ind_r B b (\lambda (b0: B).(\forall (c3:
+C).((wcpr0 (CHead c (Bind b0) u) c3) \to (\forall (t5: T).((pr0 t t5) \to
+(arity g c3 t5 a2)))))) H4 Abbr H18) in (let H26 \def (eq_ind_r B b (\lambda
+(b0: B).(arity g (CHead c (Bind b0) u) t a2)) H3 Abbr H18) in (let H27 \def
+(eq_ind_r B b (\lambda (b0: B).(not (eq B b0 Abst))) H0 Abbr H18) in
+(arity_bind g Abbr H27 c2 u2 a1 (H2 c2 H5 u2 H22) w a2 (arity_subst0 g (CHead
+c2 (Bind Abbr) u2) t4 a2 (H25 (CHead c2 (Bind Abbr) u2) (wcpr0_comp c c2 H5 u
+u2 H22 (Bind Abbr)) t4 H20) c2 u2 O (getl_refl Abbr c2 u2) w
+H12)))))))))))))) H15)) H14))))))))))))) (\lambda (b0: B).(\lambda (H8: (not
+(eq B b0 Abst))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H9: (pr0 t3
+t4)).(\lambda (H10: (((eq T t3 (THead (Bind b) u t)) \to (arity g c2 t4
+a2)))).(\lambda (u0: T).(\lambda (H11: (eq T (THead (Bind b0) u0 (lift (S O)
+O t3)) (THead (Bind b) u t))).(let H12 \def (f_equal T B (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow b0 | (TLRef _) \Rightarrow b0 |
+(THead k _ _) \Rightarrow (match k with [(Bind b1) \Rightarrow b1 | (Flat _)
+\Rightarrow b0])])) (THead (Bind b0) u0 (lift (S O) O t3)) (THead (Bind b) u
+t) H11) in ((let H13 \def (f_equal T T (\lambda (e: T).(match e with [(TSort
+_) \Rightarrow u0 | (TLRef _) \Rightarrow u0 | (THead _ t0 _) \Rightarrow
+t0])) (THead (Bind b0) u0 (lift (S O) O t3)) (THead (Bind b) u t) H11) in
+((let H14 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
+\Rightarrow (lref_map (\lambda (x: nat).(plus x (S O))) O t3) | (TLRef _)
+\Rightarrow (lref_map (\lambda (x: nat).(plus x (S O))) O t3) | (THead _ _
+t0) \Rightarrow t0])) (THead (Bind b0) u0 (lift (S O) O t3)) (THead (Bind b)
+u t) H11) in (\lambda (_: (eq T u0 u)).(\lambda (H16: (eq B b0 b)).(let H17
+\def (eq_ind B b0 (\lambda (b1: B).(not (eq B b1 Abst))) H8 b H16) in (let
+H18 \def (eq_ind_r T t (\lambda (t0: T).((eq T t3 (THead (Bind b) u t0)) \to
(arity g c2 t4 a2))) H10 (lift (S O) O t3) H14) in (let H19 \def (eq_ind_r T
t (\lambda (t0: T).(\forall (c3: C).((wcpr0 (CHead c (Bind b) u) c3) \to
(\forall (t5: T).((pr0 t0 t5) \to (arity g c3 t5 a2)))))) H4 (lift (S O) O
(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_:
(((eq T t3 (THead (Bind b) u t)) \to (arity g c2 t4 a2)))).(\lambda (u0:
T).(\lambda (H10: (eq T (THead (Flat Cast) u0 t3) (THead (Bind b) u t))).(let
-H11 \def (eq_ind T (THead (Flat Cast) u0 t3) (\lambda (ee: T).(match ee in T
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
+H11 \def (eq_ind T (THead (Flat Cast) u0 t3) (\lambda (ee: T).(match ee with
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
+\Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
True])])) I (THead (Bind b) u t) H10) in (False_ind (arity g c2 t4 a2)
H11)))))))) y t2 H7))) H6)))))))))))))))) (\lambda (c: C).(\lambda (u:
T).(\lambda (a1: A).(\lambda (_: (arity g c u (asucc g a1))).(\lambda (H1:
T).(\lambda (t4: T).(\lambda (H9: (pr0 t3 t4)).(\lambda (H10: (((eq T t3
(THead (Bind Abst) u t)) \to (arity g c2 t4 (AHead a1 a2))))).(\lambda (k:
K).(\lambda (H11: (eq T (THead k u1 t3) (THead (Bind Abst) u t))).(let H12
-\def (f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K)
-with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k0 _ _)
-\Rightarrow k0])) (THead k u1 t3) (THead (Bind Abst) u t) H11) in ((let H13
-\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T)
-with [(TSort _) \Rightarrow u1 | (TLRef _) \Rightarrow u1 | (THead _ t0 _)
-\Rightarrow t0])) (THead k u1 t3) (THead (Bind Abst) u t) H11) in ((let H14
-\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T)
-with [(TSort _) \Rightarrow t3 | (TLRef _) \Rightarrow t3 | (THead _ _ t0)
-\Rightarrow t0])) (THead k u1 t3) (THead (Bind Abst) u t) H11) in (\lambda
-(H15: (eq T u1 u)).(\lambda (H16: (eq K k (Bind Abst))).(eq_ind_r K (Bind
-Abst) (\lambda (k0: K).(arity g c2 (THead k0 u2 t4) (AHead a1 a2))) (let H17
-\def (eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead (Bind Abst) u t)) \to
-(arity g c2 t4 (AHead a1 a2)))) H10 t H14) in (let H18 \def (eq_ind T t3
-(\lambda (t0: T).(pr0 t0 t4)) H9 t H14) in (let H19 \def (eq_ind T u1
-(\lambda (t0: T).((eq T t0 (THead (Bind Abst) u t)) \to (arity g c2 u2 (AHead
-a1 a2)))) H8 u H15) in (let H20 \def (eq_ind T u1 (\lambda (t0: T).(pr0 t0
-u2)) H7 u H15) in (arity_head g c2 u2 a1 (H1 c2 H4 u2 H20) t4 a2 (H3 (CHead
-c2 (Bind Abst) u2) (wcpr0_comp c c2 H4 u u2 H20 (Bind Abst)) t4 H18)))))) k
-H16)))) H13)) H12)))))))))))) (\lambda (u0: T).(\lambda (v1: T).(\lambda (v2:
-T).(\lambda (_: (pr0 v1 v2)).(\lambda (_: (((eq T v1 (THead (Bind Abst) u t))
-\to (arity g c2 v2 (AHead a1 a2))))).(\lambda (t3: T).(\lambda (t4:
-T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Bind Abst) u t))
-\to (arity g c2 t4 (AHead a1 a2))))).(\lambda (H11: (eq T (THead (Flat Appl)
-v1 (THead (Bind Abst) u0 t3)) (THead (Bind Abst) u t))).(let H12 \def (eq_ind
-T (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3)) (\lambda (ee: T).(match ee
-in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef
-_) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
+\def (f_equal T K (\lambda (e: T).(match e with [(TSort _) \Rightarrow k |
+(TLRef _) \Rightarrow k | (THead k0 _ _) \Rightarrow k0])) (THead k u1 t3)
+(THead (Bind Abst) u t) H11) in ((let H13 \def (f_equal T T (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow u1 | (TLRef _) \Rightarrow u1 |
+(THead _ t0 _) \Rightarrow t0])) (THead k u1 t3) (THead (Bind Abst) u t) H11)
+in ((let H14 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
+\Rightarrow t3 | (TLRef _) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0]))
+(THead k u1 t3) (THead (Bind Abst) u t) H11) in (\lambda (H15: (eq T u1
+u)).(\lambda (H16: (eq K k (Bind Abst))).(eq_ind_r K (Bind Abst) (\lambda
+(k0: K).(arity g c2 (THead k0 u2 t4) (AHead a1 a2))) (let H17 \def (eq_ind T
+t3 (\lambda (t0: T).((eq T t0 (THead (Bind Abst) u t)) \to (arity g c2 t4
+(AHead a1 a2)))) H10 t H14) in (let H18 \def (eq_ind T t3 (\lambda (t0:
+T).(pr0 t0 t4)) H9 t H14) in (let H19 \def (eq_ind T u1 (\lambda (t0: T).((eq
+T t0 (THead (Bind Abst) u t)) \to (arity g c2 u2 (AHead a1 a2)))) H8 u H15)
+in (let H20 \def (eq_ind T u1 (\lambda (t0: T).(pr0 t0 u2)) H7 u H15) in
+(arity_head g c2 u2 a1 (H1 c2 H4 u2 H20) t4 a2 (H3 (CHead c2 (Bind Abst) u2)
+(wcpr0_comp c c2 H4 u u2 H20 (Bind Abst)) t4 H18)))))) k H16)))) H13))
+H12)))))))))))) (\lambda (u0: T).(\lambda (v1: T).(\lambda (v2: T).(\lambda
+(_: (pr0 v1 v2)).(\lambda (_: (((eq T v1 (THead (Bind Abst) u t)) \to (arity
+g c2 v2 (AHead a1 a2))))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0
+t3 t4)).(\lambda (_: (((eq T t3 (THead (Bind Abst) u t)) \to (arity g c2 t4
+(AHead a1 a2))))).(\lambda (H11: (eq T (THead (Flat Appl) v1 (THead (Bind
+Abst) u0 t3)) (THead (Bind Abst) u t))).(let H12 \def (eq_ind T (THead (Flat
+Appl) v1 (THead (Bind Abst) u0 t3)) (\lambda (ee: T).(match ee with [(TSort
+_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
+\Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
True])])) I (THead (Bind Abst) u t) H11) in (False_ind (arity g c2 (THead
(Bind Abbr) v2 t4) (AHead a1 a2)) H12)))))))))))) (\lambda (b: B).(\lambda
(_: (not (eq B b Abst))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (_: (pr0
t4)).(\lambda (_: (((eq T t3 (THead (Bind Abst) u t)) \to (arity g c2 t4
(AHead a1 a2))))).(\lambda (H14: (eq T (THead (Flat Appl) v1 (THead (Bind b)
u1 t3)) (THead (Bind Abst) u t))).(let H15 \def (eq_ind T (THead (Flat Appl)
-v1 (THead (Bind b) u1 t3)) (\lambda (ee: T).(match ee in T return (\lambda
-(_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
-| (THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind
-Abst) u t) H14) in (False_ind (arity g c2 (THead (Bind b) u2 (THead (Flat
-Appl) (lift (S O) O v2) t4)) (AHead a1 a2)) H15))))))))))))))))) (\lambda
-(u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (_: (((eq T u1
-(THead (Bind Abst) u t)) \to (arity g c2 u2 (AHead a1 a2))))).(\lambda (t3:
-T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead
-(Bind Abst) u t)) \to (arity g c2 t4 (AHead a1 a2))))).(\lambda (w:
-T).(\lambda (_: (subst0 O u2 t4 w)).(\lambda (H12: (eq T (THead (Bind Abbr)
-u1 t3) (THead (Bind Abst) u t))).(let H13 \def (eq_ind T (THead (Bind Abbr)
-u1 t3) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with
-[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
-True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat _)
-\Rightarrow False])])) I (THead (Bind Abst) u t) H12) in (False_ind (arity g
-c2 (THead (Bind Abbr) u2 w) (AHead a1 a2)) H13))))))))))))) (\lambda (b:
-B).(\lambda (H7: (not (eq B b Abst))).(\lambda (t3: T).(\lambda (t4:
-T).(\lambda (_: (pr0 t3 t4)).(\lambda (H9: (((eq T t3 (THead (Bind Abst) u
-t)) \to (arity g c2 t4 (AHead a1 a2))))).(\lambda (u0: T).(\lambda (H10: (eq
-T (THead (Bind b) u0 (lift (S O) O t3)) (THead (Bind Abst) u t))).(let H11
-\def (f_equal T B (\lambda (e: T).(match e in T return (\lambda (_: T).B)
-with [(TSort _) \Rightarrow b | (TLRef _) \Rightarrow b | (THead k _ _)
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b0)
+v1 (THead (Bind b) u1 t3)) (\lambda (ee: T).(match ee with [(TSort _)
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
+(match k with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I
+(THead (Bind Abst) u t) H14) in (False_ind (arity g c2 (THead (Bind b) u2
+(THead (Flat Appl) (lift (S O) O v2) t4)) (AHead a1 a2)) H15)))))))))))))))))
+(\lambda (u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (_:
+(((eq T u1 (THead (Bind Abst) u t)) \to (arity g c2 u2 (AHead a1
+a2))))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda
+(_: (((eq T t3 (THead (Bind Abst) u t)) \to (arity g c2 t4 (AHead a1
+a2))))).(\lambda (w: T).(\lambda (_: (subst0 O u2 t4 w)).(\lambda (H12: (eq T
+(THead (Bind Abbr) u1 t3) (THead (Bind Abst) u t))).(let H13 \def (eq_ind T
+(THead (Bind Abbr) u1 t3) (\lambda (ee: T).(match ee with [(TSort _)
+\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
+(match k with [(Bind b) \Rightarrow (match b with [Abbr \Rightarrow True |
+Abst \Rightarrow False | Void \Rightarrow False]) | (Flat _) \Rightarrow
+False])])) I (THead (Bind Abst) u t) H12) in (False_ind (arity g c2 (THead
+(Bind Abbr) u2 w) (AHead a1 a2)) H13))))))))))))) (\lambda (b: B).(\lambda
+(H7: (not (eq B b Abst))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0
+t3 t4)).(\lambda (H9: (((eq T t3 (THead (Bind Abst) u t)) \to (arity g c2 t4
+(AHead a1 a2))))).(\lambda (u0: T).(\lambda (H10: (eq T (THead (Bind b) u0
+(lift (S O) O t3)) (THead (Bind Abst) u t))).(let H11 \def (f_equal T B
+(\lambda (e: T).(match e with [(TSort _) \Rightarrow b | (TLRef _)
+\Rightarrow b | (THead k _ _) \Rightarrow (match k with [(Bind b0)
\Rightarrow b0 | (Flat _) \Rightarrow b])])) (THead (Bind b) u0 (lift (S O) O
t3)) (THead (Bind Abst) u t) H10) in ((let H12 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow u0 |
-(TLRef _) \Rightarrow u0 | (THead _ t0 _) \Rightarrow t0])) (THead (Bind b)
-u0 (lift (S O) O t3)) (THead (Bind Abst) u t) H10) in ((let H13 \def (f_equal
-T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow ((let rec lref_map (f: ((nat \to nat))) (d: nat) (t0: T) on t0: T
-\def (match t0 with [(TSort n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow
-(TLRef (match (blt i d) with [true \Rightarrow i | false \Rightarrow (f i)]))
-| (THead k u1 t5) \Rightarrow (THead k (lref_map f d u1) (lref_map f (s k d)
-t5))]) in lref_map) (\lambda (x: nat).(plus x (S O))) O t3) | (TLRef _)
-\Rightarrow ((let rec lref_map (f: ((nat \to nat))) (d: nat) (t0: T) on t0: T
-\def (match t0 with [(TSort n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow
-(TLRef (match (blt i d) with [true \Rightarrow i | false \Rightarrow (f i)]))
-| (THead k u1 t5) \Rightarrow (THead k (lref_map f d u1) (lref_map f (s k d)
-t5))]) in lref_map) (\lambda (x: nat).(plus x (S O))) O t3) | (THead _ _ t0)
-\Rightarrow t0])) (THead (Bind b) u0 (lift (S O) O t3)) (THead (Bind Abst) u
-t) H10) in (\lambda (_: (eq T u0 u)).(\lambda (H15: (eq B b Abst)).(let H16
-\def (eq_ind B b (\lambda (b0: B).(not (eq B b0 Abst))) H7 Abst H15) in (let
-H17 \def (eq_ind_r T t (\lambda (t0: T).((eq T t3 (THead (Bind Abst) u t0))
-\to (arity g c2 t4 (AHead a1 a2)))) H9 (lift (S O) O t3) H13) in (let H18
-\def (eq_ind_r T t (\lambda (t0: T).(\forall (c3: C).((wcpr0 (CHead c (Bind
-Abst) u) c3) \to (\forall (t5: T).((pr0 t0 t5) \to (arity g c3 t5 a2)))))) H3
-(lift (S O) O t3) H13) in (let H19 \def (eq_ind_r T t (\lambda (t0: T).(arity
-g (CHead c (Bind Abst) u) t0 a2)) H2 (lift (S O) O t3) H13) in (let H20 \def
-(match (H16 (refl_equal B Abst)) in False return (\lambda (_: False).(arity g
-c2 t4 (AHead a1 a2))) with []) in H20)))))))) H12)) H11)))))))))) (\lambda
-(t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3
-(THead (Bind Abst) u t)) \to (arity g c2 t4 (AHead a1 a2))))).(\lambda (u0:
-T).(\lambda (H9: (eq T (THead (Flat Cast) u0 t3) (THead (Bind Abst) u
-t))).(let H10 \def (eq_ind T (THead (Flat Cast) u0 t3) (\lambda (ee:
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
-False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K
-return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _)
-\Rightarrow True])])) I (THead (Bind Abst) u t) H9) in (False_ind (arity g c2
-t4 (AHead a1 a2)) H10)))))))) y t2 H6))) H5)))))))))))))) (\lambda (c:
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda
-(H1: ((\forall (c2: C).((wcpr0 c c2) \to (\forall (t2: T).((pr0 u t2) \to
-(arity g c2 t2 a1))))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (H2:
-(arity g c t (AHead a1 a2))).(\lambda (H3: ((\forall (c2: C).((wcpr0 c c2)
-\to (\forall (t2: T).((pr0 t t2) \to (arity g c2 t2 (AHead a1
-a2)))))))).(\lambda (c2: C).(\lambda (H4: (wcpr0 c c2)).(\lambda (t2:
-T).(\lambda (H5: (pr0 (THead (Flat Appl) u t) t2)).(insert_eq T (THead (Flat
-Appl) u t) (\lambda (t0: T).(pr0 t0 t2)) (\lambda (_: T).(arity g c2 t2 a2))
-(\lambda (y: T).(\lambda (H6: (pr0 y t2)).(pr0_ind (\lambda (t0: T).(\lambda
-(t3: T).((eq T t0 (THead (Flat Appl) u t)) \to (arity g c2 t3 a2)))) (\lambda
-(t0: T).(\lambda (H7: (eq T t0 (THead (Flat Appl) u t))).(let H8 \def
-(f_equal T T (\lambda (e: T).e) t0 (THead (Flat Appl) u t) H7) in (eq_ind_r T
-(THead (Flat Appl) u t) (\lambda (t3: T).(arity g c2 t3 a2)) (arity_appl g c2
-u a1 (H1 c2 H4 u (pr0_refl u)) t a2 (H3 c2 H4 t (pr0_refl t))) t0 H8))))
-(\lambda (u1: T).(\lambda (u2: T).(\lambda (H7: (pr0 u1 u2)).(\lambda (H8:
-(((eq T u1 (THead (Flat Appl) u t)) \to (arity g c2 u2 a2)))).(\lambda (t3:
-T).(\lambda (t4: T).(\lambda (H9: (pr0 t3 t4)).(\lambda (H10: (((eq T t3
-(THead (Flat Appl) u t)) \to (arity g c2 t4 a2)))).(\lambda (k: K).(\lambda
-(H11: (eq T (THead k u1 t3) (THead (Flat Appl) u t))).(let H12 \def (f_equal
-T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with [(TSort _)
-\Rightarrow k | (TLRef _) \Rightarrow k | (THead k0 _ _) \Rightarrow k0]))
-(THead k u1 t3) (THead (Flat Appl) u t) H11) in ((let H13 \def (f_equal T T
-(\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow u1 | (TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0]))
-(THead k u1 t3) (THead (Flat Appl) u t) H11) in ((let H14 \def (f_equal T T
-(\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow t3 | (TLRef _) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0]))
-(THead k u1 t3) (THead (Flat Appl) u t) H11) in (\lambda (H15: (eq T u1
-u)).(\lambda (H16: (eq K k (Flat Appl))).(eq_ind_r K (Flat Appl) (\lambda
-(k0: K).(arity g c2 (THead k0 u2 t4) a2)) (let H17 \def (eq_ind T t3 (\lambda
-(t0: T).((eq T t0 (THead (Flat Appl) u t)) \to (arity g c2 t4 a2))) H10 t
-H14) in (let H18 \def (eq_ind T t3 (\lambda (t0: T).(pr0 t0 t4)) H9 t H14) in
-(let H19 \def (eq_ind T u1 (\lambda (t0: T).((eq T t0 (THead (Flat Appl) u
-t)) \to (arity g c2 u2 a2))) H8 u H15) in (let H20 \def (eq_ind T u1 (\lambda
-(t0: T).(pr0 t0 u2)) H7 u H15) in (arity_appl g c2 u2 a1 (H1 c2 H4 u2 H20) t4
-a2 (H3 c2 H4 t4 H18)))))) k H16)))) H13)) H12)))))))))))) (\lambda (u0:
-T).(\lambda (v1: T).(\lambda (v2: T).(\lambda (H7: (pr0 v1 v2)).(\lambda (H8:
-(((eq T v1 (THead (Flat Appl) u t)) \to (arity g c2 v2 a2)))).(\lambda (t3:
-T).(\lambda (t4: T).(\lambda (H9: (pr0 t3 t4)).(\lambda (H10: (((eq T t3
-(THead (Flat Appl) u t)) \to (arity g c2 t4 a2)))).(\lambda (H11: (eq T
-(THead (Flat Appl) v1 (THead (Bind Abst) u0 t3)) (THead (Flat Appl) u
-t))).(let H12 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda
-(_: T).T) with [(TSort _) \Rightarrow v1 | (TLRef _) \Rightarrow v1 | (THead
-_ t0 _) \Rightarrow t0])) (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3))
-(THead (Flat Appl) u t) H11) in ((let H13 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow (THead
-(Bind Abst) u0 t3) | (TLRef _) \Rightarrow (THead (Bind Abst) u0 t3) | (THead
-_ _ t0) \Rightarrow t0])) (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3))
-(THead (Flat Appl) u t) H11) in (\lambda (H14: (eq T v1 u)).(let H15 \def
-(eq_ind T v1 (\lambda (t0: T).((eq T t0 (THead (Flat Appl) u t)) \to (arity g
-c2 v2 a2))) H8 u H14) in (let H16 \def (eq_ind T v1 (\lambda (t0: T).(pr0 t0
-v2)) H7 u H14) in (let H17 \def (eq_ind_r T t (\lambda (t0: T).((eq T t3
-(THead (Flat Appl) u t0)) \to (arity g c2 t4 a2))) H10 (THead (Bind Abst) u0
-t3) H13) in (let H18 \def (eq_ind_r T t (\lambda (t0: T).((eq T u (THead
-(Flat Appl) u t0)) \to (arity g c2 v2 a2))) H15 (THead (Bind Abst) u0 t3)
-H13) in (let H19 \def (eq_ind_r T t (\lambda (t0: T).(\forall (c3: C).((wcpr0
-c c3) \to (\forall (t5: T).((pr0 t0 t5) \to (arity g c3 t5 (AHead a1
-a2))))))) H3 (THead (Bind Abst) u0 t3) H13) in (let H20 \def (eq_ind_r T t
-(\lambda (t0: T).(arity g c t0 (AHead a1 a2))) H2 (THead (Bind Abst) u0 t3)
-H13) in (let H21 \def (H1 c2 H4 v2 H16) in (let H22 \def (H19 c2 H4 (THead
-(Bind Abst) u0 t4) (pr0_comp u0 u0 (pr0_refl u0) t3 t4 H9 (Bind Abst))) in
-(let H23 \def (arity_gen_abst g c2 u0 t4 (AHead a1 a2) H22) in (ex3_2_ind A A
-(\lambda (a3: A).(\lambda (a4: A).(eq A (AHead a1 a2) (AHead a3 a4))))
-(\lambda (a3: A).(\lambda (_: A).(arity g c2 u0 (asucc g a3)))) (\lambda (_:
-A).(\lambda (a4: A).(arity g (CHead c2 (Bind Abst) u0) t4 a4))) (arity g c2
-(THead (Bind Abbr) v2 t4) a2) (\lambda (x0: A).(\lambda (x1: A).(\lambda
-(H24: (eq A (AHead a1 a2) (AHead x0 x1))).(\lambda (H25: (arity g c2 u0
-(asucc g x0))).(\lambda (H26: (arity g (CHead c2 (Bind Abst) u0) t4 x1)).(let
-H27 \def (f_equal A A (\lambda (e: A).(match e in A return (\lambda (_: A).A)
-with [(ASort _ _) \Rightarrow a1 | (AHead a0 _) \Rightarrow a0])) (AHead a1
-a2) (AHead x0 x1) H24) in ((let H28 \def (f_equal A A (\lambda (e: A).(match
-e in A return (\lambda (_: A).A) with [(ASort _ _) \Rightarrow a2 | (AHead _
-a0) \Rightarrow a0])) (AHead a1 a2) (AHead x0 x1) H24) in (\lambda (H29: (eq
-A a1 x0)).(let H30 \def (eq_ind_r A x1 (\lambda (a0: A).(arity g (CHead c2
-(Bind Abst) u0) t4 a0)) H26 a2 H28) in (let H31 \def (eq_ind_r A x0 (\lambda
-(a0: A).(arity g c2 u0 (asucc g a0))) H25 a1 H29) in (arity_bind g Abbr
-not_abbr_abst c2 v2 a1 H21 t4 a2 (csuba_arity g (CHead c2 (Bind Abst) u0) t4
-a2 H30 (CHead c2 (Bind Abbr) v2) (csuba_abst g c2 c2 (csuba_refl g c2) u0 a1
-H31 v2 H21))))))) H27))))))) H23)))))))))))) H12)))))))))))) (\lambda (b:
-B).(\lambda (H7: (not (eq B b Abst))).(\lambda (v1: T).(\lambda (v2:
-T).(\lambda (H8: (pr0 v1 v2)).(\lambda (H9: (((eq T v1 (THead (Flat Appl) u
-t)) \to (arity g c2 v2 a2)))).(\lambda (u1: T).(\lambda (u2: T).(\lambda
-(H10: (pr0 u1 u2)).(\lambda (H11: (((eq T u1 (THead (Flat Appl) u t)) \to
-(arity g c2 u2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H12: (pr0
-t3 t4)).(\lambda (H13: (((eq T t3 (THead (Flat Appl) u t)) \to (arity g c2 t4
-a2)))).(\lambda (H14: (eq T (THead (Flat Appl) v1 (THead (Bind b) u1 t3))
-(THead (Flat Appl) u t))).(let H15 \def (f_equal T T (\lambda (e: T).(match e
-in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow v1 | (TLRef _)
-\Rightarrow v1 | (THead _ t0 _) \Rightarrow t0])) (THead (Flat Appl) v1
-(THead (Bind b) u1 t3)) (THead (Flat Appl) u t) H14) in ((let H16 \def
-(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
-[(TSort _) \Rightarrow (THead (Bind b) u1 t3) | (TLRef _) \Rightarrow (THead
-(Bind b) u1 t3) | (THead _ _ t0) \Rightarrow t0])) (THead (Flat Appl) v1
-(THead (Bind b) u1 t3)) (THead (Flat Appl) u t) H14) in (\lambda (H17: (eq T
-v1 u)).(let H18 \def (eq_ind T v1 (\lambda (t0: T).((eq T t0 (THead (Flat
-Appl) u t)) \to (arity g c2 v2 a2))) H9 u H17) in (let H19 \def (eq_ind T v1
-(\lambda (t0: T).(pr0 t0 v2)) H8 u H17) in (let H20 \def (eq_ind_r T t
-(\lambda (t0: T).((eq T t3 (THead (Flat Appl) u t0)) \to (arity g c2 t4 a2)))
-H13 (THead (Bind b) u1 t3) H16) in (let H21 \def (eq_ind_r T t (\lambda (t0:
-T).((eq T u1 (THead (Flat Appl) u t0)) \to (arity g c2 u2 a2))) H11 (THead
-(Bind b) u1 t3) H16) in (let H22 \def (eq_ind_r T t (\lambda (t0: T).((eq T u
-(THead (Flat Appl) u t0)) \to (arity g c2 v2 a2))) H18 (THead (Bind b) u1 t3)
-H16) in (let H23 \def (eq_ind_r T t (\lambda (t0: T).(\forall (c3: C).((wcpr0
-c c3) \to (\forall (t5: T).((pr0 t0 t5) \to (arity g c3 t5 (AHead a1
-a2))))))) H3 (THead (Bind b) u1 t3) H16) in (let H24 \def (eq_ind_r T t
-(\lambda (t0: T).(arity g c t0 (AHead a1 a2))) H2 (THead (Bind b) u1 t3) H16)
-in (let H25 \def (H1 c2 H4 v2 H19) in (let H26 \def (H23 c2 H4 (THead (Bind
-b) u2 t4) (pr0_comp u1 u2 H10 t3 t4 H12 (Bind b))) in (let H27 \def
-(arity_gen_bind b H7 g c2 u2 t4 (AHead a1 a2) H26) in (ex2_ind A (\lambda
-(a3: A).(arity g c2 u2 a3)) (\lambda (_: A).(arity g (CHead c2 (Bind b) u2)
-t4 (AHead a1 a2))) (arity g c2 (THead (Bind b) u2 (THead (Flat Appl) (lift (S
-O) O v2) t4)) a2) (\lambda (x: A).(\lambda (H28: (arity g c2 u2 x)).(\lambda
-(H29: (arity g (CHead c2 (Bind b) u2) t4 (AHead a1 a2))).(arity_bind g b H7
-c2 u2 x H28 (THead (Flat Appl) (lift (S O) O v2) t4) a2 (arity_appl g (CHead
-c2 (Bind b) u2) (lift (S O) O v2) a1 (arity_lift g c2 v2 a1 H25 (CHead c2
-(Bind b) u2) (S O) O (drop_drop (Bind b) O c2 c2 (drop_refl c2) u2)) t4 a2
-H29))))) H27))))))))))))) H15))))))))))))))))) (\lambda (u1: T).(\lambda (u2:
-T).(\lambda (_: (pr0 u1 u2)).(\lambda (_: (((eq T u1 (THead (Flat Appl) u t))
-\to (arity g c2 u2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0
-t3 t4)).(\lambda (_: (((eq T t3 (THead (Flat Appl) u t)) \to (arity g c2 t4
-a2)))).(\lambda (w: T).(\lambda (_: (subst0 O u2 t4 w)).(\lambda (H12: (eq T
-(THead (Bind Abbr) u1 t3) (THead (Flat Appl) u t))).(let H13 \def (eq_ind T
-(THead (Bind Abbr) u1 t3) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
-[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat
-Appl) u t) H12) in (False_ind (arity g c2 (THead (Bind Abbr) u2 w) a2)
+T).(match e with [(TSort _) \Rightarrow u0 | (TLRef _) \Rightarrow u0 |
+(THead _ t0 _) \Rightarrow t0])) (THead (Bind b) u0 (lift (S O) O t3)) (THead
+(Bind Abst) u t) H10) in ((let H13 \def (f_equal T T (\lambda (e: T).(match e
+with [(TSort _) \Rightarrow (lref_map (\lambda (x: nat).(plus x (S O))) O t3)
+| (TLRef _) \Rightarrow (lref_map (\lambda (x: nat).(plus x (S O))) O t3) |
+(THead _ _ t0) \Rightarrow t0])) (THead (Bind b) u0 (lift (S O) O t3)) (THead
+(Bind Abst) u t) H10) in (\lambda (_: (eq T u0 u)).(\lambda (H15: (eq B b
+Abst)).(let H16 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0 Abst))) H7
+Abst H15) in (let H17 \def (eq_ind_r T t (\lambda (t0: T).((eq T t3 (THead
+(Bind Abst) u t0)) \to (arity g c2 t4 (AHead a1 a2)))) H9 (lift (S O) O t3)
+H13) in (let H18 \def (eq_ind_r T t (\lambda (t0: T).(\forall (c3: C).((wcpr0
+(CHead c (Bind Abst) u) c3) \to (\forall (t5: T).((pr0 t0 t5) \to (arity g c3
+t5 a2)))))) H3 (lift (S O) O t3) H13) in (let H19 \def (eq_ind_r T t (\lambda
+(t0: T).(arity g (CHead c (Bind Abst) u) t0 a2)) H2 (lift (S O) O t3) H13) in
+(let H20 \def (match (H16 (refl_equal B Abst)) in False with []) in
+H20)))))))) H12)) H11)))))))))) (\lambda (t3: T).(\lambda (t4: T).(\lambda
+(_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Bind Abst) u t)) \to (arity
+g c2 t4 (AHead a1 a2))))).(\lambda (u0: T).(\lambda (H9: (eq T (THead (Flat
+Cast) u0 t3) (THead (Bind Abst) u t))).(let H10 \def (eq_ind T (THead (Flat
+Cast) u0 t3) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False |
+(TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind
+_) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind Abst) u
+t) H9) in (False_ind (arity g c2 t4 (AHead a1 a2)) H10)))))))) y t2 H6)))
+H5)))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda
+(_: (arity g c u a1)).(\lambda (H1: ((\forall (c2: C).((wcpr0 c c2) \to
+(\forall (t2: T).((pr0 u t2) \to (arity g c2 t2 a1))))))).(\lambda (t:
+T).(\lambda (a2: A).(\lambda (H2: (arity g c t (AHead a1 a2))).(\lambda (H3:
+((\forall (c2: C).((wcpr0 c c2) \to (\forall (t2: T).((pr0 t t2) \to (arity g
+c2 t2 (AHead a1 a2)))))))).(\lambda (c2: C).(\lambda (H4: (wcpr0 c
+c2)).(\lambda (t2: T).(\lambda (H5: (pr0 (THead (Flat Appl) u t)
+t2)).(insert_eq T (THead (Flat Appl) u t) (\lambda (t0: T).(pr0 t0 t2))
+(\lambda (_: T).(arity g c2 t2 a2)) (\lambda (y: T).(\lambda (H6: (pr0 y
+t2)).(pr0_ind (\lambda (t0: T).(\lambda (t3: T).((eq T t0 (THead (Flat Appl)
+u t)) \to (arity g c2 t3 a2)))) (\lambda (t0: T).(\lambda (H7: (eq T t0
+(THead (Flat Appl) u t))).(let H8 \def (f_equal T T (\lambda (e: T).e) t0
+(THead (Flat Appl) u t) H7) in (eq_ind_r T (THead (Flat Appl) u t) (\lambda
+(t3: T).(arity g c2 t3 a2)) (arity_appl g c2 u a1 (H1 c2 H4 u (pr0_refl u)) t
+a2 (H3 c2 H4 t (pr0_refl t))) t0 H8)))) (\lambda (u1: T).(\lambda (u2:
+T).(\lambda (H7: (pr0 u1 u2)).(\lambda (H8: (((eq T u1 (THead (Flat Appl) u
+t)) \to (arity g c2 u2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H9:
+(pr0 t3 t4)).(\lambda (H10: (((eq T t3 (THead (Flat Appl) u t)) \to (arity g
+c2 t4 a2)))).(\lambda (k: K).(\lambda (H11: (eq T (THead k u1 t3) (THead
+(Flat Appl) u t))).(let H12 \def (f_equal T K (\lambda (e: T).(match e with
+[(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k0 _ _)
+\Rightarrow k0])) (THead k u1 t3) (THead (Flat Appl) u t) H11) in ((let H13
+\def (f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow u1 |
+(TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0])) (THead k u1 t3)
+(THead (Flat Appl) u t) H11) in ((let H14 \def (f_equal T T (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow t3 | (TLRef _) \Rightarrow t3 |
+(THead _ _ t0) \Rightarrow t0])) (THead k u1 t3) (THead (Flat Appl) u t) H11)
+in (\lambda (H15: (eq T u1 u)).(\lambda (H16: (eq K k (Flat Appl))).(eq_ind_r
+K (Flat Appl) (\lambda (k0: K).(arity g c2 (THead k0 u2 t4) a2)) (let H17
+\def (eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead (Flat Appl) u t)) \to
+(arity g c2 t4 a2))) H10 t H14) in (let H18 \def (eq_ind T t3 (\lambda (t0:
+T).(pr0 t0 t4)) H9 t H14) in (let H19 \def (eq_ind T u1 (\lambda (t0: T).((eq
+T t0 (THead (Flat Appl) u t)) \to (arity g c2 u2 a2))) H8 u H15) in (let H20
+\def (eq_ind T u1 (\lambda (t0: T).(pr0 t0 u2)) H7 u H15) in (arity_appl g c2
+u2 a1 (H1 c2 H4 u2 H20) t4 a2 (H3 c2 H4 t4 H18)))))) k H16)))) H13))
+H12)))))))))))) (\lambda (u0: T).(\lambda (v1: T).(\lambda (v2: T).(\lambda
+(H7: (pr0 v1 v2)).(\lambda (H8: (((eq T v1 (THead (Flat Appl) u t)) \to
+(arity g c2 v2 a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H9: (pr0 t3
+t4)).(\lambda (H10: (((eq T t3 (THead (Flat Appl) u t)) \to (arity g c2 t4
+a2)))).(\lambda (H11: (eq T (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3))
+(THead (Flat Appl) u t))).(let H12 \def (f_equal T T (\lambda (e: T).(match e
+with [(TSort _) \Rightarrow v1 | (TLRef _) \Rightarrow v1 | (THead _ t0 _)
+\Rightarrow t0])) (THead (Flat Appl) v1 (THead (Bind Abst) u0 t3)) (THead
+(Flat Appl) u t) H11) in ((let H13 \def (f_equal T T (\lambda (e: T).(match e
+with [(TSort _) \Rightarrow (THead (Bind Abst) u0 t3) | (TLRef _) \Rightarrow
+(THead (Bind Abst) u0 t3) | (THead _ _ t0) \Rightarrow t0])) (THead (Flat
+Appl) v1 (THead (Bind Abst) u0 t3)) (THead (Flat Appl) u t) H11) in (\lambda
+(H14: (eq T v1 u)).(let H15 \def (eq_ind T v1 (\lambda (t0: T).((eq T t0
+(THead (Flat Appl) u t)) \to (arity g c2 v2 a2))) H8 u H14) in (let H16 \def
+(eq_ind T v1 (\lambda (t0: T).(pr0 t0 v2)) H7 u H14) in (let H17 \def
+(eq_ind_r T t (\lambda (t0: T).((eq T t3 (THead (Flat Appl) u t0)) \to (arity
+g c2 t4 a2))) H10 (THead (Bind Abst) u0 t3) H13) in (let H18 \def (eq_ind_r T
+t (\lambda (t0: T).((eq T u (THead (Flat Appl) u t0)) \to (arity g c2 v2
+a2))) H15 (THead (Bind Abst) u0 t3) H13) in (let H19 \def (eq_ind_r T t
+(\lambda (t0: T).(\forall (c3: C).((wcpr0 c c3) \to (\forall (t5: T).((pr0 t0
+t5) \to (arity g c3 t5 (AHead a1 a2))))))) H3 (THead (Bind Abst) u0 t3) H13)
+in (let H20 \def (eq_ind_r T t (\lambda (t0: T).(arity g c t0 (AHead a1 a2)))
+H2 (THead (Bind Abst) u0 t3) H13) in (let H21 \def (H1 c2 H4 v2 H16) in (let
+H22 \def (H19 c2 H4 (THead (Bind Abst) u0 t4) (pr0_comp u0 u0 (pr0_refl u0)
+t3 t4 H9 (Bind Abst))) in (let H23 \def (arity_gen_abst g c2 u0 t4 (AHead a1
+a2) H22) in (ex3_2_ind A A (\lambda (a3: A).(\lambda (a4: A).(eq A (AHead a1
+a2) (AHead a3 a4)))) (\lambda (a3: A).(\lambda (_: A).(arity g c2 u0 (asucc g
+a3)))) (\lambda (_: A).(\lambda (a4: A).(arity g (CHead c2 (Bind Abst) u0) t4
+a4))) (arity g c2 (THead (Bind Abbr) v2 t4) a2) (\lambda (x0: A).(\lambda
+(x1: A).(\lambda (H24: (eq A (AHead a1 a2) (AHead x0 x1))).(\lambda (H25:
+(arity g c2 u0 (asucc g x0))).(\lambda (H26: (arity g (CHead c2 (Bind Abst)
+u0) t4 x1)).(let H27 \def (f_equal A A (\lambda (e: A).(match e with [(ASort
+_ _) \Rightarrow a1 | (AHead a0 _) \Rightarrow a0])) (AHead a1 a2) (AHead x0
+x1) H24) in ((let H28 \def (f_equal A A (\lambda (e: A).(match e with [(ASort
+_ _) \Rightarrow a2 | (AHead _ a0) \Rightarrow a0])) (AHead a1 a2) (AHead x0
+x1) H24) in (\lambda (H29: (eq A a1 x0)).(let H30 \def (eq_ind_r A x1
+(\lambda (a0: A).(arity g (CHead c2 (Bind Abst) u0) t4 a0)) H26 a2 H28) in
+(let H31 \def (eq_ind_r A x0 (\lambda (a0: A).(arity g c2 u0 (asucc g a0)))
+H25 a1 H29) in (arity_bind g Abbr not_abbr_abst c2 v2 a1 H21 t4 a2
+(csuba_arity g (CHead c2 (Bind Abst) u0) t4 a2 H30 (CHead c2 (Bind Abbr) v2)
+(csuba_abst g c2 c2 (csuba_refl g c2) u0 a1 H31 v2 H21))))))) H27)))))))
+H23)))))))))))) H12)))))))))))) (\lambda (b: B).(\lambda (H7: (not (eq B b
+Abst))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (H8: (pr0 v1 v2)).(\lambda
+(H9: (((eq T v1 (THead (Flat Appl) u t)) \to (arity g c2 v2 a2)))).(\lambda
+(u1: T).(\lambda (u2: T).(\lambda (H10: (pr0 u1 u2)).(\lambda (H11: (((eq T
+u1 (THead (Flat Appl) u t)) \to (arity g c2 u2 a2)))).(\lambda (t3:
+T).(\lambda (t4: T).(\lambda (H12: (pr0 t3 t4)).(\lambda (H13: (((eq T t3
+(THead (Flat Appl) u t)) \to (arity g c2 t4 a2)))).(\lambda (H14: (eq T
+(THead (Flat Appl) v1 (THead (Bind b) u1 t3)) (THead (Flat Appl) u t))).(let
+H15 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow v1
+| (TLRef _) \Rightarrow v1 | (THead _ t0 _) \Rightarrow t0])) (THead (Flat
+Appl) v1 (THead (Bind b) u1 t3)) (THead (Flat Appl) u t) H14) in ((let H16
+\def (f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow (THead
+(Bind b) u1 t3) | (TLRef _) \Rightarrow (THead (Bind b) u1 t3) | (THead _ _
+t0) \Rightarrow t0])) (THead (Flat Appl) v1 (THead (Bind b) u1 t3)) (THead
+(Flat Appl) u t) H14) in (\lambda (H17: (eq T v1 u)).(let H18 \def (eq_ind T
+v1 (\lambda (t0: T).((eq T t0 (THead (Flat Appl) u t)) \to (arity g c2 v2
+a2))) H9 u H17) in (let H19 \def (eq_ind T v1 (\lambda (t0: T).(pr0 t0 v2))
+H8 u H17) in (let H20 \def (eq_ind_r T t (\lambda (t0: T).((eq T t3 (THead
+(Flat Appl) u t0)) \to (arity g c2 t4 a2))) H13 (THead (Bind b) u1 t3) H16)
+in (let H21 \def (eq_ind_r T t (\lambda (t0: T).((eq T u1 (THead (Flat Appl)
+u t0)) \to (arity g c2 u2 a2))) H11 (THead (Bind b) u1 t3) H16) in (let H22
+\def (eq_ind_r T t (\lambda (t0: T).((eq T u (THead (Flat Appl) u t0)) \to
+(arity g c2 v2 a2))) H18 (THead (Bind b) u1 t3) H16) in (let H23 \def
+(eq_ind_r T t (\lambda (t0: T).(\forall (c3: C).((wcpr0 c c3) \to (\forall
+(t5: T).((pr0 t0 t5) \to (arity g c3 t5 (AHead a1 a2))))))) H3 (THead (Bind
+b) u1 t3) H16) in (let H24 \def (eq_ind_r T t (\lambda (t0: T).(arity g c t0
+(AHead a1 a2))) H2 (THead (Bind b) u1 t3) H16) in (let H25 \def (H1 c2 H4 v2
+H19) in (let H26 \def (H23 c2 H4 (THead (Bind b) u2 t4) (pr0_comp u1 u2 H10
+t3 t4 H12 (Bind b))) in (let H27 \def (arity_gen_bind b H7 g c2 u2 t4 (AHead
+a1 a2) H26) in (ex2_ind A (\lambda (a3: A).(arity g c2 u2 a3)) (\lambda (_:
+A).(arity g (CHead c2 (Bind b) u2) t4 (AHead a1 a2))) (arity g c2 (THead
+(Bind b) u2 (THead (Flat Appl) (lift (S O) O v2) t4)) a2) (\lambda (x:
+A).(\lambda (H28: (arity g c2 u2 x)).(\lambda (H29: (arity g (CHead c2 (Bind
+b) u2) t4 (AHead a1 a2))).(arity_bind g b H7 c2 u2 x H28 (THead (Flat Appl)
+(lift (S O) O v2) t4) a2 (arity_appl g (CHead c2 (Bind b) u2) (lift (S O) O
+v2) a1 (arity_lift g c2 v2 a1 H25 (CHead c2 (Bind b) u2) (S O) O (drop_drop
+(Bind b) O c2 c2 (drop_refl c2) u2)) t4 a2 H29))))) H27)))))))))))))
+H15))))))))))))))))) (\lambda (u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1
+u2)).(\lambda (_: (((eq T u1 (THead (Flat Appl) u t)) \to (arity g c2 u2
+a2)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda
+(_: (((eq T t3 (THead (Flat Appl) u t)) \to (arity g c2 t4 a2)))).(\lambda
+(w: T).(\lambda (_: (subst0 O u2 t4 w)).(\lambda (H12: (eq T (THead (Bind
+Abbr) u1 t3) (THead (Flat Appl) u t))).(let H13 \def (eq_ind T (THead (Bind
+Abbr) u1 t3) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False |
+(TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind
+_) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat Appl) u
+t) H12) in (False_ind (arity g c2 (THead (Bind Abbr) u2 w) a2)
H13))))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda
(t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3
(THead (Flat Appl) u t)) \to (arity g c2 t4 a2)))).(\lambda (u0: T).(\lambda
(H10: (eq T (THead (Bind b) u0 (lift (S O) O t3)) (THead (Flat Appl) u
t))).(let H11 \def (eq_ind T (THead (Bind b) u0 (lift (S O) O t3)) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
-(match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True |
+(ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow
+False | (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow True |
(Flat _) \Rightarrow False])])) I (THead (Flat Appl) u t) H10) in (False_ind
(arity g c2 t4 a2) H11)))))))))) (\lambda (t3: T).(\lambda (t4: T).(\lambda
(_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Flat Appl) u t)) \to (arity
g c2 t4 a2)))).(\lambda (u0: T).(\lambda (H9: (eq T (THead (Flat Cast) u0 t3)
(THead (Flat Appl) u t))).(let H10 \def (eq_ind T (THead (Flat Cast) u0 t3)
-(\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
-(match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False |
-(Flat f) \Rightarrow (match f in F return (\lambda (_: F).Prop) with [Appl
-\Rightarrow False | Cast \Rightarrow True])])])) I (THead (Flat Appl) u t)
-H9) in (False_ind (arity g c2 t4 a2) H10)))))))) y t2 H6))) H5))))))))))))))
+(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead k _ _) \Rightarrow (match k with [(Bind _)
+\Rightarrow False | (Flat f) \Rightarrow (match f with [Appl \Rightarrow
+False | Cast \Rightarrow True])])])) I (THead (Flat Appl) u t) H9) in
+(False_ind (arity g c2 t4 a2) H10)))))))) y t2 H6))) H5))))))))))))))
(\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_: (arity g c u
(asucc g a0))).(\lambda (H1: ((\forall (c2: C).((wcpr0 c c2) \to (\forall
(t2: T).((pr0 u t2) \to (arity g c2 t2 (asucc g a0)))))))).(\lambda (t:
(t4: T).(\lambda (H9: (pr0 t3 t4)).(\lambda (H10: (((eq T t3 (THead (Flat
Cast) u t)) \to (arity g c2 t4 a0)))).(\lambda (k: K).(\lambda (H11: (eq T
(THead k u1 t3) (THead (Flat Cast) u t))).(let H12 \def (f_equal T K (\lambda
-(e: T).(match e in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k
-| (TLRef _) \Rightarrow k | (THead k0 _ _) \Rightarrow k0])) (THead k u1 t3)
-(THead (Flat Cast) u t) H11) in ((let H13 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow u1 |
-(TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0])) (THead k u1 t3)
-(THead (Flat Cast) u t) H11) in ((let H14 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t3 |
-(TLRef _) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0])) (THead k u1 t3)
-(THead (Flat Cast) u t) H11) in (\lambda (H15: (eq T u1 u)).(\lambda (H16:
-(eq K k (Flat Cast))).(eq_ind_r K (Flat Cast) (\lambda (k0: K).(arity g c2
-(THead k0 u2 t4) a0)) (let H17 \def (eq_ind T t3 (\lambda (t0: T).((eq T t0
-(THead (Flat Cast) u t)) \to (arity g c2 t4 a0))) H10 t H14) in (let H18 \def
+(e: T).(match e with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k |
+(THead k0 _ _) \Rightarrow k0])) (THead k u1 t3) (THead (Flat Cast) u t) H11)
+in ((let H13 \def (f_equal T T (\lambda (e: T).(match e with [(TSort _)
+\Rightarrow u1 | (TLRef _) \Rightarrow u1 | (THead _ t0 _) \Rightarrow t0]))
+(THead k u1 t3) (THead (Flat Cast) u t) H11) in ((let H14 \def (f_equal T T
+(\lambda (e: T).(match e with [(TSort _) \Rightarrow t3 | (TLRef _)
+\Rightarrow t3 | (THead _ _ t0) \Rightarrow t0])) (THead k u1 t3) (THead
+(Flat Cast) u t) H11) in (\lambda (H15: (eq T u1 u)).(\lambda (H16: (eq K k
+(Flat Cast))).(eq_ind_r K (Flat Cast) (\lambda (k0: K).(arity g c2 (THead k0
+u2 t4) a0)) (let H17 \def (eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead
+(Flat Cast) u t)) \to (arity g c2 t4 a0))) H10 t H14) in (let H18 \def
(eq_ind T t3 (\lambda (t0: T).(pr0 t0 t4)) H9 t H14) in (let H19 \def (eq_ind
T u1 (\lambda (t0: T).((eq T t0 (THead (Flat Cast) u t)) \to (arity g c2 u2
a0))) H8 u H15) in (let H20 \def (eq_ind T u1 (\lambda (t0: T).(pr0 t0 u2))
T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Flat Cast) u t))
\to (arity g c2 t4 a0)))).(\lambda (H11: (eq T (THead (Flat Appl) v1 (THead
(Bind Abst) u0 t3)) (THead (Flat Cast) u t))).(let H12 \def (eq_ind T (THead
-(Flat Appl) v1 (THead (Bind Abst) u0 t3)) (\lambda (ee: T).(match ee in T
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind _) \Rightarrow False | (Flat f) \Rightarrow (match f
-in F return (\lambda (_: F).Prop) with [Appl \Rightarrow True | Cast
-\Rightarrow False])])])) I (THead (Flat Cast) u t) H11) in (False_ind (arity
-g c2 (THead (Bind Abbr) v2 t4) a0) H12)))))))))))) (\lambda (b: B).(\lambda
-(_: (not (eq B b Abst))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (_: (pr0
-v1 v2)).(\lambda (_: (((eq T v1 (THead (Flat Cast) u t)) \to (arity g c2 v2
-a0)))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda
-(_: (((eq T u1 (THead (Flat Cast) u t)) \to (arity g c2 u2 a0)))).(\lambda
-(t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3
-(THead (Flat Cast) u t)) \to (arity g c2 t4 a0)))).(\lambda (H14: (eq T
-(THead (Flat Appl) v1 (THead (Bind b) u1 t3)) (THead (Flat Cast) u t))).(let
-H15 \def (eq_ind T (THead (Flat Appl) v1 (THead (Bind b) u1 t3)) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
+(Flat Appl) v1 (THead (Bind Abst) u0 t3)) (\lambda (ee: T).(match ee with
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _)
+\Rightarrow (match k with [(Bind _) \Rightarrow False | (Flat f) \Rightarrow
+(match f with [Appl \Rightarrow True | Cast \Rightarrow False])])])) I (THead
+(Flat Cast) u t) H11) in (False_ind (arity g c2 (THead (Bind Abbr) v2 t4) a0)
+H12)))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda
+(v1: T).(\lambda (v2: T).(\lambda (_: (pr0 v1 v2)).(\lambda (_: (((eq T v1
+(THead (Flat Cast) u t)) \to (arity g c2 v2 a0)))).(\lambda (u1: T).(\lambda
+(u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (_: (((eq T u1 (THead (Flat Cast)
+u t)) \to (arity g c2 u2 a0)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda
+(_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Flat Cast) u t)) \to (arity
+g c2 t4 a0)))).(\lambda (H14: (eq T (THead (Flat Appl) v1 (THead (Bind b) u1
+t3)) (THead (Flat Cast) u t))).(let H15 \def (eq_ind T (THead (Flat Appl) v1
+(THead (Bind b) u1 t3)) (\lambda (ee: T).(match ee with [(TSort _)
\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
-(match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False |
-(Flat f) \Rightarrow (match f in F return (\lambda (_: F).Prop) with [Appl
-\Rightarrow True | Cast \Rightarrow False])])])) I (THead (Flat Cast) u t)
-H14) in (False_ind (arity g c2 (THead (Bind b) u2 (THead (Flat Appl) (lift (S
-O) O v2) t4)) a0) H15))))))))))))))))) (\lambda (u1: T).(\lambda (u2:
-T).(\lambda (_: (pr0 u1 u2)).(\lambda (_: (((eq T u1 (THead (Flat Cast) u t))
-\to (arity g c2 u2 a0)))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0
+(match k with [(Bind _) \Rightarrow False | (Flat f) \Rightarrow (match f
+with [Appl \Rightarrow True | Cast \Rightarrow False])])])) I (THead (Flat
+Cast) u t) H14) in (False_ind (arity g c2 (THead (Bind b) u2 (THead (Flat
+Appl) (lift (S O) O v2) t4)) a0) H15))))))))))))))))) (\lambda (u1:
+T).(\lambda (u2: T).(\lambda (_: (pr0 u1 u2)).(\lambda (_: (((eq T u1 (THead
+(Flat Cast) u t)) \to (arity g c2 u2 a0)))).(\lambda (t3: T).(\lambda (t4:
+T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3 (THead (Flat Cast) u t))
+\to (arity g c2 t4 a0)))).(\lambda (w: T).(\lambda (_: (subst0 O u2 t4
+w)).(\lambda (H12: (eq T (THead (Bind Abbr) u1 t3) (THead (Flat Cast) u
+t))).(let H13 \def (eq_ind T (THead (Bind Abbr) u1 t3) (\lambda (ee:
+T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
+| (THead k _ _) \Rightarrow (match k with [(Bind _) \Rightarrow True | (Flat
+_) \Rightarrow False])])) I (THead (Flat Cast) u t) H12) in (False_ind (arity
+g c2 (THead (Bind Abbr) u2 w) a0) H13))))))))))))) (\lambda (b: B).(\lambda
+(_: (not (eq B b Abst))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (pr0
t3 t4)).(\lambda (_: (((eq T t3 (THead (Flat Cast) u t)) \to (arity g c2 t4
-a0)))).(\lambda (w: T).(\lambda (_: (subst0 O u2 t4 w)).(\lambda (H12: (eq T
-(THead (Bind Abbr) u1 t3) (THead (Flat Cast) u t))).(let H13 \def (eq_ind T
-(THead (Bind Abbr) u1 t3) (\lambda (ee: T).(match ee in T return (\lambda (_:
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
-(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
+a0)))).(\lambda (u0: T).(\lambda (H10: (eq T (THead (Bind b) u0 (lift (S O) O
+t3)) (THead (Flat Cast) u t))).(let H11 \def (eq_ind T (THead (Bind b) u0
+(lift (S O) O t3)) (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow
+False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k with
[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat
-Cast) u t) H12) in (False_ind (arity g c2 (THead (Bind Abbr) u2 w) a0)
-H13))))))))))))) (\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda
-(t3: T).(\lambda (t4: T).(\lambda (_: (pr0 t3 t4)).(\lambda (_: (((eq T t3
+Cast) u t) H10) in (False_ind (arity g c2 t4 a0) H11)))))))))) (\lambda (t3:
+T).(\lambda (t4: T).(\lambda (H7: (pr0 t3 t4)).(\lambda (H8: (((eq T t3
(THead (Flat Cast) u t)) \to (arity g c2 t4 a0)))).(\lambda (u0: T).(\lambda
-(H10: (eq T (THead (Bind b) u0 (lift (S O) O t3)) (THead (Flat Cast) u
-t))).(let H11 \def (eq_ind T (THead (Bind b) u0 (lift (S O) O t3)) (\lambda
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _)
-\Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
-(match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True |
-(Flat _) \Rightarrow False])])) I (THead (Flat Cast) u t) H10) in (False_ind
-(arity g c2 t4 a0) H11)))))))))) (\lambda (t3: T).(\lambda (t4: T).(\lambda
-(H7: (pr0 t3 t4)).(\lambda (H8: (((eq T t3 (THead (Flat Cast) u t)) \to
-(arity g c2 t4 a0)))).(\lambda (u0: T).(\lambda (H9: (eq T (THead (Flat Cast)
-u0 t3) (THead (Flat Cast) u t))).(let H10 \def (f_equal T T (\lambda (e:
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow u0 |
-(TLRef _) \Rightarrow u0 | (THead _ t0 _) \Rightarrow t0])) (THead (Flat
-Cast) u0 t3) (THead (Flat Cast) u t) H9) in ((let H11 \def (f_equal T T
-(\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
-\Rightarrow t3 | (TLRef _) \Rightarrow t3 | (THead _ _ t0) \Rightarrow t0]))
-(THead (Flat Cast) u0 t3) (THead (Flat Cast) u t) H9) in (\lambda (_: (eq T
-u0 u)).(let H13 \def (eq_ind T t3 (\lambda (t0: T).((eq T t0 (THead (Flat
-Cast) u t)) \to (arity g c2 t4 a0))) H8 t H11) in (let H14 \def (eq_ind T t3
-(\lambda (t0: T).(pr0 t0 t4)) H7 t H11) in (H3 c2 H4 t4 H14))))) H10))))))))
-y t2 H6))) H5))))))))))))) (\lambda (c: C).(\lambda (t: T).(\lambda (a1:
-A).(\lambda (_: (arity g c t a1)).(\lambda (H1: ((\forall (c2: C).((wcpr0 c
-c2) \to (\forall (t2: T).((pr0 t t2) \to (arity g c2 t2 a1))))))).(\lambda
-(a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c2: C).(\lambda (H3: (wcpr0 c
-c2)).(\lambda (t2: T).(\lambda (H4: (pr0 t t2)).(arity_repl g c2 t2 a1 (H1 c2
-H3 t2 H4) a2 H2)))))))))))) c1 t1 a H))))).
-(* COMMENTS
-Initial nodes: 10246
-END *)
+(H9: (eq T (THead (Flat Cast) u0 t3) (THead (Flat Cast) u t))).(let H10 \def
+(f_equal T T (\lambda (e: T).(match e with [(TSort _) \Rightarrow u0 | (TLRef
+_) \Rightarrow u0 | (THead _ t0 _) \Rightarrow t0])) (THead (Flat Cast) u0
+t3) (THead (Flat Cast) u t) H9) in ((let H11 \def (f_equal T T (\lambda (e:
+T).(match e with [(TSort _) \Rightarrow t3 | (TLRef _) \Rightarrow t3 |
+(THead _ _ t0) \Rightarrow t0])) (THead (Flat Cast) u0 t3) (THead (Flat Cast)
+u t) H9) in (\lambda (_: (eq T u0 u)).(let H13 \def (eq_ind T t3 (\lambda
+(t0: T).((eq T t0 (THead (Flat Cast) u t)) \to (arity g c2 t4 a0))) H8 t H11)
+in (let H14 \def (eq_ind T t3 (\lambda (t0: T).(pr0 t0 t4)) H7 t H11) in (H3
+c2 H4 t4 H14))))) H10)))))))) y t2 H6))) H5))))))))))))) (\lambda (c:
+C).(\lambda (t: T).(\lambda (a1: A).(\lambda (_: (arity g c t a1)).(\lambda
+(H1: ((\forall (c2: C).((wcpr0 c c2) \to (\forall (t2: T).((pr0 t t2) \to
+(arity g c2 t2 a1))))))).(\lambda (a2: A).(\lambda (H2: (leq g a1
+a2)).(\lambda (c2: C).(\lambda (H3: (wcpr0 c c2)).(\lambda (t2: T).(\lambda
+(H4: (pr0 t t2)).(arity_repl g c2 t2 a1 (H1 c2 H3 t2 H4) a2 H2)))))))))))) c1
+t1 a H))))).
theorem arity_sred_wcpr0_pr1:
\forall (t1: T).(\forall (t2: T).((pr1 t1 t2) \to (\forall (g: G).(\forall
(arity g c1 t4 a)).(\lambda (c2: C).(\lambda (H4: (wcpr0 c1 c2)).(H2 g c2 a
(arity_sred_wcpr0_pr0 g c1 t4 a H3 c2 H4 t3 H0) c2 (wcpr0_refl
c2)))))))))))))) t1 t2 H))).
-(* COMMENTS
-Initial nodes: 213
-END *)
theorem arity_sred_pr2:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pr2 c t1 t2) \to (\forall
G).(\lambda (a: A).(\lambda (H3: (arity g c0 t3 a)).(arity_subst0 g c0 t4 a
(arity_sred_wcpr0_pr0 g c0 t3 a H3 c0 (wcpr0_refl c0) t4 H1) d u i H0 t
H2)))))))))))))) c t1 t2 H)))).
-(* COMMENTS
-Initial nodes: 205
-END *)
theorem arity_sred_pr3:
\forall (c: C).(\forall (t1: T).(\forall (t2: T).((pr3 c t1 t2) \to (\forall
t3 a) \to (arity g c t5 a)))))).(\lambda (g: G).(\lambda (a: A).(\lambda (H3:
(arity g c t4 a)).(H2 g a (arity_sred_pr2 c t4 t3 H0 g a H3))))))))))) t1 t2
H)))).
-(* COMMENTS
-Initial nodes: 151
-END *)
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/fwd.ma".
+include "basic_1/arity/fwd.ma".
theorem node_inh:
\forall (g: G).(\forall (n: nat).(\forall (k: nat).(ex_2 C T (\lambda (c:
C).(\lambda (t: T).(arity g c t (ASort k n)))))))
\def
- \lambda (g: G).(\lambda (n: nat).(\lambda (k: nat).(nat_ind (\lambda (n0:
-nat).(ex_2 C T (\lambda (c: C).(\lambda (t: T).(arity g c t (ASort n0 n))))))
-(ex_2_intro C T (\lambda (c: C).(\lambda (t: T).(arity g c t (ASort O n))))
-(CSort O) (TSort n) (arity_sort g (CSort O) n)) (\lambda (n0: nat).(\lambda
-(H: (ex_2 C T (\lambda (c: C).(\lambda (t: T).(arity g c t (ASort n0
-n)))))).(let H0 \def H in (ex_2_ind C T (\lambda (c: C).(\lambda (t:
-T).(arity g c t (ASort n0 n)))) (ex_2 C T (\lambda (c: C).(\lambda (t:
-T).(arity g c t (ASort (S n0) n))))) (\lambda (x0: C).(\lambda (x1:
-T).(\lambda (H1: (arity g x0 x1 (ASort n0 n))).(ex_2_intro C T (\lambda (c:
-C).(\lambda (t: T).(arity g c t (ASort (S n0) n)))) (CHead x0 (Bind Abst) x1)
-(TLRef O) (arity_abst g (CHead x0 (Bind Abst) x1) x0 x1 O (getl_refl Abst x0
-x1) (ASort (S n0) n) H1))))) H0)))) k))).
-(* COMMENTS
-Initial nodes: 253
-END *)
+ \lambda (g: G).(\lambda (n: nat).(\lambda (k: nat).(let TMP_3 \def (\lambda
+(n0: nat).(let TMP_2 \def (\lambda (c: C).(\lambda (t: T).(let TMP_1 \def
+(ASort n0 n) in (arity g c t TMP_1)))) in (ex_2 C T TMP_2))) in (let TMP_5
+\def (\lambda (c: C).(\lambda (t: T).(let TMP_4 \def (ASort O n) in (arity g
+c t TMP_4)))) in (let TMP_6 \def (CSort O) in (let TMP_7 \def (TSort n) in
+(let TMP_8 \def (CSort O) in (let TMP_9 \def (arity_sort g TMP_8 n) in (let
+TMP_10 \def (ex_2_intro C T TMP_5 TMP_6 TMP_7 TMP_9) in (let TMP_30 \def
+(\lambda (n0: nat).(\lambda (H: (ex_2 C T (\lambda (c: C).(\lambda (t:
+T).(arity g c t (ASort n0 n)))))).(let H0 \def H in (let TMP_12 \def (\lambda
+(c: C).(\lambda (t: T).(let TMP_11 \def (ASort n0 n) in (arity g c t
+TMP_11)))) in (let TMP_15 \def (\lambda (c: C).(\lambda (t: T).(let TMP_13
+\def (S n0) in (let TMP_14 \def (ASort TMP_13 n) in (arity g c t TMP_14)))))
+in (let TMP_16 \def (ex_2 C T TMP_15) in (let TMP_29 \def (\lambda (x0:
+C).(\lambda (x1: T).(\lambda (H1: (arity g x0 x1 (ASort n0 n))).(let TMP_19
+\def (\lambda (c: C).(\lambda (t: T).(let TMP_17 \def (S n0) in (let TMP_18
+\def (ASort TMP_17 n) in (arity g c t TMP_18))))) in (let TMP_20 \def (Bind
+Abst) in (let TMP_21 \def (CHead x0 TMP_20 x1) in (let TMP_22 \def (TLRef O)
+in (let TMP_23 \def (Bind Abst) in (let TMP_24 \def (CHead x0 TMP_23 x1) in
+(let TMP_25 \def (getl_refl Abst x0 x1) in (let TMP_26 \def (S n0) in (let
+TMP_27 \def (ASort TMP_26 n) in (let TMP_28 \def (arity_abst g TMP_24 x0 x1 O
+TMP_25 TMP_27 H1) in (ex_2_intro C T TMP_19 TMP_21 TMP_22
+TMP_28)))))))))))))) in (ex_2_ind C T TMP_12 TMP_16 TMP_29 H0)))))))) in
+(nat_ind TMP_3 TMP_10 TMP_30 k))))))))))).
theorem arity_lift:
\forall (g: G).(\forall (c2: C).(\forall (t: T).(\forall (a: A).((arity g c2
c2) \to (arity g c1 (lift h d t) a)))))))))
\def
\lambda (g: G).(\lambda (c2: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c2 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
-A).(\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
-(arity g c1 (lift h d t0) a0)))))))) (\lambda (c: C).(\lambda (n:
-nat).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (_: (drop
-h d c1 c)).(eq_ind_r T (TSort n) (\lambda (t0: T).(arity g c1 t0 (ASort O
-n))) (arity_sort g c1 n) (lift h d (TSort n)) (lift_sort n h d))))))))
-(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda
-(H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (H1:
-(arity g d u a0)).(\lambda (H2: ((\forall (c1: C).(\forall (h: nat).(\forall
-(d0: nat).((drop h d0 c1 d) \to (arity g c1 (lift h d0 u) a0))))))).(\lambda
-(c1: C).(\lambda (h: nat).(\lambda (d0: nat).(\lambda (H3: (drop h d0 c1
-c)).(lt_le_e i d0 (arity g c1 (lift h d0 (TLRef i)) a0) (\lambda (H4: (lt i
-d0)).(eq_ind_r T (TLRef i) (\lambda (t0: T).(arity g c1 t0 a0)) (let H5 \def
-(drop_getl_trans_le i d0 (le_S_n i d0 (le_S (S i) d0 H4)) c1 c h H3 (CHead d
-(Bind Abbr) u) H0) in (ex3_2_ind C C (\lambda (e0: C).(\lambda (_: C).(drop i
-O c1 e0))) (\lambda (e0: C).(\lambda (e1: C).(drop h (minus d0 i) e0 e1)))
-(\lambda (_: C).(\lambda (e1: C).(clear e1 (CHead d (Bind Abbr) u)))) (arity
-g c1 (TLRef i) a0) (\lambda (x0: C).(\lambda (x1: C).(\lambda (H6: (drop i O
-c1 x0)).(\lambda (H7: (drop h (minus d0 i) x0 x1)).(\lambda (H8: (clear x1
-(CHead d (Bind Abbr) u))).(let H9 \def (eq_ind nat (minus d0 i) (\lambda (n:
-nat).(drop h n x0 x1)) H7 (S (minus d0 (S i))) (minus_x_Sy d0 i H4)) in (let
-H10 \def (drop_clear_S x1 x0 h (minus d0 (S i)) H9 Abbr d u H8) in (ex2_ind C
-(\lambda (c3: C).(clear x0 (CHead c3 (Bind Abbr) (lift h (minus d0 (S i))
-u)))) (\lambda (c3: C).(drop h (minus d0 (S i)) c3 d)) (arity g c1 (TLRef i)
-a0) (\lambda (x: C).(\lambda (H11: (clear x0 (CHead x (Bind Abbr) (lift h
-(minus d0 (S i)) u)))).(\lambda (H12: (drop h (minus d0 (S i)) x
-d)).(arity_abbr g c1 x (lift h (minus d0 (S i)) u) i (getl_intro i c1 (CHead
-x (Bind Abbr) (lift h (minus d0 (S i)) u)) x0 H6 H11) a0 (H2 x h (minus d0 (S
-i)) H12))))) H10)))))))) H5)) (lift h d0 (TLRef i)) (lift_lref_lt i h d0
-H4))) (\lambda (H4: (le d0 i)).(eq_ind_r T (TLRef (plus i h)) (\lambda (t0:
-T).(arity g c1 t0 a0)) (arity_abbr g c1 d u (plus i h) (drop_getl_trans_ge i
-c1 c d0 h H3 (CHead d (Bind Abbr) u) H0 H4) a0 H1) (lift h d0 (TLRef i))
-(lift_lref_ge i h d0 H4)))))))))))))))) (\lambda (c: C).(\lambda (d:
+(arity g c2 t a)).(let TMP_2 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
+(a0: A).(\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c)
+\to (let TMP_1 \def (lift h d t0) in (arity g c1 TMP_1 a0))))))))) in (let
+TMP_10 \def (\lambda (c: C).(\lambda (n: nat).(\lambda (c1: C).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (_: (drop h d c1 c)).(let TMP_3 \def (TSort
+n) in (let TMP_5 \def (\lambda (t0: T).(let TMP_4 \def (ASort O n) in (arity
+g c1 t0 TMP_4))) in (let TMP_6 \def (arity_sort g c1 n) in (let TMP_7 \def
+(TSort n) in (let TMP_8 \def (lift h d TMP_7) in (let TMP_9 \def (lift_sort n
+h d) in (eq_ind_r T TMP_3 TMP_5 TMP_6 TMP_8 TMP_9))))))))))))) in (let TMP_86
+\def (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
+nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0:
+A).(\lambda (H1: (arity g d u a0)).(\lambda (H2: ((\forall (c1: C).(\forall
+(h: nat).(\forall (d0: nat).((drop h d0 c1 d) \to (arity g c1 (lift h d0 u)
+a0))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d0: nat).(\lambda (H3:
+(drop h d0 c1 c)).(let TMP_11 \def (TLRef i) in (let TMP_12 \def (lift h d0
+TMP_11) in (let TMP_13 \def (arity g c1 TMP_12 a0) in (let TMP_73 \def
+(\lambda (H4: (lt i d0)).(let TMP_14 \def (TLRef i) in (let TMP_15 \def
+(\lambda (t0: T).(arity g c1 t0 a0)) in (let TMP_16 \def (S i) in (let TMP_17
+\def (S d0) in (let TMP_18 \def (S i) in (let TMP_19 \def (S TMP_18) in (let
+TMP_20 \def (S d0) in (let TMP_21 \def (S i) in (let TMP_22 \def (le_n_S
+TMP_21 d0 H4) in (let TMP_23 \def (le_S TMP_19 TMP_20 TMP_22) in (let TMP_24
+\def (le_S_n TMP_16 TMP_17 TMP_23) in (let TMP_25 \def (le_S_n i d0 TMP_24)
+in (let TMP_26 \def (Bind Abbr) in (let TMP_27 \def (CHead d TMP_26 u) in
+(let H5 \def (drop_getl_trans_le i d0 TMP_25 c1 c h H3 TMP_27 H0) in (let
+TMP_28 \def (\lambda (e0: C).(\lambda (_: C).(drop i O c1 e0))) in (let
+TMP_30 \def (\lambda (e0: C).(\lambda (e1: C).(let TMP_29 \def (minus d0 i)
+in (drop h TMP_29 e0 e1)))) in (let TMP_33 \def (\lambda (_: C).(\lambda (e1:
+C).(let TMP_31 \def (Bind Abbr) in (let TMP_32 \def (CHead d TMP_31 u) in
+(clear e1 TMP_32))))) in (let TMP_34 \def (TLRef i) in (let TMP_35 \def
+(arity g c1 TMP_34 a0) in (let TMP_68 \def (\lambda (x0: C).(\lambda (x1:
+C).(\lambda (H6: (drop i O c1 x0)).(\lambda (H7: (drop h (minus d0 i) x0
+x1)).(\lambda (H8: (clear x1 (CHead d (Bind Abbr) u))).(let TMP_36 \def
+(minus d0 i) in (let TMP_37 \def (\lambda (n: nat).(drop h n x0 x1)) in (let
+TMP_38 \def (S i) in (let TMP_39 \def (minus d0 TMP_38) in (let TMP_40 \def
+(S TMP_39) in (let TMP_41 \def (minus_x_Sy d0 i H4) in (let H9 \def (eq_ind
+nat TMP_36 TMP_37 H7 TMP_40 TMP_41) in (let TMP_42 \def (S i) in (let TMP_43
+\def (minus d0 TMP_42) in (let H10 \def (drop_clear_S x1 x0 h TMP_43 H9 Abbr
+d u H8) in (let TMP_49 \def (\lambda (c3: C).(let TMP_44 \def (Bind Abbr) in
+(let TMP_45 \def (S i) in (let TMP_46 \def (minus d0 TMP_45) in (let TMP_47
+\def (lift h TMP_46 u) in (let TMP_48 \def (CHead c3 TMP_44 TMP_47) in (clear
+x0 TMP_48))))))) in (let TMP_52 \def (\lambda (c3: C).(let TMP_50 \def (S i)
+in (let TMP_51 \def (minus d0 TMP_50) in (drop h TMP_51 c3 d)))) in (let
+TMP_53 \def (TLRef i) in (let TMP_54 \def (arity g c1 TMP_53 a0) in (let
+TMP_67 \def (\lambda (x: C).(\lambda (H11: (clear x0 (CHead x (Bind Abbr)
+(lift h (minus d0 (S i)) u)))).(\lambda (H12: (drop h (minus d0 (S i)) x
+d)).(let TMP_55 \def (S i) in (let TMP_56 \def (minus d0 TMP_55) in (let
+TMP_57 \def (lift h TMP_56 u) in (let TMP_58 \def (Bind Abbr) in (let TMP_59
+\def (S i) in (let TMP_60 \def (minus d0 TMP_59) in (let TMP_61 \def (lift h
+TMP_60 u) in (let TMP_62 \def (CHead x TMP_58 TMP_61) in (let TMP_63 \def
+(getl_intro i c1 TMP_62 x0 H6 H11) in (let TMP_64 \def (S i) in (let TMP_65
+\def (minus d0 TMP_64) in (let TMP_66 \def (H2 x h TMP_65 H12) in (arity_abbr
+g c1 x TMP_57 i TMP_63 a0 TMP_66)))))))))))))))) in (ex2_ind C TMP_49 TMP_52
+TMP_54 TMP_67 H10))))))))))))))))))))) in (let TMP_69 \def (ex3_2_ind C C
+TMP_28 TMP_30 TMP_33 TMP_35 TMP_68 H5) in (let TMP_70 \def (TLRef i) in (let
+TMP_71 \def (lift h d0 TMP_70) in (let TMP_72 \def (lift_lref_lt i h d0 H4)
+in (eq_ind_r T TMP_14 TMP_15 TMP_69 TMP_71 TMP_72)))))))))))))))))))))))))))
+in (let TMP_85 \def (\lambda (H4: (le d0 i)).(let TMP_74 \def (plus i h) in
+(let TMP_75 \def (TLRef TMP_74) in (let TMP_76 \def (\lambda (t0: T).(arity g
+c1 t0 a0)) in (let TMP_77 \def (plus i h) in (let TMP_78 \def (Bind Abbr) in
+(let TMP_79 \def (CHead d TMP_78 u) in (let TMP_80 \def (drop_getl_trans_ge i
+c1 c d0 h H3 TMP_79 H0 H4) in (let TMP_81 \def (arity_abbr g c1 d u TMP_77
+TMP_80 a0 H1) in (let TMP_82 \def (TLRef i) in (let TMP_83 \def (lift h d0
+TMP_82) in (let TMP_84 \def (lift_lref_ge i h d0 H4) in (eq_ind_r T TMP_75
+TMP_76 TMP_81 TMP_83 TMP_84))))))))))))) in (lt_le_e i d0 TMP_13 TMP_73
+TMP_85)))))))))))))))))) in (let TMP_162 \def (\lambda (c: C).(\lambda (d:
C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind
Abst) u))).(\lambda (a0: A).(\lambda (H1: (arity g d u (asucc g
a0))).(\lambda (H2: ((\forall (c1: C).(\forall (h: nat).(\forall (d0:
nat).((drop h d0 c1 d) \to (arity g c1 (lift h d0 u) (asucc g
a0)))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d0: nat).(\lambda
-(H3: (drop h d0 c1 c)).(lt_le_e i d0 (arity g c1 (lift h d0 (TLRef i)) a0)
-(\lambda (H4: (lt i d0)).(eq_ind_r T (TLRef i) (\lambda (t0: T).(arity g c1
-t0 a0)) (let H5 \def (drop_getl_trans_le i d0 (le_S_n i d0 (le_S (S i) d0
-H4)) c1 c h H3 (CHead d (Bind Abst) u) H0) in (ex3_2_ind C C (\lambda (e0:
-C).(\lambda (_: C).(drop i O c1 e0))) (\lambda (e0: C).(\lambda (e1: C).(drop
-h (minus d0 i) e0 e1))) (\lambda (_: C).(\lambda (e1: C).(clear e1 (CHead d
-(Bind Abst) u)))) (arity g c1 (TLRef i) a0) (\lambda (x0: C).(\lambda (x1:
-C).(\lambda (H6: (drop i O c1 x0)).(\lambda (H7: (drop h (minus d0 i) x0
-x1)).(\lambda (H8: (clear x1 (CHead d (Bind Abst) u))).(let H9 \def (eq_ind
-nat (minus d0 i) (\lambda (n: nat).(drop h n x0 x1)) H7 (S (minus d0 (S i)))
-(minus_x_Sy d0 i H4)) in (let H10 \def (drop_clear_S x1 x0 h (minus d0 (S i))
-H9 Abst d u H8) in (ex2_ind C (\lambda (c3: C).(clear x0 (CHead c3 (Bind
-Abst) (lift h (minus d0 (S i)) u)))) (\lambda (c3: C).(drop h (minus d0 (S
-i)) c3 d)) (arity g c1 (TLRef i) a0) (\lambda (x: C).(\lambda (H11: (clear x0
-(CHead x (Bind Abst) (lift h (minus d0 (S i)) u)))).(\lambda (H12: (drop h
-(minus d0 (S i)) x d)).(arity_abst g c1 x (lift h (minus d0 (S i)) u) i
-(getl_intro i c1 (CHead x (Bind Abst) (lift h (minus d0 (S i)) u)) x0 H6 H11)
-a0 (H2 x h (minus d0 (S i)) H12))))) H10)))))))) H5)) (lift h d0 (TLRef i))
-(lift_lref_lt i h d0 H4))) (\lambda (H4: (le d0 i)).(eq_ind_r T (TLRef (plus
-i h)) (\lambda (t0: T).(arity g c1 t0 a0)) (arity_abst g c1 d u (plus i h)
-(drop_getl_trans_ge i c1 c d0 h H3 (CHead d (Bind Abst) u) H0 H4) a0 H1)
-(lift h d0 (TLRef i)) (lift_lref_ge i h d0 H4)))))))))))))))) (\lambda (b:
-B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2: ((\forall
-(c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to (arity g c1
-(lift h d u) a1))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity
-g (CHead c (Bind b) u) t0 a2)).(\lambda (H4: ((\forall (c1: C).(\forall (h:
-nat).(\forall (d: nat).((drop h d c1 (CHead c (Bind b) u)) \to (arity g c1
-(lift h d t0) a2))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d:
-nat).(\lambda (H5: (drop h d c1 c)).(eq_ind_r T (THead (Bind b) (lift h d u)
-(lift h (s (Bind b) d) t0)) (\lambda (t1: T).(arity g c1 t1 a2)) (arity_bind
-g b H0 c1 (lift h d u) a1 (H2 c1 h d H5) (lift h (s (Bind b) d) t0) a2 (H4
-(CHead c1 (Bind b) (lift h d u)) h (s (Bind b) d) (drop_skip_bind h d c1 c H5
-b u))) (lift h d (THead (Bind b) u t0)) (lift_head (Bind b) u t0 h
-d))))))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda
-(_: (arity g c u (asucc g a1))).(\lambda (H1: ((\forall (c1: C).(\forall (h:
-nat).(\forall (d: nat).((drop h d c1 c) \to (arity g c1 (lift h d u) (asucc g
+(H3: (drop h d0 c1 c)).(let TMP_87 \def (TLRef i) in (let TMP_88 \def (lift h
+d0 TMP_87) in (let TMP_89 \def (arity g c1 TMP_88 a0) in (let TMP_149 \def
+(\lambda (H4: (lt i d0)).(let TMP_90 \def (TLRef i) in (let TMP_91 \def
+(\lambda (t0: T).(arity g c1 t0 a0)) in (let TMP_92 \def (S i) in (let TMP_93
+\def (S d0) in (let TMP_94 \def (S i) in (let TMP_95 \def (S TMP_94) in (let
+TMP_96 \def (S d0) in (let TMP_97 \def (S i) in (let TMP_98 \def (le_n_S
+TMP_97 d0 H4) in (let TMP_99 \def (le_S TMP_95 TMP_96 TMP_98) in (let TMP_100
+\def (le_S_n TMP_92 TMP_93 TMP_99) in (let TMP_101 \def (le_S_n i d0 TMP_100)
+in (let TMP_102 \def (Bind Abst) in (let TMP_103 \def (CHead d TMP_102 u) in
+(let H5 \def (drop_getl_trans_le i d0 TMP_101 c1 c h H3 TMP_103 H0) in (let
+TMP_104 \def (\lambda (e0: C).(\lambda (_: C).(drop i O c1 e0))) in (let
+TMP_106 \def (\lambda (e0: C).(\lambda (e1: C).(let TMP_105 \def (minus d0 i)
+in (drop h TMP_105 e0 e1)))) in (let TMP_109 \def (\lambda (_: C).(\lambda
+(e1: C).(let TMP_107 \def (Bind Abst) in (let TMP_108 \def (CHead d TMP_107
+u) in (clear e1 TMP_108))))) in (let TMP_110 \def (TLRef i) in (let TMP_111
+\def (arity g c1 TMP_110 a0) in (let TMP_144 \def (\lambda (x0: C).(\lambda
+(x1: C).(\lambda (H6: (drop i O c1 x0)).(\lambda (H7: (drop h (minus d0 i) x0
+x1)).(\lambda (H8: (clear x1 (CHead d (Bind Abst) u))).(let TMP_112 \def
+(minus d0 i) in (let TMP_113 \def (\lambda (n: nat).(drop h n x0 x1)) in (let
+TMP_114 \def (S i) in (let TMP_115 \def (minus d0 TMP_114) in (let TMP_116
+\def (S TMP_115) in (let TMP_117 \def (minus_x_Sy d0 i H4) in (let H9 \def
+(eq_ind nat TMP_112 TMP_113 H7 TMP_116 TMP_117) in (let TMP_118 \def (S i) in
+(let TMP_119 \def (minus d0 TMP_118) in (let H10 \def (drop_clear_S x1 x0 h
+TMP_119 H9 Abst d u H8) in (let TMP_125 \def (\lambda (c3: C).(let TMP_120
+\def (Bind Abst) in (let TMP_121 \def (S i) in (let TMP_122 \def (minus d0
+TMP_121) in (let TMP_123 \def (lift h TMP_122 u) in (let TMP_124 \def (CHead
+c3 TMP_120 TMP_123) in (clear x0 TMP_124))))))) in (let TMP_128 \def (\lambda
+(c3: C).(let TMP_126 \def (S i) in (let TMP_127 \def (minus d0 TMP_126) in
+(drop h TMP_127 c3 d)))) in (let TMP_129 \def (TLRef i) in (let TMP_130 \def
+(arity g c1 TMP_129 a0) in (let TMP_143 \def (\lambda (x: C).(\lambda (H11:
+(clear x0 (CHead x (Bind Abst) (lift h (minus d0 (S i)) u)))).(\lambda (H12:
+(drop h (minus d0 (S i)) x d)).(let TMP_131 \def (S i) in (let TMP_132 \def
+(minus d0 TMP_131) in (let TMP_133 \def (lift h TMP_132 u) in (let TMP_134
+\def (Bind Abst) in (let TMP_135 \def (S i) in (let TMP_136 \def (minus d0
+TMP_135) in (let TMP_137 \def (lift h TMP_136 u) in (let TMP_138 \def (CHead
+x TMP_134 TMP_137) in (let TMP_139 \def (getl_intro i c1 TMP_138 x0 H6 H11)
+in (let TMP_140 \def (S i) in (let TMP_141 \def (minus d0 TMP_140) in (let
+TMP_142 \def (H2 x h TMP_141 H12) in (arity_abst g c1 x TMP_133 i TMP_139 a0
+TMP_142)))))))))))))))) in (ex2_ind C TMP_125 TMP_128 TMP_130 TMP_143
+H10))))))))))))))))))))) in (let TMP_145 \def (ex3_2_ind C C TMP_104 TMP_106
+TMP_109 TMP_111 TMP_144 H5) in (let TMP_146 \def (TLRef i) in (let TMP_147
+\def (lift h d0 TMP_146) in (let TMP_148 \def (lift_lref_lt i h d0 H4) in
+(eq_ind_r T TMP_90 TMP_91 TMP_145 TMP_147 TMP_148)))))))))))))))))))))))))))
+in (let TMP_161 \def (\lambda (H4: (le d0 i)).(let TMP_150 \def (plus i h) in
+(let TMP_151 \def (TLRef TMP_150) in (let TMP_152 \def (\lambda (t0:
+T).(arity g c1 t0 a0)) in (let TMP_153 \def (plus i h) in (let TMP_154 \def
+(Bind Abst) in (let TMP_155 \def (CHead d TMP_154 u) in (let TMP_156 \def
+(drop_getl_trans_ge i c1 c d0 h H3 TMP_155 H0 H4) in (let TMP_157 \def
+(arity_abst g c1 d u TMP_153 TMP_156 a0 H1) in (let TMP_158 \def (TLRef i) in
+(let TMP_159 \def (lift h d0 TMP_158) in (let TMP_160 \def (lift_lref_ge i h
+d0 H4) in (eq_ind_r T TMP_151 TMP_152 TMP_157 TMP_159 TMP_160))))))))))))) in
+(lt_le_e i d0 TMP_89 TMP_149 TMP_161)))))))))))))))))) in (let TMP_188 \def
+(\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda
+(u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2:
+((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
+(arity g c1 (lift h d u) a1))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda
+(_: (arity g (CHead c (Bind b) u) t0 a2)).(\lambda (H4: ((\forall (c1:
+C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 (CHead c (Bind b) u))
+\to (arity g c1 (lift h d t0) a2))))))).(\lambda (c1: C).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (H5: (drop h d c1 c)).(let TMP_163 \def (Bind
+b) in (let TMP_164 \def (lift h d u) in (let TMP_165 \def (Bind b) in (let
+TMP_166 \def (s TMP_165 d) in (let TMP_167 \def (lift h TMP_166 t0) in (let
+TMP_168 \def (THead TMP_163 TMP_164 TMP_167) in (let TMP_169 \def (\lambda
+(t1: T).(arity g c1 t1 a2)) in (let TMP_170 \def (lift h d u) in (let TMP_171
+\def (H2 c1 h d H5) in (let TMP_172 \def (Bind b) in (let TMP_173 \def (s
+TMP_172 d) in (let TMP_174 \def (lift h TMP_173 t0) in (let TMP_175 \def
+(Bind b) in (let TMP_176 \def (lift h d u) in (let TMP_177 \def (CHead c1
+TMP_175 TMP_176) in (let TMP_178 \def (Bind b) in (let TMP_179 \def (s
+TMP_178 d) in (let TMP_180 \def (drop_skip_bind h d c1 c H5 b u) in (let
+TMP_181 \def (H4 TMP_177 h TMP_179 TMP_180) in (let TMP_182 \def (arity_bind
+g b H0 c1 TMP_170 a1 TMP_171 TMP_174 a2 TMP_181) in (let TMP_183 \def (Bind
+b) in (let TMP_184 \def (THead TMP_183 u t0) in (let TMP_185 \def (lift h d
+TMP_184) in (let TMP_186 \def (Bind b) in (let TMP_187 \def (lift_head
+TMP_186 u t0 h d) in (eq_ind_r T TMP_168 TMP_169 TMP_182 TMP_185
+TMP_187))))))))))))))))))))))))))))))))))))))))) in (let TMP_215 \def
+(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
+(asucc g a1))).(\lambda (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
+nat).((drop h d c1 c) \to (arity g c1 (lift h d u) (asucc g
a1)))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c
(Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (c1: C).(\forall (h:
nat).(\forall (d: nat).((drop h d c1 (CHead c (Bind Abst) u)) \to (arity g c1
(lift h d t0) a2))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d:
-nat).(\lambda (H4: (drop h d c1 c)).(eq_ind_r T (THead (Bind Abst) (lift h d
-u) (lift h (s (Bind Abst) d) t0)) (\lambda (t1: T).(arity g c1 t1 (AHead a1
-a2))) (arity_head g c1 (lift h d u) a1 (H1 c1 h d H4) (lift h (s (Bind Abst)
-d) t0) a2 (H3 (CHead c1 (Bind Abst) (lift h d u)) h (s (Bind Abst) d)
-(drop_skip_bind h d c1 c H4 Abst u))) (lift h d (THead (Bind Abst) u t0))
-(lift_head (Bind Abst) u t0 h d))))))))))))))) (\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H1: ((\forall
-(c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to (arity g c1
-(lift h d u) a1))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity
-g c t0 (AHead a1 a2))).(\lambda (H3: ((\forall (c1: C).(\forall (h:
-nat).(\forall (d: nat).((drop h d c1 c) \to (arity g c1 (lift h d t0) (AHead
-a1 a2)))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d: nat).(\lambda
-(H4: (drop h d c1 c)).(eq_ind_r T (THead (Flat Appl) (lift h d u) (lift h (s
-(Flat Appl) d) t0)) (\lambda (t1: T).(arity g c1 t1 a2)) (arity_appl g c1
-(lift h d u) a1 (H1 c1 h d H4) (lift h (s (Flat Appl) d) t0) a2 (H3 c1 h (s
-(Flat Appl) d) H4)) (lift h d (THead (Flat Appl) u t0)) (lift_head (Flat
-Appl) u t0 h d))))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a0:
-A).(\lambda (_: (arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c1:
-C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to (arity g c1 (lift
-h d u) (asucc g a0)))))))).(\lambda (t0: T).(\lambda (_: (arity g c t0
-a0)).(\lambda (H3: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
-nat).((drop h d c1 c) \to (arity g c1 (lift h d t0) a0))))))).(\lambda (c1:
-C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H4: (drop h d c1
-c)).(eq_ind_r T (THead (Flat Cast) (lift h d u) (lift h (s (Flat Cast) d)
-t0)) (\lambda (t1: T).(arity g c1 t1 a0)) (arity_cast g c1 (lift h d u) a0
-(H1 c1 h d H4) (lift h (s (Flat Cast) d) t0) (H3 c1 h (s (Flat Cast) d) H4))
-(lift h d (THead (Flat Cast) u t0)) (lift_head (Flat Cast) u t0 h
-d)))))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda
-(_: (arity g c t0 a1)).(\lambda (H1: ((\forall (c1: C).(\forall (h:
-nat).(\forall (d: nat).((drop h d c1 c) \to (arity g c1 (lift h d t0)
-a1))))))).(\lambda (a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c1:
-C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H3: (drop h d c1
-c)).(arity_repl g c1 (lift h d t0) a1 (H1 c1 h d H3) a2 H2)))))))))))) c2 t a
-H))))).
-(* COMMENTS
-Initial nodes: 2661
-END *)
+nat).(\lambda (H4: (drop h d c1 c)).(let TMP_189 \def (Bind Abst) in (let
+TMP_190 \def (lift h d u) in (let TMP_191 \def (Bind Abst) in (let TMP_192
+\def (s TMP_191 d) in (let TMP_193 \def (lift h TMP_192 t0) in (let TMP_194
+\def (THead TMP_189 TMP_190 TMP_193) in (let TMP_196 \def (\lambda (t1:
+T).(let TMP_195 \def (AHead a1 a2) in (arity g c1 t1 TMP_195))) in (let
+TMP_197 \def (lift h d u) in (let TMP_198 \def (H1 c1 h d H4) in (let TMP_199
+\def (Bind Abst) in (let TMP_200 \def (s TMP_199 d) in (let TMP_201 \def
+(lift h TMP_200 t0) in (let TMP_202 \def (Bind Abst) in (let TMP_203 \def
+(lift h d u) in (let TMP_204 \def (CHead c1 TMP_202 TMP_203) in (let TMP_205
+\def (Bind Abst) in (let TMP_206 \def (s TMP_205 d) in (let TMP_207 \def
+(drop_skip_bind h d c1 c H4 Abst u) in (let TMP_208 \def (H3 TMP_204 h
+TMP_206 TMP_207) in (let TMP_209 \def (arity_head g c1 TMP_197 a1 TMP_198
+TMP_201 a2 TMP_208) in (let TMP_210 \def (Bind Abst) in (let TMP_211 \def
+(THead TMP_210 u t0) in (let TMP_212 \def (lift h d TMP_211) in (let TMP_213
+\def (Bind Abst) in (let TMP_214 \def (lift_head TMP_213 u t0 h d) in
+(eq_ind_r T TMP_194 TMP_196 TMP_209 TMP_212
+TMP_214))))))))))))))))))))))))))))))))))))))) in (let TMP_237 \def (\lambda
+(c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
+a1)).(\lambda (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
+nat).((drop h d c1 c) \to (arity g c1 (lift h d u) a1))))))).(\lambda (t0:
+T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3:
+((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
+(arity g c1 (lift h d t0) (AHead a1 a2)))))))).(\lambda (c1: C).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (H4: (drop h d c1 c)).(let TMP_216 \def (Flat
+Appl) in (let TMP_217 \def (lift h d u) in (let TMP_218 \def (Flat Appl) in
+(let TMP_219 \def (s TMP_218 d) in (let TMP_220 \def (lift h TMP_219 t0) in
+(let TMP_221 \def (THead TMP_216 TMP_217 TMP_220) in (let TMP_222 \def
+(\lambda (t1: T).(arity g c1 t1 a2)) in (let TMP_223 \def (lift h d u) in
+(let TMP_224 \def (H1 c1 h d H4) in (let TMP_225 \def (Flat Appl) in (let
+TMP_226 \def (s TMP_225 d) in (let TMP_227 \def (lift h TMP_226 t0) in (let
+TMP_228 \def (Flat Appl) in (let TMP_229 \def (s TMP_228 d) in (let TMP_230
+\def (H3 c1 h TMP_229 H4) in (let TMP_231 \def (arity_appl g c1 TMP_223 a1
+TMP_224 TMP_227 a2 TMP_230) in (let TMP_232 \def (Flat Appl) in (let TMP_233
+\def (THead TMP_232 u t0) in (let TMP_234 \def (lift h d TMP_233) in (let
+TMP_235 \def (Flat Appl) in (let TMP_236 \def (lift_head TMP_235 u t0 h d) in
+(eq_ind_r T TMP_221 TMP_222 TMP_231 TMP_234
+TMP_236))))))))))))))))))))))))))))))))))) in (let TMP_259 \def (\lambda (c:
+C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_: (arity g c u (asucc g
+a0))).(\lambda (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
+nat).((drop h d c1 c) \to (arity g c1 (lift h d u) (asucc g
+a0)))))))).(\lambda (t0: T).(\lambda (_: (arity g c t0 a0)).(\lambda (H3:
+((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
+(arity g c1 (lift h d t0) a0))))))).(\lambda (c1: C).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (H4: (drop h d c1 c)).(let TMP_238 \def (Flat
+Cast) in (let TMP_239 \def (lift h d u) in (let TMP_240 \def (Flat Cast) in
+(let TMP_241 \def (s TMP_240 d) in (let TMP_242 \def (lift h TMP_241 t0) in
+(let TMP_243 \def (THead TMP_238 TMP_239 TMP_242) in (let TMP_244 \def
+(\lambda (t1: T).(arity g c1 t1 a0)) in (let TMP_245 \def (lift h d u) in
+(let TMP_246 \def (H1 c1 h d H4) in (let TMP_247 \def (Flat Cast) in (let
+TMP_248 \def (s TMP_247 d) in (let TMP_249 \def (lift h TMP_248 t0) in (let
+TMP_250 \def (Flat Cast) in (let TMP_251 \def (s TMP_250 d) in (let TMP_252
+\def (H3 c1 h TMP_251 H4) in (let TMP_253 \def (arity_cast g c1 TMP_245 a0
+TMP_246 TMP_249 TMP_252) in (let TMP_254 \def (Flat Cast) in (let TMP_255
+\def (THead TMP_254 u t0) in (let TMP_256 \def (lift h d TMP_255) in (let
+TMP_257 \def (Flat Cast) in (let TMP_258 \def (lift_head TMP_257 u t0 h d) in
+(eq_ind_r T TMP_243 TMP_244 TMP_253 TMP_256
+TMP_258)))))))))))))))))))))))))))))))))) in (let TMP_262 \def (\lambda (c:
+C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda
+(H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c)
+\to (arity g c1 (lift h d t0) a1))))))).(\lambda (a2: A).(\lambda (H2: (leq g
+a1 a2)).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H3:
+(drop h d c1 c)).(let TMP_260 \def (lift h d t0) in (let TMP_261 \def (H1 c1
+h d H3) in (arity_repl g c1 TMP_260 a1 TMP_261 a2 H2)))))))))))))) in
+(arity_ind g TMP_2 TMP_10 TMP_86 TMP_162 TMP_188 TMP_215 TMP_237 TMP_259
+TMP_262 c2 t a H)))))))))))))).
theorem arity_mono:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a1: A).((arity g c
t a1) \to (\forall (a2: A).((arity g c t a2) \to (leq g a1 a2)))))))
\def
\lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a1: A).(\lambda (H:
-(arity g c t a1)).(arity_ind g (\lambda (c0: C).(\lambda (t0: T).(\lambda (a:
-A).(\forall (a2: A).((arity g c0 t0 a2) \to (leq g a a2)))))) (\lambda (c0:
-C).(\lambda (n: nat).(\lambda (a2: A).(\lambda (H0: (arity g c0 (TSort n)
-a2)).(leq_sym g a2 (ASort O n) (arity_gen_sort g c0 n a2 H0)))))) (\lambda
-(c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl
-i c0 (CHead d (Bind Abbr) u))).(\lambda (a: A).(\lambda (_: (arity g d u
-a)).(\lambda (H2: ((\forall (a2: A).((arity g d u a2) \to (leq g a
-a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef i) a2)).(let H4
-\def (arity_gen_lref g c0 i a2 H3) in (or_ind (ex2_2 C T (\lambda (d0:
-C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0:
-C).(\lambda (u0: T).(arity g d0 u0 a2)))) (ex2_2 C T (\lambda (d0:
-C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0:
-C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2))))) (leq g a a2) (\lambda
-(H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind
-Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
-a2))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0
-(Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a2)))
-(leq g a a2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0
-(CHead x0 (Bind Abbr) x1))).(\lambda (H7: (arity g x0 x1 a2)).(let H8 \def
-(eq_ind C (CHead d (Bind Abbr) u) (\lambda (c1: C).(getl i c0 c1)) H0 (CHead
-x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abbr) u) i H0 (CHead x0 (Bind
-Abbr) x1) H6)) in (let H9 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c1 _ _)
-\Rightarrow c1])) (CHead d (Bind Abbr) u) (CHead x0 (Bind Abbr) x1)
-(getl_mono c0 (CHead d (Bind Abbr) u) i H0 (CHead x0 (Bind Abbr) x1) H6)) in
-((let H10 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead
-d (Bind Abbr) u) (CHead x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abbr)
-u) i H0 (CHead x0 (Bind Abbr) x1) H6)) in (\lambda (H11: (eq C d x0)).(let
-H12 \def (eq_ind_r T x1 (\lambda (t0: T).(getl i c0 (CHead x0 (Bind Abbr)
-t0))) H8 u H10) in (let H13 \def (eq_ind_r T x1 (\lambda (t0: T).(arity g x0
-t0 a2)) H7 u H10) in (let H14 \def (eq_ind_r C x0 (\lambda (c1: C).(getl i c0
-(CHead c1 (Bind Abbr) u))) H12 d H11) in (let H15 \def (eq_ind_r C x0
-(\lambda (c1: C).(arity g c1 u a2)) H13 d H11) in (H2 a2 H15))))))) H9)))))))
-H5)) (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
-(CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
-(asucc g a2)))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
-(CHead d0 (Bind Abst) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
-(asucc g a2)))) (leq g a a2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6:
-(getl i c0 (CHead x0 (Bind Abst) x1))).(\lambda (_: (arity g x0 x1 (asucc g
-a2))).(let H8 \def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (c1: C).(getl i
-c0 c1)) H0 (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind Abbr) u) i
-H0 (CHead x0 (Bind Abst) x1) H6)) in (let H9 \def (eq_ind C (CHead d (Bind
-Abbr) u) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with
-[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B return
-(\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow False |
-Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead x0 (Bind
-Abst) x1) (getl_mono c0 (CHead d (Bind Abbr) u) i H0 (CHead x0 (Bind Abst)
-x1) H6)) in (False_ind (leq g a a2) H9))))))) H5)) H4)))))))))))) (\lambda
+(arity g c t a1)).(let TMP_1 \def (\lambda (c0: C).(\lambda (t0: T).(\lambda
+(a: A).(\forall (a2: A).((arity g c0 t0 a2) \to (leq g a a2)))))) in (let
+TMP_4 \def (\lambda (c0: C).(\lambda (n: nat).(\lambda (a2: A).(\lambda (H0:
+(arity g c0 (TSort n) a2)).(let TMP_2 \def (ASort O n) in (let TMP_3 \def
+(arity_gen_sort g c0 n a2 H0) in (leq_sym g a2 TMP_2 TMP_3))))))) in (let
+TMP_92 \def (\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
+nat).(\lambda (H0: (getl i c0 (CHead d (Bind Abbr) u))).(\lambda (a:
+A).(\lambda (_: (arity g d u a)).(\lambda (H2: ((\forall (a2: A).((arity g d
+u a2) \to (leq g a a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef
+i) a2)).(let H4 \def (arity_gen_lref g c0 i a2 H3) in (let TMP_7 \def
+(\lambda (d0: C).(\lambda (u0: T).(let TMP_5 \def (Bind Abbr) in (let TMP_6
+\def (CHead d0 TMP_5 u0) in (getl i c0 TMP_6))))) in (let TMP_8 \def (\lambda
+(d0: C).(\lambda (u0: T).(arity g d0 u0 a2))) in (let TMP_9 \def (ex2_2 C T
+TMP_7 TMP_8) in (let TMP_12 \def (\lambda (d0: C).(\lambda (u0: T).(let
+TMP_10 \def (Bind Abst) in (let TMP_11 \def (CHead d0 TMP_10 u0) in (getl i
+c0 TMP_11))))) in (let TMP_14 \def (\lambda (d0: C).(\lambda (u0: T).(let
+TMP_13 \def (asucc g a2) in (arity g d0 u0 TMP_13)))) in (let TMP_15 \def
+(ex2_2 C T TMP_12 TMP_14) in (let TMP_16 \def (leq g a a2) in (let TMP_62
+\def (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
+(CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
+a2))))).(let TMP_19 \def (\lambda (d0: C).(\lambda (u0: T).(let TMP_17 \def
+(Bind Abbr) in (let TMP_18 \def (CHead d0 TMP_17 u0) in (getl i c0
+TMP_18))))) in (let TMP_20 \def (\lambda (d0: C).(\lambda (u0: T).(arity g d0
+u0 a2))) in (let TMP_21 \def (leq g a a2) in (let TMP_61 \def (\lambda (x0:
+C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind Abbr)
+x1))).(\lambda (H7: (arity g x0 x1 a2)).(let TMP_22 \def (Bind Abbr) in (let
+TMP_23 \def (CHead d TMP_22 u) in (let TMP_24 \def (\lambda (c1: C).(getl i
+c0 c1)) in (let TMP_25 \def (Bind Abbr) in (let TMP_26 \def (CHead x0 TMP_25
+x1) in (let TMP_27 \def (Bind Abbr) in (let TMP_28 \def (CHead d TMP_27 u) in
+(let TMP_29 \def (Bind Abbr) in (let TMP_30 \def (CHead x0 TMP_29 x1) in (let
+TMP_31 \def (getl_mono c0 TMP_28 i H0 TMP_30 H6) in (let H8 \def (eq_ind C
+TMP_23 TMP_24 H0 TMP_26 TMP_31) in (let TMP_32 \def (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) in (let
+TMP_33 \def (Bind Abbr) in (let TMP_34 \def (CHead d TMP_33 u) in (let TMP_35
+\def (Bind Abbr) in (let TMP_36 \def (CHead x0 TMP_35 x1) in (let TMP_37 \def
+(Bind Abbr) in (let TMP_38 \def (CHead d TMP_37 u) in (let TMP_39 \def (Bind
+Abbr) in (let TMP_40 \def (CHead x0 TMP_39 x1) in (let TMP_41 \def (getl_mono
+c0 TMP_38 i H0 TMP_40 H6) in (let H9 \def (f_equal C C TMP_32 TMP_34 TMP_36
+TMP_41) in (let TMP_42 \def (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_43 \def (Bind
+Abbr) in (let TMP_44 \def (CHead d TMP_43 u) in (let TMP_45 \def (Bind Abbr)
+in (let TMP_46 \def (CHead x0 TMP_45 x1) in (let TMP_47 \def (Bind Abbr) in
+(let TMP_48 \def (CHead d TMP_47 u) in (let TMP_49 \def (Bind Abbr) in (let
+TMP_50 \def (CHead x0 TMP_49 x1) in (let TMP_51 \def (getl_mono c0 TMP_48 i
+H0 TMP_50 H6) in (let H10 \def (f_equal C T TMP_42 TMP_44 TMP_46 TMP_51) in
+(let TMP_60 \def (\lambda (H11: (eq C d x0)).(let TMP_54 \def (\lambda (t0:
+T).(let TMP_52 \def (Bind Abbr) in (let TMP_53 \def (CHead x0 TMP_52 t0) in
+(getl i c0 TMP_53)))) in (let H12 \def (eq_ind_r T x1 TMP_54 H8 u H10) in
+(let TMP_55 \def (\lambda (t0: T).(arity g x0 t0 a2)) in (let H13 \def
+(eq_ind_r T x1 TMP_55 H7 u H10) in (let TMP_58 \def (\lambda (c1: C).(let
+TMP_56 \def (Bind Abbr) in (let TMP_57 \def (CHead c1 TMP_56 u) in (getl i c0
+TMP_57)))) in (let H14 \def (eq_ind_r C x0 TMP_58 H12 d H11) in (let TMP_59
+\def (\lambda (c1: C).(arity g c1 u a2)) in (let H15 \def (eq_ind_r C x0
+TMP_59 H13 d H11) in (H2 a2 H15)))))))))) in (TMP_60
+H9))))))))))))))))))))))))))))))))))))))) in (ex2_2_ind C T TMP_19 TMP_20
+TMP_21 TMP_61 H5)))))) in (let TMP_91 \def (\lambda (H5: (ex2_2 C T (\lambda
+(d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda
+(d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2)))))).(let TMP_65 \def
+(\lambda (d0: C).(\lambda (u0: T).(let TMP_63 \def (Bind Abst) in (let TMP_64
+\def (CHead d0 TMP_63 u0) in (getl i c0 TMP_64))))) in (let TMP_67 \def
+(\lambda (d0: C).(\lambda (u0: T).(let TMP_66 \def (asucc g a2) in (arity g
+d0 u0 TMP_66)))) in (let TMP_68 \def (leq g a a2) in (let TMP_90 \def
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind
+Abst) x1))).(\lambda (_: (arity g x0 x1 (asucc g a2))).(let TMP_69 \def (Bind
+Abbr) in (let TMP_70 \def (CHead d TMP_69 u) in (let TMP_71 \def (\lambda
+(c1: C).(getl i c0 c1)) in (let TMP_72 \def (Bind Abst) in (let TMP_73 \def
+(CHead x0 TMP_72 x1) in (let TMP_74 \def (Bind Abbr) in (let TMP_75 \def
+(CHead d TMP_74 u) in (let TMP_76 \def (Bind Abst) in (let TMP_77 \def (CHead
+x0 TMP_76 x1) in (let TMP_78 \def (getl_mono c0 TMP_75 i H0 TMP_77 H6) in
+(let H8 \def (eq_ind C TMP_70 TMP_71 H0 TMP_73 TMP_78) in (let TMP_79 \def
+(Bind Abbr) in (let TMP_80 \def (CHead d TMP_79 u) in (let TMP_81 \def
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) in (let TMP_82 \def (Bind Abst) in (let TMP_83 \def
+(CHead x0 TMP_82 x1) in (let TMP_84 \def (Bind Abbr) in (let TMP_85 \def
+(CHead d TMP_84 u) in (let TMP_86 \def (Bind Abst) in (let TMP_87 \def (CHead
+x0 TMP_86 x1) in (let TMP_88 \def (getl_mono c0 TMP_85 i H0 TMP_87 H6) in
+(let H9 \def (eq_ind C TMP_80 TMP_81 I TMP_83 TMP_88) in (let TMP_89 \def
+(leq g a a2) in (False_ind TMP_89 H9)))))))))))))))))))))))))))) in
+(ex2_2_ind C T TMP_65 TMP_67 TMP_68 TMP_90 H5)))))) in (or_ind TMP_9 TMP_15
+TMP_16 TMP_62 TMP_91 H4))))))))))))))))))))) in (let TMP_184 \def (\lambda
(c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl
i c0 (CHead d (Bind Abst) u))).(\lambda (a: A).(\lambda (_: (arity g d u
(asucc g a))).(\lambda (H2: ((\forall (a2: A).((arity g d u a2) \to (leq g
(asucc g a) a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef i)
-a2)).(let H4 \def (arity_gen_lref g c0 i a2 H3) in (or_ind (ex2_2 C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abbr) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a2)))) (ex2_2 C T (\lambda
-(d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda
-(d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2))))) (leq g a a2)
-(\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead
-d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
-a2))))).(ex2_2_ind C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0
-(Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 a2)))
-(leq g a a2) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0
-(CHead x0 (Bind Abbr) x1))).(\lambda (_: (arity g x0 x1 a2)).(let H8 \def
-(eq_ind C (CHead d (Bind Abst) u) (\lambda (c1: C).(getl i c0 c1)) H0 (CHead
-x0 (Bind Abbr) x1) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead x0 (Bind
-Abbr) x1) H6)) in (let H9 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda
-(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b) \Rightarrow (match b in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow True | Void
-\Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead x0 (Bind Abbr)
-x1) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead x0 (Bind Abbr) x1) H6))
-in (False_ind (leq g a a2) H9))))))) H5)) (\lambda (H5: (ex2_2 C T (\lambda
-(d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda
-(d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2)))))).(ex2_2_ind C T
-(\lambda (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0))))
-(\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2)))) (leq g a a2)
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind
-Abst) x1))).(\lambda (H7: (arity g x0 x1 (asucc g a2))).(let H8 \def (eq_ind
-C (CHead d (Bind Abst) u) (\lambda (c1: C).(getl i c0 c1)) H0 (CHead x0 (Bind
-Abst) x1) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead x0 (Bind Abst)
-x1) H6)) in (let H9 \def (f_equal C C (\lambda (e: C).(match e in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c1 _ _) \Rightarrow
-c1])) (CHead d (Bind Abst) u) (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead
-d (Bind Abst) u) i H0 (CHead x0 (Bind Abst) x1) H6)) in ((let H10 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind
-Abst) u) (CHead x0 (Bind Abst) x1) (getl_mono c0 (CHead d (Bind Abst) u) i H0
-(CHead x0 (Bind Abst) x1) H6)) in (\lambda (H11: (eq C d x0)).(let H12 \def
-(eq_ind_r T x1 (\lambda (t0: T).(getl i c0 (CHead x0 (Bind Abst) t0))) H8 u
-H10) in (let H13 \def (eq_ind_r T x1 (\lambda (t0: T).(arity g x0 t0 (asucc g
-a2))) H7 u H10) in (let H14 \def (eq_ind_r C x0 (\lambda (c1: C).(getl i c0
-(CHead c1 (Bind Abst) u))) H12 d H11) in (let H15 \def (eq_ind_r C x0
-(\lambda (c1: C).(arity g c1 u (asucc g a2))) H13 d H11) in (asucc_inj g a a2
-(H2 (asucc g a2) H15)))))))) H9))))))) H5)) H4)))))))))))) (\lambda (b:
-B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c0: C).(\lambda (u:
-T).(\lambda (a2: A).(\lambda (_: (arity g c0 u a2)).(\lambda (_: ((\forall
-(a3: A).((arity g c0 u a3) \to (leq g a2 a3))))).(\lambda (t0: T).(\lambda
-(a3: A).(\lambda (_: (arity g (CHead c0 (Bind b) u) t0 a3)).(\lambda (H4:
-((\forall (a4: A).((arity g (CHead c0 (Bind b) u) t0 a4) \to (leq g a3
-a4))))).(\lambda (a0: A).(\lambda (H5: (arity g c0 (THead (Bind b) u t0)
-a0)).(let H6 \def (arity_gen_bind b H0 g c0 u t0 a0 H5) in (ex2_ind A
-(\lambda (a4: A).(arity g c0 u a4)) (\lambda (_: A).(arity g (CHead c0 (Bind
-b) u) t0 a0)) (leq g a3 a0) (\lambda (x: A).(\lambda (_: (arity g c0 u
-x)).(\lambda (H8: (arity g (CHead c0 (Bind b) u) t0 a0)).(H4 a0 H8))))
-H6))))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a2: A).(\lambda
-(_: (arity g c0 u (asucc g a2))).(\lambda (H1: ((\forall (a3: A).((arity g c0
-u a3) \to (leq g (asucc g a2) a3))))).(\lambda (t0: T).(\lambda (a3:
-A).(\lambda (_: (arity g (CHead c0 (Bind Abst) u) t0 a3)).(\lambda (H3:
-((\forall (a4: A).((arity g (CHead c0 (Bind Abst) u) t0 a4) \to (leq g a3
-a4))))).(\lambda (a0: A).(\lambda (H4: (arity g c0 (THead (Bind Abst) u t0)
-a0)).(let H5 \def (arity_gen_abst g c0 u t0 a0 H4) in (ex3_2_ind A A (\lambda
-(a4: A).(\lambda (a5: A).(eq A a0 (AHead a4 a5)))) (\lambda (a4: A).(\lambda
-(_: A).(arity g c0 u (asucc g a4)))) (\lambda (_: A).(\lambda (a5: A).(arity
-g (CHead c0 (Bind Abst) u) t0 a5))) (leq g (AHead a2 a3) a0) (\lambda (x0:
-A).(\lambda (x1: A).(\lambda (H6: (eq A a0 (AHead x0 x1))).(\lambda (H7:
+a2)).(let H4 \def (arity_gen_lref g c0 i a2 H3) in (let TMP_95 \def (\lambda
+(d0: C).(\lambda (u0: T).(let TMP_93 \def (Bind Abbr) in (let TMP_94 \def
+(CHead d0 TMP_93 u0) in (getl i c0 TMP_94))))) in (let TMP_96 \def (\lambda
+(d0: C).(\lambda (u0: T).(arity g d0 u0 a2))) in (let TMP_97 \def (ex2_2 C T
+TMP_95 TMP_96) in (let TMP_100 \def (\lambda (d0: C).(\lambda (u0: T).(let
+TMP_98 \def (Bind Abst) in (let TMP_99 \def (CHead d0 TMP_98 u0) in (getl i
+c0 TMP_99))))) in (let TMP_102 \def (\lambda (d0: C).(\lambda (u0: T).(let
+TMP_101 \def (asucc g a2) in (arity g d0 u0 TMP_101)))) in (let TMP_103 \def
+(ex2_2 C T TMP_100 TMP_102) in (let TMP_104 \def (leq g a a2) in (let TMP_132
+\def (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
+(CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
+a2))))).(let TMP_107 \def (\lambda (d0: C).(\lambda (u0: T).(let TMP_105 \def
+(Bind Abbr) in (let TMP_106 \def (CHead d0 TMP_105 u0) in (getl i c0
+TMP_106))))) in (let TMP_108 \def (\lambda (d0: C).(\lambda (u0: T).(arity g
+d0 u0 a2))) in (let TMP_109 \def (leq g a a2) in (let TMP_131 \def (\lambda
+(x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind Abbr)
+x1))).(\lambda (_: (arity g x0 x1 a2)).(let TMP_110 \def (Bind Abst) in (let
+TMP_111 \def (CHead d TMP_110 u) in (let TMP_112 \def (\lambda (c1: C).(getl
+i c0 c1)) in (let TMP_113 \def (Bind Abbr) in (let TMP_114 \def (CHead x0
+TMP_113 x1) in (let TMP_115 \def (Bind Abst) in (let TMP_116 \def (CHead d
+TMP_115 u) in (let TMP_117 \def (Bind Abbr) in (let TMP_118 \def (CHead x0
+TMP_117 x1) in (let TMP_119 \def (getl_mono c0 TMP_116 i H0 TMP_118 H6) in
+(let H8 \def (eq_ind C TMP_111 TMP_112 H0 TMP_114 TMP_119) in (let TMP_120
+\def (Bind Abst) in (let TMP_121 \def (CHead d TMP_120 u) in (let TMP_122
+\def (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _
+k _) \Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) in (let TMP_123 \def (Bind Abbr) in (let TMP_124
+\def (CHead x0 TMP_123 x1) in (let TMP_125 \def (Bind Abst) in (let TMP_126
+\def (CHead d TMP_125 u) in (let TMP_127 \def (Bind Abbr) in (let TMP_128
+\def (CHead x0 TMP_127 x1) in (let TMP_129 \def (getl_mono c0 TMP_126 i H0
+TMP_128 H6) in (let H9 \def (eq_ind C TMP_121 TMP_122 I TMP_124 TMP_129) in
+(let TMP_130 \def (leq g a a2) in (False_ind TMP_130
+H9)))))))))))))))))))))))))))) in (ex2_2_ind C T TMP_107 TMP_108 TMP_109
+TMP_131 H5)))))) in (let TMP_183 \def (\lambda (H5: (ex2_2 C T (\lambda (d0:
+C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0:
+C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2)))))).(let TMP_135 \def
+(\lambda (d0: C).(\lambda (u0: T).(let TMP_133 \def (Bind Abst) in (let
+TMP_134 \def (CHead d0 TMP_133 u0) in (getl i c0 TMP_134))))) in (let TMP_137
+\def (\lambda (d0: C).(\lambda (u0: T).(let TMP_136 \def (asucc g a2) in
+(arity g d0 u0 TMP_136)))) in (let TMP_138 \def (leq g a a2) in (let TMP_182
+\def (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0
+(Bind Abst) x1))).(\lambda (H7: (arity g x0 x1 (asucc g a2))).(let TMP_139
+\def (Bind Abst) in (let TMP_140 \def (CHead d TMP_139 u) in (let TMP_141
+\def (\lambda (c1: C).(getl i c0 c1)) in (let TMP_142 \def (Bind Abst) in
+(let TMP_143 \def (CHead x0 TMP_142 x1) in (let TMP_144 \def (Bind Abst) in
+(let TMP_145 \def (CHead d TMP_144 u) in (let TMP_146 \def (Bind Abst) in
+(let TMP_147 \def (CHead x0 TMP_146 x1) in (let TMP_148 \def (getl_mono c0
+TMP_145 i H0 TMP_147 H6) in (let H8 \def (eq_ind C TMP_140 TMP_141 H0 TMP_143
+TMP_148) in (let TMP_149 \def (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_150 \def (Bind
+Abst) in (let TMP_151 \def (CHead d TMP_150 u) in (let TMP_152 \def (Bind
+Abst) in (let TMP_153 \def (CHead x0 TMP_152 x1) in (let TMP_154 \def (Bind
+Abst) in (let TMP_155 \def (CHead d TMP_154 u) in (let TMP_156 \def (Bind
+Abst) in (let TMP_157 \def (CHead x0 TMP_156 x1) in (let TMP_158 \def
+(getl_mono c0 TMP_155 i H0 TMP_157 H6) in (let H9 \def (f_equal C C TMP_149
+TMP_151 TMP_153 TMP_158) in (let TMP_159 \def (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_160
+\def (Bind Abst) in (let TMP_161 \def (CHead d TMP_160 u) in (let TMP_162
+\def (Bind Abst) in (let TMP_163 \def (CHead x0 TMP_162 x1) in (let TMP_164
+\def (Bind Abst) in (let TMP_165 \def (CHead d TMP_164 u) in (let TMP_166
+\def (Bind Abst) in (let TMP_167 \def (CHead x0 TMP_166 x1) in (let TMP_168
+\def (getl_mono c0 TMP_165 i H0 TMP_167 H6) in (let H10 \def (f_equal C T
+TMP_159 TMP_161 TMP_163 TMP_168) in (let TMP_181 \def (\lambda (H11: (eq C d
+x0)).(let TMP_171 \def (\lambda (t0: T).(let TMP_169 \def (Bind Abst) in (let
+TMP_170 \def (CHead x0 TMP_169 t0) in (getl i c0 TMP_170)))) in (let H12 \def
+(eq_ind_r T x1 TMP_171 H8 u H10) in (let TMP_173 \def (\lambda (t0: T).(let
+TMP_172 \def (asucc g a2) in (arity g x0 t0 TMP_172))) in (let H13 \def
+(eq_ind_r T x1 TMP_173 H7 u H10) in (let TMP_176 \def (\lambda (c1: C).(let
+TMP_174 \def (Bind Abst) in (let TMP_175 \def (CHead c1 TMP_174 u) in (getl i
+c0 TMP_175)))) in (let H14 \def (eq_ind_r C x0 TMP_176 H12 d H11) in (let
+TMP_178 \def (\lambda (c1: C).(let TMP_177 \def (asucc g a2) in (arity g c1 u
+TMP_177))) in (let H15 \def (eq_ind_r C x0 TMP_178 H13 d H11) in (let TMP_179
+\def (asucc g a2) in (let TMP_180 \def (H2 TMP_179 H15) in (asucc_inj g a a2
+TMP_180)))))))))))) in (TMP_181 H9))))))))))))))))))))))))))))))))))))))) in
+(ex2_2_ind C T TMP_135 TMP_137 TMP_138 TMP_182 H5)))))) in (or_ind TMP_97
+TMP_103 TMP_104 TMP_132 TMP_183 H4))))))))))))))))))))) in (let TMP_191 \def
+(\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c0: C).(\lambda
+(u: T).(\lambda (a2: A).(\lambda (_: (arity g c0 u a2)).(\lambda (_:
+((\forall (a3: A).((arity g c0 u a3) \to (leq g a2 a3))))).(\lambda (t0:
+T).(\lambda (a3: A).(\lambda (_: (arity g (CHead c0 (Bind b) u) t0
+a3)).(\lambda (H4: ((\forall (a4: A).((arity g (CHead c0 (Bind b) u) t0 a4)
+\to (leq g a3 a4))))).(\lambda (a0: A).(\lambda (H5: (arity g c0 (THead (Bind
+b) u t0) a0)).(let H6 \def (arity_gen_bind b H0 g c0 u t0 a0 H5) in (let
+TMP_185 \def (\lambda (a4: A).(arity g c0 u a4)) in (let TMP_188 \def
+(\lambda (_: A).(let TMP_186 \def (Bind b) in (let TMP_187 \def (CHead c0
+TMP_186 u) in (arity g TMP_187 t0 a0)))) in (let TMP_189 \def (leq g a3 a0)
+in (let TMP_190 \def (\lambda (x: A).(\lambda (_: (arity g c0 u x)).(\lambda
+(H8: (arity g (CHead c0 (Bind b) u) t0 a0)).(H4 a0 H8)))) in (ex2_ind A
+TMP_185 TMP_188 TMP_189 TMP_190 H6))))))))))))))))))) in (let TMP_210 \def
+(\lambda (c0: C).(\lambda (u: T).(\lambda (a2: A).(\lambda (_: (arity g c0 u
+(asucc g a2))).(\lambda (H1: ((\forall (a3: A).((arity g c0 u a3) \to (leq g
+(asucc g a2) a3))))).(\lambda (t0: T).(\lambda (a3: A).(\lambda (_: (arity g
+(CHead c0 (Bind Abst) u) t0 a3)).(\lambda (H3: ((\forall (a4: A).((arity g
+(CHead c0 (Bind Abst) u) t0 a4) \to (leq g a3 a4))))).(\lambda (a0:
+A).(\lambda (H4: (arity g c0 (THead (Bind Abst) u t0) a0)).(let H5 \def
+(arity_gen_abst g c0 u t0 a0 H4) in (let TMP_193 \def (\lambda (a4:
+A).(\lambda (a5: A).(let TMP_192 \def (AHead a4 a5) in (eq A a0 TMP_192))))
+in (let TMP_195 \def (\lambda (a4: A).(\lambda (_: A).(let TMP_194 \def
+(asucc g a4) in (arity g c0 u TMP_194)))) in (let TMP_198 \def (\lambda (_:
+A).(\lambda (a5: A).(let TMP_196 \def (Bind Abst) in (let TMP_197 \def (CHead
+c0 TMP_196 u) in (arity g TMP_197 t0 a5))))) in (let TMP_199 \def (AHead a2
+a3) in (let TMP_200 \def (leq g TMP_199 a0) in (let TMP_209 \def (\lambda
+(x0: A).(\lambda (x1: A).(\lambda (H6: (eq A a0 (AHead x0 x1))).(\lambda (H7:
(arity g c0 u (asucc g x0))).(\lambda (H8: (arity g (CHead c0 (Bind Abst) u)
-t0 x1)).(eq_ind_r A (AHead x0 x1) (\lambda (a: A).(leq g (AHead a2 a3) a))
-(leq_head g a2 x0 (asucc_inj g a2 x0 (H1 (asucc g x0) H7)) a3 x1 (H3 x1 H8))
-a0 H6)))))) H5))))))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (a2:
-A).(\lambda (_: (arity g c0 u a2)).(\lambda (_: ((\forall (a3: A).((arity g
-c0 u a3) \to (leq g a2 a3))))).(\lambda (t0: T).(\lambda (a3: A).(\lambda (_:
-(arity g c0 t0 (AHead a2 a3))).(\lambda (H3: ((\forall (a4: A).((arity g c0
-t0 a4) \to (leq g (AHead a2 a3) a4))))).(\lambda (a0: A).(\lambda (H4: (arity
-g c0 (THead (Flat Appl) u t0) a0)).(let H5 \def (arity_gen_appl g c0 u t0 a0
-H4) in (ex2_ind A (\lambda (a4: A).(arity g c0 u a4)) (\lambda (a4: A).(arity
-g c0 t0 (AHead a4 a0))) (leq g a3 a0) (\lambda (x: A).(\lambda (_: (arity g
-c0 u x)).(\lambda (H7: (arity g c0 t0 (AHead x a0))).(ahead_inj_snd g a2 a3 x
-a0 (H3 (AHead x a0) H7))))) H5))))))))))))) (\lambda (c0: C).(\lambda (u:
+t0 x1)).(let TMP_201 \def (AHead x0 x1) in (let TMP_203 \def (\lambda (a:
+A).(let TMP_202 \def (AHead a2 a3) in (leq g TMP_202 a))) in (let TMP_204
+\def (asucc g x0) in (let TMP_205 \def (H1 TMP_204 H7) in (let TMP_206 \def
+(asucc_inj g a2 x0 TMP_205) in (let TMP_207 \def (H3 x1 H8) in (let TMP_208
+\def (leq_head g a2 x0 TMP_206 a3 x1 TMP_207) in (eq_ind_r A TMP_201 TMP_203
+TMP_208 a0 H6))))))))))))) in (ex3_2_ind A A TMP_193 TMP_195 TMP_198 TMP_200
+TMP_209 H5))))))))))))))))))) in (let TMP_218 \def (\lambda (c0: C).(\lambda
+(u: T).(\lambda (a2: A).(\lambda (_: (arity g c0 u a2)).(\lambda (_:
+((\forall (a3: A).((arity g c0 u a3) \to (leq g a2 a3))))).(\lambda (t0:
+T).(\lambda (a3: A).(\lambda (_: (arity g c0 t0 (AHead a2 a3))).(\lambda (H3:
+((\forall (a4: A).((arity g c0 t0 a4) \to (leq g (AHead a2 a3)
+a4))))).(\lambda (a0: A).(\lambda (H4: (arity g c0 (THead (Flat Appl) u t0)
+a0)).(let H5 \def (arity_gen_appl g c0 u t0 a0 H4) in (let TMP_211 \def
+(\lambda (a4: A).(arity g c0 u a4)) in (let TMP_213 \def (\lambda (a4:
+A).(let TMP_212 \def (AHead a4 a0) in (arity g c0 t0 TMP_212))) in (let
+TMP_214 \def (leq g a3 a0) in (let TMP_217 \def (\lambda (x: A).(\lambda (_:
+(arity g c0 u x)).(\lambda (H7: (arity g c0 t0 (AHead x a0))).(let TMP_215
+\def (AHead x a0) in (let TMP_216 \def (H3 TMP_215 H7) in (ahead_inj_snd g a2
+a3 x a0 TMP_216)))))) in (ex2_ind A TMP_211 TMP_213 TMP_214 TMP_217
+H5))))))))))))))))) in (let TMP_224 \def (\lambda (c0: C).(\lambda (u:
T).(\lambda (a: A).(\lambda (_: (arity g c0 u (asucc g a))).(\lambda (_:
((\forall (a2: A).((arity g c0 u a2) \to (leq g (asucc g a) a2))))).(\lambda
(t0: T).(\lambda (_: (arity g c0 t0 a)).(\lambda (H3: ((\forall (a2:
A).((arity g c0 t0 a2) \to (leq g a a2))))).(\lambda (a2: A).(\lambda (H4:
(arity g c0 (THead (Flat Cast) u t0) a2)).(let H5 \def (arity_gen_cast g c0 u
-t0 a2 H4) in (land_ind (arity g c0 u (asucc g a2)) (arity g c0 t0 a2) (leq g
-a a2) (\lambda (_: (arity g c0 u (asucc g a2))).(\lambda (H7: (arity g c0 t0
-a2)).(H3 a2 H7))) H5)))))))))))) (\lambda (c0: C).(\lambda (t0: T).(\lambda
-(a2: A).(\lambda (_: (arity g c0 t0 a2)).(\lambda (H1: ((\forall (a3:
-A).((arity g c0 t0 a3) \to (leq g a2 a3))))).(\lambda (a3: A).(\lambda (H2:
-(leq g a2 a3)).(\lambda (a0: A).(\lambda (H3: (arity g c0 t0 a0)).(leq_trans
-g a3 a2 (leq_sym g a2 a3 H2) a0 (H1 a0 H3))))))))))) c t a1 H))))).
-(* COMMENTS
-Initial nodes: 2947
-END *)
+t0 a2 H4) in (let TMP_219 \def (asucc g a2) in (let TMP_220 \def (arity g c0
+u TMP_219) in (let TMP_221 \def (arity g c0 t0 a2) in (let TMP_222 \def (leq
+g a a2) in (let TMP_223 \def (\lambda (_: (arity g c0 u (asucc g
+a2))).(\lambda (H7: (arity g c0 t0 a2)).(H3 a2 H7))) in (land_ind TMP_220
+TMP_221 TMP_222 TMP_223 H5))))))))))))))))) in (let TMP_227 \def (\lambda
+(c0: C).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g c0 t0
+a2)).(\lambda (H1: ((\forall (a3: A).((arity g c0 t0 a3) \to (leq g a2
+a3))))).(\lambda (a3: A).(\lambda (H2: (leq g a2 a3)).(\lambda (a0:
+A).(\lambda (H3: (arity g c0 t0 a0)).(let TMP_225 \def (leq_sym g a2 a3 H2)
+in (let TMP_226 \def (H1 a0 H3) in (leq_trans g a3 a2 TMP_225 a0
+TMP_226)))))))))))) in (arity_ind g TMP_1 TMP_4 TMP_92 TMP_184 TMP_191
+TMP_210 TMP_218 TMP_224 TMP_227 c t a1 H)))))))))))))).
theorem arity_repellent:
\forall (g: G).(\forall (c: C).(\forall (w: T).(\forall (t: T).(\forall (a1:
\lambda (g: G).(\lambda (c: C).(\lambda (w: T).(\lambda (t: T).(\lambda (a1:
A).(\lambda (H: (arity g (CHead c (Bind Abst) w) t a1)).(\lambda (a2:
A).(\lambda (H0: (arity g c (THead (Bind Abst) w t) a2)).(\lambda (H1: (leq g
-a1 a2)).(\lambda (P: Prop).(let H_y \def (arity_repl g (CHead c (Bind Abst)
-w) t a1 H a2 H1) in (let H2 \def (arity_gen_abst g c w t a2 H0) in (ex3_2_ind
-A A (\lambda (a3: A).(\lambda (a4: A).(eq A a2 (AHead a3 a4)))) (\lambda (a3:
-A).(\lambda (_: A).(arity g c w (asucc g a3)))) (\lambda (_: A).(\lambda (a4:
-A).(arity g (CHead c (Bind Abst) w) t a4))) P (\lambda (x0: A).(\lambda (x1:
+a1 a2)).(\lambda (P: Prop).(let TMP_1 \def (Bind Abst) in (let TMP_2 \def
+(CHead c TMP_1 w) in (let H_y \def (arity_repl g TMP_2 t a1 H a2 H1) in (let
+H2 \def (arity_gen_abst g c w t a2 H0) in (let TMP_4 \def (\lambda (a3:
+A).(\lambda (a4: A).(let TMP_3 \def (AHead a3 a4) in (eq A a2 TMP_3)))) in
+(let TMP_6 \def (\lambda (a3: A).(\lambda (_: A).(let TMP_5 \def (asucc g a3)
+in (arity g c w TMP_5)))) in (let TMP_9 \def (\lambda (_: A).(\lambda (a4:
+A).(let TMP_7 \def (Bind Abst) in (let TMP_8 \def (CHead c TMP_7 w) in (arity
+g TMP_8 t a4))))) in (let TMP_18 \def (\lambda (x0: A).(\lambda (x1:
A).(\lambda (H3: (eq A a2 (AHead x0 x1))).(\lambda (_: (arity g c w (asucc g
-x0))).(\lambda (H5: (arity g (CHead c (Bind Abst) w) t x1)).(let H6 \def
-(eq_ind A a2 (\lambda (a: A).(arity g (CHead c (Bind Abst) w) t a)) H_y
-(AHead x0 x1) H3) in (leq_ahead_false_2 g x1 x0 (arity_mono g (CHead c (Bind
-Abst) w) t (AHead x0 x1) H6 x1 H5) P))))))) H2)))))))))))).
-(* COMMENTS
-Initial nodes: 283
-END *)
+x0))).(\lambda (H5: (arity g (CHead c (Bind Abst) w) t x1)).(let TMP_12 \def
+(\lambda (a: A).(let TMP_10 \def (Bind Abst) in (let TMP_11 \def (CHead c
+TMP_10 w) in (arity g TMP_11 t a)))) in (let TMP_13 \def (AHead x0 x1) in
+(let H6 \def (eq_ind A a2 TMP_12 H_y TMP_13 H3) in (let TMP_14 \def (Bind
+Abst) in (let TMP_15 \def (CHead c TMP_14 w) in (let TMP_16 \def (AHead x0
+x1) in (let TMP_17 \def (arity_mono g TMP_15 t TMP_16 H6 x1 H5) in
+(leq_ahead_false_2 g x1 x0 TMP_17 P))))))))))))) in (ex3_2_ind A A TMP_4
+TMP_6 TMP_9 P TMP_18 H2)))))))))))))))))).
theorem arity_appls_cast:
\forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (vs:
vs (THead (Flat Cast) u t)) a))))))))
\def
\lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(\lambda (vs:
-TList).(TList_ind (\lambda (t0: TList).(\forall (a: A).((arity g c (THeads
-(Flat Appl) t0 u) (asucc g a)) \to ((arity g c (THeads (Flat Appl) t0 t) a)
-\to (arity g c (THeads (Flat Appl) t0 (THead (Flat Cast) u t)) a)))))
-(\lambda (a: A).(\lambda (H: (arity g c u (asucc g a))).(\lambda (H0: (arity
-g c t a)).(arity_cast g c u a H t H0)))) (\lambda (t0: T).(\lambda (t1:
-TList).(\lambda (H: ((\forall (a: A).((arity g c (THeads (Flat Appl) t1 u)
-(asucc g a)) \to ((arity g c (THeads (Flat Appl) t1 t) a) \to (arity g c
-(THeads (Flat Appl) t1 (THead (Flat Cast) u t)) a)))))).(\lambda (a:
-A).(\lambda (H0: (arity g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1 u))
-(asucc g a))).(\lambda (H1: (arity g c (THead (Flat Appl) t0 (THeads (Flat
-Appl) t1 t)) a)).(let H2 \def (arity_gen_appl g c t0 (THeads (Flat Appl) t1
-t) a H1) in (ex2_ind A (\lambda (a1: A).(arity g c t0 a1)) (\lambda (a1:
-A).(arity g c (THeads (Flat Appl) t1 t) (AHead a1 a))) (arity g c (THead
-(Flat Appl) t0 (THeads (Flat Appl) t1 (THead (Flat Cast) u t))) a) (\lambda
-(x: A).(\lambda (H3: (arity g c t0 x)).(\lambda (H4: (arity g c (THeads (Flat
-Appl) t1 t) (AHead x a))).(let H5 \def (arity_gen_appl g c t0 (THeads (Flat
-Appl) t1 u) (asucc g a) H0) in (ex2_ind A (\lambda (a1: A).(arity g c t0 a1))
-(\lambda (a1: A).(arity g c (THeads (Flat Appl) t1 u) (AHead a1 (asucc g
-a)))) (arity g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1 (THead (Flat
-Cast) u t))) a) (\lambda (x0: A).(\lambda (H6: (arity g c t0 x0)).(\lambda
-(H7: (arity g c (THeads (Flat Appl) t1 u) (AHead x0 (asucc g
-a)))).(arity_appl g c t0 x H3 (THeads (Flat Appl) t1 (THead (Flat Cast) u t))
-a (H (AHead x a) (arity_repl g c (THeads (Flat Appl) t1 u) (AHead x (asucc g
-a)) (arity_repl g c (THeads (Flat Appl) t1 u) (AHead x0 (asucc g a)) H7
-(AHead x (asucc g a)) (leq_head g x0 x (arity_mono g c t0 x0 H6 x H3) (asucc
-g a) (asucc g a) (leq_refl g (asucc g a)))) (asucc g (AHead x a)) (leq_refl g
-(asucc g (AHead x a)))) H4))))) H5))))) H2)))))))) vs))))).
-(* COMMENTS
-Initial nodes: 707
-END *)
+TList).(let TMP_5 \def (\lambda (t0: TList).(\forall (a: A).((arity g c
+(THeads (Flat Appl) t0 u) (asucc g a)) \to ((arity g c (THeads (Flat Appl) t0
+t) a) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def (Flat Cast) in (let
+TMP_3 \def (THead TMP_2 u t) in (let TMP_4 \def (THeads TMP_1 t0 TMP_3) in
+(arity g c TMP_4 a))))))))) in (let TMP_6 \def (\lambda (a: A).(\lambda (H:
+(arity g c u (asucc g a))).(\lambda (H0: (arity g c t a)).(arity_cast g c u a
+H t H0)))) in (let TMP_68 \def (\lambda (t0: T).(\lambda (t1: TList).(\lambda
+(H: ((\forall (a: A).((arity g c (THeads (Flat Appl) t1 u) (asucc g a)) \to
+((arity g c (THeads (Flat Appl) t1 t) a) \to (arity g c (THeads (Flat Appl)
+t1 (THead (Flat Cast) u t)) a)))))).(\lambda (a: A).(\lambda (H0: (arity g c
+(THead (Flat Appl) t0 (THeads (Flat Appl) t1 u)) (asucc g a))).(\lambda (H1:
+(arity g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1 t)) a)).(let TMP_7
+\def (Flat Appl) in (let TMP_8 \def (THeads TMP_7 t1 t) in (let H2 \def
+(arity_gen_appl g c t0 TMP_8 a H1) in (let TMP_9 \def (\lambda (a1: A).(arity
+g c t0 a1)) in (let TMP_13 \def (\lambda (a1: A).(let TMP_10 \def (Flat Appl)
+in (let TMP_11 \def (THeads TMP_10 t1 t) in (let TMP_12 \def (AHead a1 a) in
+(arity g c TMP_11 TMP_12))))) in (let TMP_14 \def (Flat Appl) in (let TMP_15
+\def (Flat Appl) in (let TMP_16 \def (Flat Cast) in (let TMP_17 \def (THead
+TMP_16 u t) in (let TMP_18 \def (THeads TMP_15 t1 TMP_17) in (let TMP_19 \def
+(THead TMP_14 t0 TMP_18) in (let TMP_20 \def (arity g c TMP_19 a) in (let
+TMP_67 \def (\lambda (x: A).(\lambda (H3: (arity g c t0 x)).(\lambda (H4:
+(arity g c (THeads (Flat Appl) t1 t) (AHead x a))).(let TMP_21 \def (Flat
+Appl) in (let TMP_22 \def (THeads TMP_21 t1 u) in (let TMP_23 \def (asucc g
+a) in (let H5 \def (arity_gen_appl g c t0 TMP_22 TMP_23 H0) in (let TMP_24
+\def (\lambda (a1: A).(arity g c t0 a1)) in (let TMP_29 \def (\lambda (a1:
+A).(let TMP_25 \def (Flat Appl) in (let TMP_26 \def (THeads TMP_25 t1 u) in
+(let TMP_27 \def (asucc g a) in (let TMP_28 \def (AHead a1 TMP_27) in (arity
+g c TMP_26 TMP_28)))))) in (let TMP_30 \def (Flat Appl) in (let TMP_31 \def
+(Flat Appl) in (let TMP_32 \def (Flat Cast) in (let TMP_33 \def (THead TMP_32
+u t) in (let TMP_34 \def (THeads TMP_31 t1 TMP_33) in (let TMP_35 \def (THead
+TMP_30 t0 TMP_34) in (let TMP_36 \def (arity g c TMP_35 a) in (let TMP_66
+\def (\lambda (x0: A).(\lambda (H6: (arity g c t0 x0)).(\lambda (H7: (arity g
+c (THeads (Flat Appl) t1 u) (AHead x0 (asucc g a)))).(let TMP_37 \def (Flat
+Appl) in (let TMP_38 \def (Flat Cast) in (let TMP_39 \def (THead TMP_38 u t)
+in (let TMP_40 \def (THeads TMP_37 t1 TMP_39) in (let TMP_41 \def (AHead x a)
+in (let TMP_42 \def (Flat Appl) in (let TMP_43 \def (THeads TMP_42 t1 u) in
+(let TMP_44 \def (asucc g a) in (let TMP_45 \def (AHead x TMP_44) in (let
+TMP_46 \def (Flat Appl) in (let TMP_47 \def (THeads TMP_46 t1 u) in (let
+TMP_48 \def (asucc g a) in (let TMP_49 \def (AHead x0 TMP_48) in (let TMP_50
+\def (asucc g a) in (let TMP_51 \def (AHead x TMP_50) in (let TMP_52 \def
+(arity_mono g c t0 x0 H6 x H3) in (let TMP_53 \def (asucc g a) in (let TMP_54
+\def (asucc g a) in (let TMP_55 \def (asucc g a) in (let TMP_56 \def
+(leq_refl g TMP_55) in (let TMP_57 \def (leq_head g x0 x TMP_52 TMP_53 TMP_54
+TMP_56) in (let TMP_58 \def (arity_repl g c TMP_47 TMP_49 H7 TMP_51 TMP_57)
+in (let TMP_59 \def (AHead x a) in (let TMP_60 \def (asucc g TMP_59) in (let
+TMP_61 \def (AHead x a) in (let TMP_62 \def (asucc g TMP_61) in (let TMP_63
+\def (leq_refl g TMP_62) in (let TMP_64 \def (arity_repl g c TMP_43 TMP_45
+TMP_58 TMP_60 TMP_63) in (let TMP_65 \def (H TMP_41 TMP_64 H4) in (arity_appl
+g c t0 x H3 TMP_40 a TMP_65))))))))))))))))))))))))))))))))) in (ex2_ind A
+TMP_24 TMP_29 TMP_36 TMP_66 H5)))))))))))))))))) in (ex2_ind A TMP_9 TMP_13
+TMP_20 TMP_67 H2)))))))))))))))))))) in (TList_ind TMP_5 TMP_6 TMP_68
+vs)))))))).
theorem arity_appls_abbr:
\forall (g: G).(\forall (c: C).(\forall (d: C).(\forall (v: T).(\forall (i:
\def
\lambda (g: G).(\lambda (c: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i:
nat).(\lambda (H: (getl i c (CHead d (Bind Abbr) v))).(\lambda (vs:
-TList).(TList_ind (\lambda (t: TList).(\forall (a: A).((arity g c (THeads
-(Flat Appl) t (lift (S i) O v)) a) \to (arity g c (THeads (Flat Appl) t
-(TLRef i)) a)))) (\lambda (a: A).(\lambda (H0: (arity g c (lift (S i) O v)
-a)).(arity_abbr g c d v i H a (arity_gen_lift g c v a (S i) O H0 d (getl_drop
-Abbr c d v i H))))) (\lambda (t: T).(\lambda (t0: TList).(\lambda (H0:
-((\forall (a: A).((arity g c (THeads (Flat Appl) t0 (lift (S i) O v)) a) \to
-(arity g c (THeads (Flat Appl) t0 (TLRef i)) a))))).(\lambda (a: A).(\lambda
-(H1: (arity g c (THead (Flat Appl) t (THeads (Flat Appl) t0 (lift (S i) O
-v))) a)).(let H2 \def (arity_gen_appl g c t (THeads (Flat Appl) t0 (lift (S
-i) O v)) a H1) in (ex2_ind A (\lambda (a1: A).(arity g c t a1)) (\lambda (a1:
-A).(arity g c (THeads (Flat Appl) t0 (lift (S i) O v)) (AHead a1 a))) (arity
-g c (THead (Flat Appl) t (THeads (Flat Appl) t0 (TLRef i))) a) (\lambda (x:
-A).(\lambda (H3: (arity g c t x)).(\lambda (H4: (arity g c (THeads (Flat
-Appl) t0 (lift (S i) O v)) (AHead x a))).(arity_appl g c t x H3 (THeads (Flat
-Appl) t0 (TLRef i)) a (H0 (AHead x a) H4))))) H2))))))) vs))))))).
-(* COMMENTS
-Initial nodes: 425
-END *)
+TList).(let TMP_4 \def (\lambda (t: TList).(\forall (a: A).((arity g c
+(THeads (Flat Appl) t (lift (S i) O v)) a) \to (let TMP_1 \def (Flat Appl) in
+(let TMP_2 \def (TLRef i) in (let TMP_3 \def (THeads TMP_1 t TMP_2) in (arity
+g c TMP_3 a))))))) in (let TMP_8 \def (\lambda (a: A).(\lambda (H0: (arity g
+c (lift (S i) O v) a)).(let TMP_5 \def (S i) in (let TMP_6 \def (getl_drop
+Abbr c d v i H) in (let TMP_7 \def (arity_gen_lift g c v a TMP_5 O H0 d
+TMP_6) in (arity_abbr g c d v i H a TMP_7)))))) in (let TMP_32 \def (\lambda
+(t: T).(\lambda (t0: TList).(\lambda (H0: ((\forall (a: A).((arity g c
+(THeads (Flat Appl) t0 (lift (S i) O v)) a) \to (arity g c (THeads (Flat
+Appl) t0 (TLRef i)) a))))).(\lambda (a: A).(\lambda (H1: (arity g c (THead
+(Flat Appl) t (THeads (Flat Appl) t0 (lift (S i) O v))) a)).(let TMP_9 \def
+(Flat Appl) in (let TMP_10 \def (S i) in (let TMP_11 \def (lift TMP_10 O v)
+in (let TMP_12 \def (THeads TMP_9 t0 TMP_11) in (let H2 \def (arity_gen_appl
+g c t TMP_12 a H1) in (let TMP_13 \def (\lambda (a1: A).(arity g c t a1)) in
+(let TMP_19 \def (\lambda (a1: A).(let TMP_14 \def (Flat Appl) in (let TMP_15
+\def (S i) in (let TMP_16 \def (lift TMP_15 O v) in (let TMP_17 \def (THeads
+TMP_14 t0 TMP_16) in (let TMP_18 \def (AHead a1 a) in (arity g c TMP_17
+TMP_18))))))) in (let TMP_20 \def (Flat Appl) in (let TMP_21 \def (Flat Appl)
+in (let TMP_22 \def (TLRef i) in (let TMP_23 \def (THeads TMP_21 t0 TMP_22)
+in (let TMP_24 \def (THead TMP_20 t TMP_23) in (let TMP_25 \def (arity g c
+TMP_24 a) in (let TMP_31 \def (\lambda (x: A).(\lambda (H3: (arity g c t
+x)).(\lambda (H4: (arity g c (THeads (Flat Appl) t0 (lift (S i) O v)) (AHead
+x a))).(let TMP_26 \def (Flat Appl) in (let TMP_27 \def (TLRef i) in (let
+TMP_28 \def (THeads TMP_26 t0 TMP_27) in (let TMP_29 \def (AHead x a) in (let
+TMP_30 \def (H0 TMP_29 H4) in (arity_appl g c t x H3 TMP_28 a TMP_30)))))))))
+in (ex2_ind A TMP_13 TMP_19 TMP_25 TMP_31 H2)))))))))))))))))))) in
+(TList_ind TMP_4 TMP_8 TMP_32 vs)))))))))).
theorem arity_appls_bind:
\forall (g: G).(\forall (b: B).((not (eq B b Abst)) \to (\forall (c:
\def
\lambda (g: G).(\lambda (b: B).(\lambda (H: (not (eq B b Abst))).(\lambda
(c: C).(\lambda (v: T).(\lambda (a1: A).(\lambda (H0: (arity g c v
-a1)).(\lambda (t: T).(\lambda (vs: TList).(TList_ind (\lambda (t0:
+a1)).(\lambda (t: T).(\lambda (vs: TList).(let TMP_5 \def (\lambda (t0:
TList).(\forall (a2: A).((arity g (CHead c (Bind b) v) (THeads (Flat Appl)
-(lifts (S O) O t0) t) a2) \to (arity g c (THeads (Flat Appl) t0 (THead (Bind
-b) v t)) a2)))) (\lambda (a2: A).(\lambda (H1: (arity g (CHead c (Bind b) v)
-t a2)).(arity_bind g b H c v a1 H0 t a2 H1))) (\lambda (t0: T).(\lambda (t1:
+(lifts (S O) O t0) t) a2) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def
+(Bind b) in (let TMP_3 \def (THead TMP_2 v t) in (let TMP_4 \def (THeads
+TMP_1 t0 TMP_3) in (arity g c TMP_4 a2)))))))) in (let TMP_6 \def (\lambda
+(a2: A).(\lambda (H1: (arity g (CHead c (Bind b) v) t a2)).(arity_bind g b H
+c v a1 H0 t a2 H1))) in (let TMP_49 \def (\lambda (t0: T).(\lambda (t1:
TList).(\lambda (H1: ((\forall (a2: A).((arity g (CHead c (Bind b) v) (THeads
(Flat Appl) (lifts (S O) O t1) t) a2) \to (arity g c (THeads (Flat Appl) t1
(THead (Bind b) v t)) a2))))).(\lambda (a2: A).(\lambda (H2: (arity g (CHead
c (Bind b) v) (THead (Flat Appl) (lift (S O) O t0) (THeads (Flat Appl) (lifts
-(S O) O t1) t)) a2)).(let H3 \def (arity_gen_appl g (CHead c (Bind b) v)
-(lift (S O) O t0) (THeads (Flat Appl) (lifts (S O) O t1) t) a2 H2) in
-(ex2_ind A (\lambda (a3: A).(arity g (CHead c (Bind b) v) (lift (S O) O t0)
-a3)) (\lambda (a3: A).(arity g (CHead c (Bind b) v) (THeads (Flat Appl)
-(lifts (S O) O t1) t) (AHead a3 a2))) (arity g c (THead (Flat Appl) t0
-(THeads (Flat Appl) t1 (THead (Bind b) v t))) a2) (\lambda (x: A).(\lambda
-(H4: (arity g (CHead c (Bind b) v) (lift (S O) O t0) x)).(\lambda (H5: (arity
-g (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S O) O t1) t) (AHead x
-a2))).(arity_appl g c t0 x (arity_gen_lift g (CHead c (Bind b) v) t0 x (S O)
-O H4 c (drop_drop (Bind b) O c c (drop_refl c) v)) (THeads (Flat Appl) t1
-(THead (Bind b) v t)) a2 (H1 (AHead x a2) H5))))) H3))))))) vs))))))))).
-(* COMMENTS
-Initial nodes: 567
-END *)
+(S O) O t1) t)) a2)).(let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead c
+TMP_7 v) in (let TMP_9 \def (S O) in (let TMP_10 \def (lift TMP_9 O t0) in
+(let TMP_11 \def (Flat Appl) in (let TMP_12 \def (S O) in (let TMP_13 \def
+(lifts TMP_12 O t1) in (let TMP_14 \def (THeads TMP_11 TMP_13 t) in (let H3
+\def (arity_gen_appl g TMP_8 TMP_10 TMP_14 a2 H2) in (let TMP_19 \def
+(\lambda (a3: A).(let TMP_15 \def (Bind b) in (let TMP_16 \def (CHead c
+TMP_15 v) in (let TMP_17 \def (S O) in (let TMP_18 \def (lift TMP_17 O t0) in
+(arity g TMP_16 TMP_18 a3)))))) in (let TMP_27 \def (\lambda (a3: A).(let
+TMP_20 \def (Bind b) in (let TMP_21 \def (CHead c TMP_20 v) in (let TMP_22
+\def (Flat Appl) in (let TMP_23 \def (S O) in (let TMP_24 \def (lifts TMP_23
+O t1) in (let TMP_25 \def (THeads TMP_22 TMP_24 t) in (let TMP_26 \def (AHead
+a3 a2) in (arity g TMP_21 TMP_25 TMP_26))))))))) in (let TMP_28 \def (Flat
+Appl) in (let TMP_29 \def (Flat Appl) in (let TMP_30 \def (Bind b) in (let
+TMP_31 \def (THead TMP_30 v t) in (let TMP_32 \def (THeads TMP_29 t1 TMP_31)
+in (let TMP_33 \def (THead TMP_28 t0 TMP_32) in (let TMP_34 \def (arity g c
+TMP_33 a2) in (let TMP_48 \def (\lambda (x: A).(\lambda (H4: (arity g (CHead
+c (Bind b) v) (lift (S O) O t0) x)).(\lambda (H5: (arity g (CHead c (Bind b)
+v) (THeads (Flat Appl) (lifts (S O) O t1) t) (AHead x a2))).(let TMP_35 \def
+(Bind b) in (let TMP_36 \def (CHead c TMP_35 v) in (let TMP_37 \def (S O) in
+(let TMP_38 \def (Bind b) in (let TMP_39 \def (drop_refl c) in (let TMP_40
+\def (drop_drop TMP_38 O c c TMP_39 v) in (let TMP_41 \def (arity_gen_lift g
+TMP_36 t0 x TMP_37 O H4 c TMP_40) in (let TMP_42 \def (Flat Appl) in (let
+TMP_43 \def (Bind b) in (let TMP_44 \def (THead TMP_43 v t) in (let TMP_45
+\def (THeads TMP_42 t1 TMP_44) in (let TMP_46 \def (AHead x a2) in (let
+TMP_47 \def (H1 TMP_46 H5) in (arity_appl g c t0 x TMP_41 TMP_45 a2
+TMP_47))))))))))))))))) in (ex2_ind A TMP_19 TMP_27 TMP_34 TMP_48
+H3))))))))))))))))))))))))) in (TList_ind TMP_5 TMP_6 TMP_49 vs)))))))))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/props.ma".
+include "basic_1/arity/props.ma".
-include "Basic-1/fsubst0/fwd.ma".
+include "basic_1/fsubst0/fwd.ma".
-include "Basic-1/csubst0/getl.ma".
+include "basic_1/csubst0/getl.ma".
-include "Basic-1/subst0/dec.ma".
+include "basic_1/subst0/dec.ma".
-include "Basic-1/subst0/fwd.ma".
+include "basic_1/subst0/fwd.ma".
-include "Basic-1/getl/getl.ma".
+include "basic_1/getl/getl.ma".
theorem arity_gen_cvoid_subst0:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((arity g c t
(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
(CHead d (Bind Abbr) u) i H0 (CHead d0 (Bind Void) u0) H7)) in (let H9 \def
-(eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _)
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
-True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat _)
-\Rightarrow False])])) I (CHead d0 (Bind Void) u0) (getl_mono c0 (CHead d
-(Bind Abbr) u) i H0 (CHead d0 (Bind Void) u0) H7)) in (False_ind P H9))))))
-(subst0_gen_lref w v i0 i H4)))))))))))))))))) (\lambda (c0: C).(\lambda (d:
-C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d (Bind
-Abst) u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda
-(_: ((\forall (d0: C).(\forall (u0: T).(\forall (i0: nat).((getl i0 d (CHead
-d0 (Bind Void) u0)) \to (\forall (w: T).(\forall (v: T).((subst0 i0 w u v)
-\to (\forall (P: Prop).P)))))))))).(\lambda (d0: C).(\lambda (u0: T).(\lambda
+(eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b)
+\Rightarrow (match b with [Abbr \Rightarrow True | Abst \Rightarrow False |
+Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d0 (Bind
+Void) u0) (getl_mono c0 (CHead d (Bind Abbr) u) i H0 (CHead d0 (Bind Void)
+u0) H7)) in (False_ind P H9)))))) (subst0_gen_lref w v i0 i
+H4)))))))))))))))))) (\lambda (c0: C).(\lambda (d: C).(\lambda (u:
+T).(\lambda (i: nat).(\lambda (H0: (getl i c0 (CHead d (Bind Abst)
+u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g a0))).(\lambda (_:
+((\forall (d0: C).(\forall (u0: T).(\forall (i0: nat).((getl i0 d (CHead d0
+(Bind Void) u0)) \to (\forall (w: T).(\forall (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).(land_ind (eq nat i i0) (eq T v (lift (S i) O w)) P (\lambda (H5: (eq
H8 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (c1: C).(getl i c0 c1)) H0
(CHead d0 (Bind Void) u0) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead
d0 (Bind Void) u0) H7)) in (let H9 \def (eq_ind C (CHead d (Bind Abst) u)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b) \Rightarrow (match b in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow True | Void
-\Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d0 (Bind Void)
-u0) (getl_mono c0 (CHead d (Bind Abst) u) i H0 (CHead d0 (Bind Void) u0) H7))
-in (False_ind P H9)))))) (subst0_gen_lref w v i0 i H4))))))))))))))))))
-(\lambda (b: B).(\lambda (_: (not (eq B b Abst))).(\lambda (c0: C).(\lambda
-(u: T).(\lambda (a1: A).(\lambda (_: (arity g c0 u a1)).(\lambda (H2:
-((\forall (d: C).(\forall (u0: T).(\forall (i: nat).((getl i c0 (CHead d
-(Bind Void) u0)) \to (\forall (w: T).(\forall (v: T).((subst0 i w u v) \to
-(\forall (P: Prop).P)))))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_:
-(arity g (CHead c0 (Bind b) u) t0 a2)).(\lambda (H4: ((\forall (d:
-C).(\forall (u0: T).(\forall (i: nat).((getl i (CHead c0 (Bind b) u) (CHead d
-(Bind Void) u0)) \to (\forall (w: T).(\forall (v: T).((subst0 i w t0 v) \to
-(\forall (P: Prop).P)))))))))).(\lambda (d: C).(\lambda (u0: T).(\lambda (i:
-nat).(\lambda (H5: (getl i c0 (CHead d (Bind Void) u0))).(\lambda (w:
-T).(\lambda (v: T).(\lambda (H6: (subst0 i w (THead (Bind b) u t0)
-v)).(\lambda (P: Prop).(or3_ind (ex2 T (\lambda (u2: T).(eq T v (THead (Bind
-b) u2 t0))) (\lambda (u2: T).(subst0 i w u u2))) (ex2 T (\lambda (t2: T).(eq
-T v (THead (Bind b) u t2))) (\lambda (t2: T).(subst0 (s (Bind b) i) w t0
-t2))) (ex3_2 T T (\lambda (u2: T).(\lambda (t2: T).(eq T v (THead (Bind b) u2
-t2)))) (\lambda (u2: T).(\lambda (_: T).(subst0 i w u u2))) (\lambda (_:
-T).(\lambda (t2: T).(subst0 (s (Bind b) i) w t0 t2)))) P (\lambda (H7: (ex2 T
-(\lambda (u2: T).(eq T v (THead (Bind b) u2 t0))) (\lambda (u2: T).(subst0 i
-w u u2)))).(ex2_ind T (\lambda (u2: T).(eq T v (THead (Bind b) u2 t0)))
-(\lambda (u2: T).(subst0 i w u u2)) P (\lambda (x: T).(\lambda (_: (eq T v
-(THead (Bind b) x t0))).(\lambda (H9: (subst0 i w u x)).(H2 d u0 i H5 w x H9
-P)))) H7)) (\lambda (H7: (ex2 T (\lambda (t2: T).(eq T v (THead (Bind b) u
-t2))) (\lambda (t2: T).(subst0 (s (Bind b) i) w t0 t2)))).(ex2_ind T (\lambda
-(t2: T).(eq T v (THead (Bind b) u t2))) (\lambda (t2: T).(subst0 (s (Bind b)
-i) w t0 t2)) P (\lambda (x: T).(\lambda (_: (eq T v (THead (Bind b) u
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) I (CHead d0 (Bind Void) u0) (getl_mono c0 (CHead d
+(Bind Abst) u) i H0 (CHead d0 (Bind Void) u0) H7)) in (False_ind P H9))))))
+(subst0_gen_lref w v i0 i H4)))))))))))))))))) (\lambda (b: B).(\lambda (_:
+(not (eq B b Abst))).(\lambda (c0: C).(\lambda (u: T).(\lambda (a1:
+A).(\lambda (_: (arity g c0 u a1)).(\lambda (H2: ((\forall (d: C).(\forall
+(u0: T).(\forall (i: nat).((getl i c0 (CHead d (Bind Void) u0)) \to (\forall
+(w: T).(\forall (v: T).((subst0 i w u v) \to (\forall (P:
+Prop).P)))))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g
+(CHead c0 (Bind b) u) t0 a2)).(\lambda (H4: ((\forall (d: C).(\forall (u0:
+T).(\forall (i: nat).((getl i (CHead c0 (Bind b) u) (CHead d (Bind Void) u0))
+\to (\forall (w: T).(\forall (v: T).((subst0 i w t0 v) \to (\forall (P:
+Prop).P)))))))))).(\lambda (d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda
+(H5: (getl i c0 (CHead d (Bind Void) u0))).(\lambda (w: T).(\lambda (v:
+T).(\lambda (H6: (subst0 i w (THead (Bind b) u t0) v)).(\lambda (P:
+Prop).(or3_ind (ex2 T (\lambda (u2: T).(eq T v (THead (Bind b) u2 t0)))
+(\lambda (u2: T).(subst0 i w u u2))) (ex2 T (\lambda (t2: T).(eq T v (THead
+(Bind b) u t2))) (\lambda (t2: T).(subst0 (s (Bind b) i) w t0 t2))) (ex3_2 T
+T (\lambda (u2: T).(\lambda (t2: T).(eq T v (THead (Bind b) u2 t2))))
+(\lambda (u2: T).(\lambda (_: T).(subst0 i w u u2))) (\lambda (_: T).(\lambda
+(t2: T).(subst0 (s (Bind b) i) w t0 t2)))) P (\lambda (H7: (ex2 T (\lambda
+(u2: T).(eq T v (THead (Bind b) u2 t0))) (\lambda (u2: T).(subst0 i w u
+u2)))).(ex2_ind T (\lambda (u2: T).(eq T v (THead (Bind b) u2 t0))) (\lambda
+(u2: T).(subst0 i w u u2)) P (\lambda (x: T).(\lambda (_: (eq T v (THead
+(Bind b) x t0))).(\lambda (H9: (subst0 i w u x)).(H2 d u0 i H5 w x H9 P))))
+H7)) (\lambda (H7: (ex2 T (\lambda (t2: T).(eq T v (THead (Bind b) u t2)))
+(\lambda (t2: T).(subst0 (s (Bind b) i) w t0 t2)))).(ex2_ind T (\lambda (t2:
+T).(eq T v (THead (Bind b) u t2))) (\lambda (t2: T).(subst0 (s (Bind b) i) w
+t0 t2)) P (\lambda (x: T).(\lambda (_: (eq T v (THead (Bind b) u
x))).(\lambda (H9: (subst0 (s (Bind b) i) w t0 x)).(H4 d u0 (S i)
(getl_clear_bind b (CHead c0 (Bind b) u) c0 u (clear_bind b c0 u) (CHead d
(Bind Void) u0) i H5) w x H9 P)))) H7)) (\lambda (H7: (ex3_2 T T (\lambda
nat).(\lambda (H3: (getl i c0 (CHead d (Bind Void) u))).(\lambda (w:
T).(\lambda (v: T).(\lambda (H4: (subst0 i w t0 v)).(\lambda (P: Prop).(H1 d
u i H3 w v H4 P)))))))))))))))) c t a H))))).
-(* COMMENTS
-Initial nodes: 4131
-END *)
theorem arity_gen_cvoid:
\forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((arity g c t
x) (\lambda (t0: T).(ex T (\lambda (v: T).(eq T t0 (lift (S O) i v)))))
(ex_intro T (\lambda (v: T).(eq T (lift (S O) i x) (lift (S O) i v))) x
(refl_equal T (lift (S O) i x))) t H3))) H2))) H1))))))))))).
-(* COMMENTS
-Initial nodes: 423
-END *)
theorem arity_fsubst0:
\forall (g: G).(\forall (c1: C).(\forall (t1: T).(\forall (a: A).((arity g
(n: nat).(getl n c (CHead d1 (Bind Abbr) u0))) H3 i H9) in (let H12 \def
(eq_ind C (CHead d (Bind Abbr) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead
d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead d1 (Bind
-Abbr) u0) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _)
-\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0)
-(getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead d1 (Bind Abbr) u0) H11)) in
-((let H14 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead d
-(Bind Abbr) u) (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u)
-i H0 (CHead d1 (Bind Abbr) u0) H11)) in (\lambda (H15: (eq C d d1)).(let H16
-\def (eq_ind_r T u0 (\lambda (t: T).(getl i c (CHead d1 (Bind Abbr) t))) H12
-u H14) in (eq_ind T u (\lambda (t: T).(arity g c (lift (S i) O t) a0)) (let
-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))).(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 (csubst0_getl_lt i0 i H9 c c2 u0 H8
-(CHead d (Bind Abbr) u) H0) in (or4_ind (getl i c2 (CHead d (Bind Abbr) u))
-(ex3_4 B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u1: T).(\lambda (_:
-T).(eq C (CHead d (Bind Abbr) u) (CHead e0 (Bind b) u1)))))) (\lambda (b:
-B).(\lambda (e0: C).(\lambda (_: T).(\lambda (w: T).(getl i c2 (CHead e0
-(Bind b) w)))))) (\lambda (_: B).(\lambda (_: C).(\lambda (u1: T).(\lambda
-(w: T).(subst0 (minus i0 (S i)) u0 u1 w)))))) (ex3_4 B C C T (\lambda (b:
-B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(eq C (CHead d (Bind
-Abbr) u) (CHead e1 (Bind b) u1)))))) (\lambda (b: B).(\lambda (_: C).(\lambda
-(e2: C).(\lambda (u1: T).(getl i c2 (CHead e2 (Bind b) u1)))))) (\lambda (_:
-B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(csubst0 (minus i0 (S
-i)) u0 e1 e2)))))) (ex4_5 B C C T T (\lambda (b: B).(\lambda (e1: C).(\lambda
-(_: C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead
-e1 (Bind b) u1))))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e2:
-C).(\lambda (_: T).(\lambda (w: T).(getl i c2 (CHead e2 (Bind b) w)))))))
-(\lambda (_: B).(\lambda (_: C).(\lambda (_: C).(\lambda (u1: T).(\lambda (w:
-T).(subst0 (minus i0 (S i)) u0 u1 w)))))) (\lambda (_: B).(\lambda (e1:
-C).(\lambda (e2: C).(\lambda (_: T).(\lambda (_: T).(csubst0 (minus i0 (S i))
-u0 e1 e2))))))) (arity g c2 (TLRef i) a0) (\lambda (H11: (getl i c2 (CHead d
-(Bind Abbr) u))).(let H12 \def (eq_ind nat (minus i0 i) (\lambda (n:
-nat).(getl n (CHead d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0)))
-(getl_conf_le i0 (CHead d1 (Bind Abbr) u0) c H3 (CHead d (Bind Abbr) u) i H0
-(le_S_n i i0 (le_S (S i) i0 H9))) (S (minus i0 (S i))) (minus_x_Sy i0 i H9))
-in (arity_abbr g c2 d u i H11 a0 H1))) (\lambda (H11: (ex3_4 B C T T (\lambda
+Abbr) u0) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind
+Abbr) u) (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) i H0
+(CHead d1 (Bind Abbr) u0) H11)) in ((let H14 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
+(CHead d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind
+Abbr) u) i H0 (CHead d1 (Bind Abbr) u0) H11)) in (\lambda (H15: (eq C d
+d1)).(let H16 \def (eq_ind_r T u0 (\lambda (t: T).(getl i c (CHead d1 (Bind
+Abbr) t))) H12 u H14) in (eq_ind T u (\lambda (t: T).(arity g c (lift (S i) O
+t) a0)) (let 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))).(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
+(csubst0_getl_lt i0 i H9 c c2 u0 H8 (CHead d (Bind Abbr) u) H0) in (or4_ind
+(getl i c2 (CHead d (Bind Abbr) u)) (ex3_4 B C T T (\lambda (b: B).(\lambda
+(e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abbr) u) (CHead
+e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_:
+T).(\lambda (w: T).(getl i c2 (CHead e0 (Bind b) w)))))) (\lambda (_:
+B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i0 (S i))
+u0 u1 w)))))) (ex3_4 B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_:
+C).(\lambda (u1: T).(eq C (CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1))))))
+(\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl i c2
+(CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2:
+C).(\lambda (_: T).(csubst0 (minus i0 (S i)) u0 e1 e2)))))) (ex4_5 B C C T T
+(\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda
+(_: T).(eq C (CHead d (Bind Abbr) u) (CHead e1 (Bind b) u1))))))) (\lambda
+(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl
+i c2 (CHead e2 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
+C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i0 (S i)) u0 u1 w))))))
+(\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda
+(_: T).(csubst0 (minus i0 (S i)) u0 e1 e2))))))) (arity g c2 (TLRef i) a0)
+(\lambda (H11: (getl i c2 (CHead d (Bind Abbr) u))).(let H12 \def (eq_ind nat
+(minus i0 i) (\lambda (n: nat).(getl n (CHead d (Bind Abbr) u) (CHead d1
+(Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind Abbr) u0) c H3 (CHead d
+(Bind Abbr) u) i H0 (le_S_n i i0 (le_S_n (S i) (S i0) (le_S (S (S i)) (S i0)
+(le_n_S (S i) i0 H9))))) (S (minus i0 (S i))) (minus_x_Sy i0 i H9)) in
+(arity_abbr g c2 d u i H11 a0 H1))) (\lambda (H11: (ex3_4 B C T T (\lambda
(b: B).(\lambda (e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind
Abbr) u) (CHead e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda (e0:
C).(\lambda (_: T).(\lambda (w: T).(getl i c2 (CHead e0 (Bind b) w))))))
x0) x3))).(\lambda (H14: (subst0 (minus i0 (S i)) u0 x2 x3)).(let H15 \def
(eq_ind nat (minus i0 i) (\lambda (n: nat).(getl n (CHead d (Bind Abbr) u)
(CHead d1 (Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind Abbr) u0) c H3
-(CHead d (Bind Abbr) u) i H0 (le_S_n i i0 (le_S (S i) i0 H9))) (S (minus i0
-(S i))) (minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d |
-(CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0)
-x2) H12) in ((let H17 \def (f_equal C B (\lambda (e: C).(match e in C return
-(\lambda (_: C).B) with [(CSort _) \Rightarrow Abbr | (CHead _ k _)
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b)
-\Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead d (Bind Abbr) u) (CHead
-x1 (Bind x0) x2) H12) in ((let H18 \def (f_equal C T (\lambda (e: C).(match e
-in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t)
+(CHead d (Bind Abbr) u) i H0 (le_S_n i i0 (le_S_n (S i) (S i0) (le_S (S (S
+i)) (S i0) (le_n_S (S i) i0 H9))))) (S (minus i0 (S i))) (minus_x_Sy i0 i
+H9)) in (let H16 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
+(CHead x1 (Bind x0) x2) H12) in ((let H17 \def (f_equal C B (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow
+(match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead
+d (Bind Abbr) u) (CHead x1 (Bind x0) x2) H12) in ((let H18 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t)
\Rightarrow t])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) H12) in
(\lambda (H19: (eq B Abbr x0)).(\lambda (H20: (eq C d x1)).(let H21 \def
(eq_ind_r T x2 (\lambda (t: T).(subst0 (minus i0 (S i)) u0 t x3)) H14 u H18)
(CHead x2 (Bind x0) x3))).(\lambda (H14: (csubst0 (minus i0 (S i)) u0 x1
x2)).(let H15 \def (eq_ind nat (minus i0 i) (\lambda (n: nat).(getl n (CHead
d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind
-Abbr) u0) c H3 (CHead d (Bind Abbr) u) i H0 (le_S_n i i0 (le_S (S i) i0 H9)))
-(S (minus i0 (S i))) (minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abbr) u)
-(CHead x1 (Bind x0) x3) H12) in ((let H17 \def (f_equal C B (\lambda (e:
-C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abbr |
-(CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind
-b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead d (Bind Abbr) u)
-(CHead x1 (Bind x0) x3) H12) in ((let H18 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
+Abbr) u0) c H3 (CHead d (Bind Abbr) u) i H0 (le_S_n i i0 (le_S_n (S i) (S i0)
+(le_S (S (S i)) (S i0) (le_n_S (S i) i0 H9))))) (S (minus i0 (S i)))
+(minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d
+(Bind Abbr) u) (CHead x1 (Bind x0) x3) H12) in ((let H17 \def (f_equal C B
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow Abbr | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
+Abbr])])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H12) in ((let H18
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u |
(CHead _ _ t) \Rightarrow t])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0)
x3) H12) in (\lambda (H19: (eq B Abbr x0)).(\lambda (H20: (eq C d x1)).(let
H21 \def (eq_ind_r T x3 (\lambda (t: T).(getl i c2 (CHead x2 (Bind x0) t)))
(csubst0 (minus i0 (S i)) u0 x1 x2)).(let H16 \def (eq_ind nat (minus i0 i)
(\lambda (n: nat).(getl n (CHead d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0)))
(getl_conf_le i0 (CHead d1 (Bind Abbr) u0) c H3 (CHead d (Bind Abbr) u) i H0
-(le_S_n i i0 (le_S (S i) i0 H9))) (S (minus i0 (S i))) (minus_x_Sy i0 i H9))
-in (let H17 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0]))
-(CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H12) in ((let H18 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
-Abbr])])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H12) in ((let H19
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
+(le_S_n i i0 (le_S_n (S i) (S i0) (le_S (S (S i)) (S i0) (le_n_S (S i) i0
+H9))))) (S (minus i0 (S i))) (minus_x_Sy i0 i H9)) in (let H17 \def (f_equal
+C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow d | (CHead c0 _ _)
+\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x3) H12) in
+((let H18 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow Abbr | (CHead _ k _) \Rightarrow (match k with [(Bind b)
+\Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead d (Bind Abbr) u) (CHead
+x1 (Bind x0) x3) H12) in ((let H19 \def (f_equal C T (\lambda (e: C).(match e
with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead d (Bind
Abbr) u) (CHead x1 (Bind x0) x3) H12) in (\lambda (H20: (eq B Abbr
x0)).(\lambda (H21: (eq C d x1)).(let H22 \def (eq_ind_r T x3 (\lambda (t:
(n: nat).(getl n c (CHead d1 (Bind Abbr) u0))) H3 i H9) in (let H13 \def
(eq_ind C (CHead d (Bind Abbr) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead
d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead d1 (Bind
-Abbr) u0) H12)) in (let H14 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _)
-\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0)
-(getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead d1 (Bind Abbr) u0) H12)) in
-((let H15 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead d
-(Bind Abbr) u) (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u)
-i H0 (CHead d1 (Bind Abbr) u0) H12)) in (\lambda (H16: (eq C d d1)).(let H17
-\def (eq_ind_r T u0 (\lambda (t: T).(getl i c (CHead d1 (Bind Abbr) t))) H13
-u H15) in (let H18 \def (eq_ind_r T u0 (\lambda (t: T).(csubst0 i t c c2))
-H11 u H15) in (eq_ind T u (\lambda (t: T).(arity g c2 (lift (S i) O t) a0))
-(let H19 \def (eq_ind_r C d1 (\lambda (c0: C).(getl i c (CHead c0 (Bind Abbr)
-u))) H17 d H16) in (arity_lift g d u a0 H1 c2 (S i) O (getl_drop Abbr c2 d u
-i (csubst0_getl_ge i i (le_n i) c c2 u H18 (CHead d (Bind Abbr) u) H19)))) u0
-H15))))) H14))))) t2 H10))) (subst0_gen_lref u0 t2 i0 i H7)))) H6))
-H5)))))))))))))))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda
-(i: nat).(\lambda (H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0:
-A).(\lambda (H1: (arity g d u (asucc g a0))).(\lambda (H2: ((\forall (d1:
-C).(\forall (u0: T).(\forall (i0: nat).((getl i0 d (CHead d1 (Bind Abbr) u0))
-\to (\forall (c2: C).(\forall (t2: T).((fsubst0 i0 u0 d u c2 t2) \to (arity g
-c2 t2 (asucc g a0))))))))))).(\lambda (d1: C).(\lambda (u0: T).(\lambda (i0:
-nat).(\lambda (H3: (getl i0 c (CHead d1 (Bind Abbr) u0))).(\lambda (c2:
-C).(\lambda (t2: T).(\lambda (H4: (fsubst0 i0 u0 c (TLRef i) c2 t2)).(let H_x
-\def (fsubst0_gen_base c c2 (TLRef i) t2 u0 i0 H4) in (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))).(land_ind (eq C c c2) (subst0 i0 u0 (TLRef i) t2) (arity g c2 t2 a0)
+Abbr) u0) H12)) in (let H14 \def (f_equal C C (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind
+Abbr) u) (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abbr) u) i H0
+(CHead d1 (Bind Abbr) u0) H12)) in ((let H15 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
+(CHead d (Bind Abbr) u) (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind
+Abbr) u) i H0 (CHead d1 (Bind Abbr) u0) H12)) in (\lambda (H16: (eq C d
+d1)).(let H17 \def (eq_ind_r T u0 (\lambda (t: T).(getl i c (CHead d1 (Bind
+Abbr) t))) H13 u H15) in (let H18 \def (eq_ind_r T u0 (\lambda (t:
+T).(csubst0 i t c c2)) H11 u H15) in (eq_ind T u (\lambda (t: T).(arity g c2
+(lift (S i) O t) a0)) (let H19 \def (eq_ind_r C d1 (\lambda (c0: C).(getl i c
+(CHead c0 (Bind Abbr) u))) H17 d H16) in (arity_lift g d u a0 H1 c2 (S i) O
+(getl_drop Abbr c2 d u i (csubst0_getl_ge i i (le_n i) c c2 u H18 (CHead d
+(Bind Abbr) u) H19)))) u0 H15))))) H14))))) t2 H10))) (subst0_gen_lref u0 t2
+i0 i H7)))) H6)) H5)))))))))))))))))) (\lambda (c: C).(\lambda (d:
+C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind
+Abst) u))).(\lambda (a0: A).(\lambda (H1: (arity g d u (asucc g
+a0))).(\lambda (H2: ((\forall (d1: C).(\forall (u0: T).(\forall (i0:
+nat).((getl i0 d (CHead d1 (Bind Abbr) u0)) \to (\forall (c2: C).(\forall
+(t2: T).((fsubst0 i0 u0 d u c2 t2) \to (arity g c2 t2 (asucc g
+a0))))))))))).(\lambda (d1: C).(\lambda (u0: T).(\lambda (i0: nat).(\lambda
+(H3: (getl i0 c (CHead d1 (Bind Abbr) u0))).(\lambda (c2: C).(\lambda (t2:
+T).(\lambda (H4: (fsubst0 i0 u0 c (TLRef i) c2 t2)).(let H_x \def
+(fsubst0_gen_base c c2 (TLRef i) t2 u0 i0 H4) in (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))).(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)) (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
c (CHead d1 (Bind Abbr) u0))) H3 i H9) in (let H12 \def (eq_ind C (CHead d
(Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead d1 (Bind Abbr) u0)
(getl_mono c (CHead d (Bind Abst) u) i H0 (CHead d1 (Bind Abbr) u0) H11)) in
-(let H13 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee in
-C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k
-_) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
-False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat _)
-\Rightarrow False])])) I (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d
-(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))).(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
-(csubst0_getl_lt i0 i H9 c c2 u0 H8 (CHead d (Bind Abst) u) H0) in (or4_ind
-(getl i c2 (CHead d (Bind Abst) u)) (ex3_4 B C T T (\lambda (b: B).(\lambda
-(e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abst) u) (CHead
-e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda (e0: C).(\lambda (_:
-T).(\lambda (w: T).(getl i c2 (CHead e0 (Bind b) w)))))) (\lambda (_:
-B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i0 (S i))
-u0 u1 w)))))) (ex3_4 B C C T (\lambda (b: B).(\lambda (e1: C).(\lambda (_:
-C).(\lambda (u1: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))
-(\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (u1: T).(getl i c2
-(CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2:
-C).(\lambda (_: T).(csubst0 (minus i0 (S i)) u0 e1 e2)))))) (ex4_5 B C C T T
-(\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda (u1: T).(\lambda
-(_: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b) u1))))))) (\lambda
-(b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_: T).(\lambda (w: T).(getl
-i c2 (CHead e2 (Bind b) w))))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_:
-C).(\lambda (u1: T).(\lambda (w: T).(subst0 (minus i0 (S i)) u0 u1 w))))))
-(\lambda (_: B).(\lambda (e1: C).(\lambda (e2: C).(\lambda (_: T).(\lambda
-(_: T).(csubst0 (minus i0 (S i)) u0 e1 e2))))))) (arity g c2 (TLRef i) a0)
-(\lambda (H11: (getl i c2 (CHead d (Bind Abst) u))).(let H12 \def (eq_ind nat
-(minus i0 i) (\lambda (n: nat).(getl n (CHead d (Bind Abst) u) (CHead d1
-(Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind Abbr) u0) c H3 (CHead d
-(Bind Abst) u) i H0 (le_S_n i i0 (le_S (S i) i0 H9))) (S (minus i0 (S i)))
+(let H13 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee
+with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with
+[(Bind b) \Rightarrow (match b with [Abbr \Rightarrow False | Abst
+\Rightarrow True | Void \Rightarrow False]) | (Flat _) \Rightarrow False])]))
+I (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d (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))).(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 (csubst0_getl_lt i0 i H9 c c2 u0 H8 (CHead d (Bind
+Abst) u) H0) in (or4_ind (getl i c2 (CHead d (Bind Abst) u)) (ex3_4 B C T T
+(\lambda (b: B).(\lambda (e0: C).(\lambda (u1: T).(\lambda (_: T).(eq C
+(CHead d (Bind Abst) u) (CHead e0 (Bind b) u1)))))) (\lambda (b: B).(\lambda
+(e0: C).(\lambda (_: T).(\lambda (w: T).(getl i c2 (CHead e0 (Bind b) w))))))
+(\lambda (_: B).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0
+(minus i0 (S i)) u0 u1 w)))))) (ex3_4 B C C T (\lambda (b: B).(\lambda (e1:
+C).(\lambda (_: C).(\lambda (u1: T).(eq C (CHead d (Bind Abst) u) (CHead e1
+(Bind b) u1)))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda
+(u1: T).(getl i c2 (CHead e2 (Bind b) u1)))))) (\lambda (_: B).(\lambda (e1:
+C).(\lambda (e2: C).(\lambda (_: T).(csubst0 (minus i0 (S i)) u0 e1 e2))))))
+(ex4_5 B C C T T (\lambda (b: B).(\lambda (e1: C).(\lambda (_: C).(\lambda
+(u1: T).(\lambda (_: T).(eq C (CHead d (Bind Abst) u) (CHead e1 (Bind b)
+u1))))))) (\lambda (b: B).(\lambda (_: C).(\lambda (e2: C).(\lambda (_:
+T).(\lambda (w: T).(getl i c2 (CHead e2 (Bind b) w))))))) (\lambda (_:
+B).(\lambda (_: C).(\lambda (_: C).(\lambda (u1: T).(\lambda (w: T).(subst0
+(minus i0 (S i)) u0 u1 w)))))) (\lambda (_: B).(\lambda (e1: C).(\lambda (e2:
+C).(\lambda (_: T).(\lambda (_: T).(csubst0 (minus i0 (S i)) u0 e1 e2)))))))
+(arity g c2 (TLRef i) a0) (\lambda (H11: (getl i c2 (CHead d (Bind Abst)
+u))).(let H12 \def (eq_ind nat (minus i0 i) (\lambda (n: nat).(getl n (CHead
+d (Bind Abst) u) (CHead d1 (Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind
+Abbr) u0) c H3 (CHead d (Bind Abst) u) i H0 (le_S_n i i0 (le_S_n (S i) (S i0)
+(le_S (S (S i)) (S i0) (le_n_S (S i) i0 H9))))) (S (minus i0 (S i)))
(minus_x_Sy i0 i H9)) in (arity_abst g c2 d u i H11 a0 H1))) (\lambda (H11:
(ex3_4 B C T T (\lambda (b: B).(\lambda (e0: C).(\lambda (u1: T).(\lambda (_:
T).(eq C (CHead d (Bind Abst) u) (CHead e0 (Bind b) u1)))))) (\lambda (b:
(CHead x1 (Bind x0) x3))).(\lambda (H14: (subst0 (minus i0 (S i)) u0 x2
x3)).(let H15 \def (eq_ind nat (minus i0 i) (\lambda (n: nat).(getl n (CHead
d (Bind Abst) u) (CHead d1 (Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind
-Abbr) u0) c H3 (CHead d (Bind Abst) u) i H0 (le_S_n i i0 (le_S (S i) i0 H9)))
-(S (minus i0 (S i))) (minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abst) u)
-(CHead x1 (Bind x0) x2) H12) in ((let H17 \def (f_equal C B (\lambda (e:
-C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abst |
-(CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind
-b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead d (Bind Abst) u)
-(CHead x1 (Bind x0) x2) H12) in ((let H18 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
+Abbr) u0) c H3 (CHead d (Bind Abst) u) i H0 (le_S_n i i0 (le_S_n (S i) (S i0)
+(le_S (S (S i)) (S i0) (le_n_S (S i) i0 H9))))) (S (minus i0 (S i)))
+(minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d
+(Bind Abst) u) (CHead x1 (Bind x0) x2) H12) in ((let H17 \def (f_equal C B
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow Abst | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
+Abst])])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) H12) in ((let H18
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u |
(CHead _ _ t) \Rightarrow t])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
x2) H12) in (\lambda (H19: (eq B Abst x0)).(\lambda (H20: (eq C d x1)).(let
H21 \def (eq_ind_r T x2 (\lambda (t: T).(subst0 (minus i0 (S i)) u0 t x3))
(CHead x2 (Bind x0) x3))).(\lambda (H14: (csubst0 (minus i0 (S i)) u0 x1
x2)).(let H15 \def (eq_ind nat (minus i0 i) (\lambda (n: nat).(getl n (CHead
d (Bind Abst) u) (CHead d1 (Bind Abbr) u0))) (getl_conf_le i0 (CHead d1 (Bind
-Abbr) u0) c H3 (CHead d (Bind Abst) u) i H0 (le_S_n i i0 (le_S (S i) i0 H9)))
-(S (minus i0 (S i))) (minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d (Bind Abst) u)
-(CHead x1 (Bind x0) x3) H12) in ((let H17 \def (f_equal C B (\lambda (e:
-C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abst |
-(CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind
-b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead d (Bind Abst) u)
-(CHead x1 (Bind x0) x3) H12) in ((let H18 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
+Abbr) u0) c H3 (CHead d (Bind Abst) u) i H0 (le_S_n i i0 (le_S_n (S i) (S i0)
+(le_S (S (S i)) (S i0) (le_n_S (S i) i0 H9))))) (S (minus i0 (S i)))
+(minus_x_Sy i0 i H9)) in (let H16 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) (CHead d
+(Bind Abst) u) (CHead x1 (Bind x0) x3) H12) in ((let H17 \def (f_equal C B
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow Abst | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
+Abst])])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H12) in ((let H18
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u |
(CHead _ _ t) \Rightarrow t])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0)
x3) H12) in (\lambda (H19: (eq B Abst x0)).(\lambda (H20: (eq C d x1)).(let
H21 \def (eq_ind_r T x3 (\lambda (t: T).(getl i c2 (CHead x2 (Bind x0) t)))
(csubst0 (minus i0 (S i)) u0 x1 x2)).(let H16 \def (eq_ind nat (minus i0 i)
(\lambda (n: nat).(getl n (CHead d (Bind Abst) u) (CHead d1 (Bind Abbr) u0)))
(getl_conf_le i0 (CHead d1 (Bind Abbr) u0) c H3 (CHead d (Bind Abst) u) i H0
-(le_S_n i i0 (le_S (S i) i0 H9))) (S (minus i0 (S i))) (minus_x_Sy i0 i H9))
-in (let H17 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0]))
-(CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H12) in ((let H18 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
-Abst])])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H12) in ((let H19
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
+(le_S_n i i0 (le_S_n (S i) (S i0) (le_S (S (S i)) (S i0) (le_n_S (S i) i0
+H9))))) (S (minus i0 (S i))) (minus_x_Sy i0 i H9)) in (let H17 \def (f_equal
+C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow d | (CHead c0 _ _)
+\Rightarrow c0])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x3) H12) in
+((let H18 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow Abst | (CHead _ k _) \Rightarrow (match k with [(Bind b)
+\Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead d (Bind Abst) u) (CHead
+x1 (Bind x0) x3) H12) in ((let H19 \def (f_equal C T (\lambda (e: C).(match e
with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead d (Bind
Abst) u) (CHead x1 (Bind x0) x3) H12) in (\lambda (H20: (eq B Abst
x0)).(\lambda (H21: (eq C d x1)).(let H22 \def (eq_ind_r T x3 (\lambda (t:
(eq_ind C (CHead d (Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead
d1 (Bind Abbr) u0) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead d1 (Bind
Abbr) u0) H12)) in (let H14 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda
-(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b) \Rightarrow (match b in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow True | Void
-\Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abbr)
-u0) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead d1 (Bind Abbr) u0) H12))
-in (False_ind (arity g c2 (lift (S i) O u0) a0) H14))))) t2 H10)))
-(subst0_gen_lref u0 t2 i0 i H7)))) H6)) H5)))))))))))))))))) (\lambda (b:
-B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (H1: (arity g c u a1)).(\lambda (H2: ((\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 a1)))))))))).(\lambda (t: T).(\lambda (a2: A).(\lambda (_:
-(arity g (CHead c (Bind b) u) t a2)).(\lambda (H4: ((\forall (d1: C).(\forall
-(u0: T).(\forall (i: nat).((getl i (CHead c (Bind b) u) (CHead d1 (Bind Abbr)
-u0)) \to (\forall (c2: C).(\forall (t2: T).((fsubst0 i u0 (CHead c (Bind b)
-u) t c2 t2) \to (arity g c2 t2 a2)))))))))).(\lambda (d1: C).(\lambda (u0:
-T).(\lambda (i: nat).(\lambda (H5: (getl i c (CHead d1 (Bind Abbr)
-u0))).(\lambda (c2: C).(\lambda (t2: T).(\lambda (H6: (fsubst0 i u0 c (THead
-(Bind b) u t) c2 t2)).(let H_x \def (fsubst0_gen_base c c2 (THead (Bind b) u
-t) t2 u0 i H6) in (let H7 \def H_x in (or3_ind (land (eq C c c2) (subst0 i u0
-(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))).(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
-(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:
+(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) I (CHead d1 (Bind Abbr) u0) (getl_mono c (CHead d
+(Bind Abst) u) i H0 (CHead d1 (Bind Abbr) u0) H12)) in (False_ind (arity g c2
+(lift (S i) O u0) a0) H14))))) t2 H10))) (subst0_gen_lref u0 t2 i0 i H7))))
+H6)) H5)))))))))))))))))) (\lambda (b: B).(\lambda (H0: (not (eq B b
+Abst))).(\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (H1: (arity
+g c u a1)).(\lambda (H2: ((\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 a1)))))))))).(\lambda (t:
+T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind b) u) t
+a2)).(\lambda (H4: ((\forall (d1: C).(\forall (u0: T).(\forall (i:
+nat).((getl i (CHead c (Bind b) u) (CHead d1 (Bind Abbr) u0)) \to (\forall
+(c2: C).(\forall (t2: T).((fsubst0 i u0 (CHead c (Bind b) u) t c2 t2) \to
+(arity g c2 t2 a2)))))))))).(\lambda (d1: C).(\lambda (u0: T).(\lambda (i:
+nat).(\lambda (H5: (getl i c (CHead d1 (Bind Abbr) u0))).(\lambda (c2:
+C).(\lambda (t2: T).(\lambda (H6: (fsubst0 i u0 c (THead (Bind b) u t) c2
+t2)).(let H_x \def (fsubst0_gen_base c c2 (THead (Bind b) u t) t2 u0 i H6) in
+(let H7 \def H_x in (or3_ind (land (eq C c c2) (subst0 i u0 (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))).(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 (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 c 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 (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))))).
-(* COMMENTS
-Initial nodes: 20387
-END *)
theorem arity_subst0:
\forall (g: G).(\forall (c: C).(\forall (t1: T).(\forall (a: A).((arity g c
(H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (t2: T).(\lambda (H1:
(subst0 i u t1 t2)).(arity_fsubst0 g c t1 a H d u i H0 c t2 (fsubst0_snd i u
c t1 t2 H1)))))))))))).
-(* COMMENTS
-Initial nodes: 89
-END *)
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/getl.ma".
+include "basic_1/csuba/getl.ma".
-include "Basic-1/csuba/props.ma".
+include "basic_1/csuba/props.ma".
-include "Basic-1/arity/props.ma".
+include "basic_1/arity/fwd.ma".
-include "Basic-1/csubv/getl.ma".
+include "basic_1/csubv/getl.ma".
theorem csuba_arity:
\forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1
t a) \to (\forall (c2: C).((csuba g c1 c2) \to (arity g c2 t a)))))))
\def
\lambda (g: G).(\lambda (c1: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c1 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
-A).(\forall (c2: C).((csuba g c c2) \to (arity g c2 t0 a0)))))) (\lambda (c:
-C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_: (csuba g c
-c2)).(arity_sort g c2 n))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u:
-T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr)
-u))).(\lambda (a0: A).(\lambda (_: (arity g d u a0)).(\lambda (H2: ((\forall
-(c2: C).((csuba g d c2) \to (arity g c2 u a0))))).(\lambda (c2: C).(\lambda
-(H3: (csuba g c c2)).(let H4 \def (csuba_getl_abbr g c d u i H0 c2 H3) in
-(ex2_ind C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda
-(d2: C).(csuba g d d2)) (arity g c2 (TLRef i) a0) (\lambda (x: C).(\lambda
-(H5: (getl i c2 (CHead x (Bind Abbr) u))).(\lambda (H6: (csuba g d
-x)).(arity_abbr g c2 x u i H5 a0 (H2 x H6))))) H4)))))))))))) (\lambda (c:
+(arity g c1 t a)).(let TMP_1 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
+(a0: A).(\forall (c2: C).((csuba g c c2) \to (arity g c2 t0 a0)))))) in (let
+TMP_2 \def (\lambda (c: C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_:
+(csuba g c c2)).(arity_sort g c2 n))))) in (let TMP_11 \def (\lambda (c:
C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c
-(CHead d (Bind Abst) u))).(\lambda (a0: A).(\lambda (H1: (arity g d u (asucc
-g a0))).(\lambda (H2: ((\forall (c2: C).((csuba g d c2) \to (arity g c2 u
-(asucc g a0)))))).(\lambda (c2: C).(\lambda (H3: (csuba g c c2)).(let H4 \def
-(csuba_getl_abst g c d u i H0 c2 H3) in (or_ind (ex2 C (\lambda (d2: C).(getl
-i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d d2))) (ex4_3 C T
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2
-(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d u (asucc
-g a1))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2
-a1))))) (arity g c2 (TLRef i) a0) (\lambda (H5: (ex2 C (\lambda (d2: C).(getl
-i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d d2)))).(ex2_ind C
-(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d d2)) (arity g c2 (TLRef i) a0) (\lambda (x: C).(\lambda (H6:
-(getl i c2 (CHead x (Bind Abst) u))).(\lambda (H7: (csuba g d x)).(arity_abst
-g c2 x u i H6 a0 (H2 x H7))))) H5)) (\lambda (H5: (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d d2)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d u (asucc g a1)))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2
-a1)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
-A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
-T).(\lambda (_: A).(csuba g d d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a1: A).(arity g d u (asucc g a1))))) (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (a1: A).(arity g d2 u2 a1)))) (arity g c2 (TLRef i) a0) (\lambda
-(x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H6: (getl i c2 (CHead x0
-(Bind Abbr) x1))).(\lambda (_: (csuba g d x0)).(\lambda (H8: (arity g d u
-(asucc g x2))).(\lambda (H9: (arity g x0 x1 x2)).(arity_repl g c2 (TLRef i)
-x2 (arity_abbr g c2 x0 x1 i H6 x2 H9) a0 (asucc_inj g x2 a0 (arity_mono g d u
-(asucc g x2) H8 (asucc g a0) H1)))))))))) H5)) H4)))))))))))) (\lambda (b:
-B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2: ((\forall
-(c2: C).((csuba g c c2) \to (arity g c2 u a1))))).(\lambda (t0: T).(\lambda
-(a2: A).(\lambda (_: (arity g (CHead c (Bind b) u) t0 a2)).(\lambda (H4:
-((\forall (c2: C).((csuba g (CHead c (Bind b) u) c2) \to (arity g c2 t0
-a2))))).(\lambda (c2: C).(\lambda (H5: (csuba g c c2)).(arity_bind g b H0 c2
-u a1 (H2 c2 H5) t0 a2 (H4 (CHead c2 (Bind b) u) (csuba_head g c c2 H5 (Bind
-b) u)))))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a1:
-A).(\lambda (_: (arity g c u (asucc g a1))).(\lambda (H1: ((\forall (c2:
-C).((csuba g c c2) \to (arity g c2 u (asucc g a1)))))).(\lambda (t0:
-T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind Abst) u) t0
-a2)).(\lambda (H3: ((\forall (c2: C).((csuba g (CHead c (Bind Abst) u) c2)
-\to (arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda (H4: (csuba g c
-c2)).(arity_head g c2 u a1 (H1 c2 H4) t0 a2 (H3 (CHead c2 (Bind Abst) u)
-(csuba_head g c c2 H4 (Bind Abst) u)))))))))))))) (\lambda (c: C).(\lambda
-(u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H1:
+(CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity g d u
+a0)).(\lambda (H2: ((\forall (c2: C).((csuba g d c2) \to (arity g c2 u
+a0))))).(\lambda (c2: C).(\lambda (H3: (csuba g c c2)).(let H4 \def
+(csuba_getl_abbr g c d u i H0 c2 H3) in (let TMP_5 \def (\lambda (d2: C).(let
+TMP_3 \def (Bind Abbr) in (let TMP_4 \def (CHead d2 TMP_3 u) in (getl i c2
+TMP_4)))) in (let TMP_6 \def (\lambda (d2: C).(csuba g d d2)) in (let TMP_7
+\def (TLRef i) in (let TMP_8 \def (arity g c2 TMP_7 a0) in (let TMP_10 \def
+(\lambda (x: C).(\lambda (H5: (getl i c2 (CHead x (Bind Abbr) u))).(\lambda
+(H6: (csuba g d x)).(let TMP_9 \def (H2 x H6) in (arity_abbr g c2 x u i H5 a0
+TMP_9))))) in (ex2_ind C TMP_5 TMP_6 TMP_8 TMP_10 H4))))))))))))))))) in (let
+TMP_53 \def (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
+nat).(\lambda (H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0:
+A).(\lambda (H1: (arity g d u (asucc g a0))).(\lambda (H2: ((\forall (c2:
+C).((csuba g d c2) \to (arity g c2 u (asucc g a0)))))).(\lambda (c2:
+C).(\lambda (H3: (csuba g c c2)).(let H4 \def (csuba_getl_abst g c d u i H0
+c2 H3) in (let TMP_14 \def (\lambda (d2: C).(let TMP_12 \def (Bind Abst) in
+(let TMP_13 \def (CHead d2 TMP_12 u) in (getl i c2 TMP_13)))) in (let TMP_15
+\def (\lambda (d2: C).(csuba g d d2)) in (let TMP_16 \def (ex2 C TMP_14
+TMP_15) in (let TMP_19 \def (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
+A).(let TMP_17 \def (Bind Abbr) in (let TMP_18 \def (CHead d2 TMP_17 u2) in
+(getl i c2 TMP_18)))))) in (let TMP_20 \def (\lambda (d2: C).(\lambda (_:
+T).(\lambda (_: A).(csuba g d d2)))) in (let TMP_22 \def (\lambda (_:
+C).(\lambda (_: T).(\lambda (a1: A).(let TMP_21 \def (asucc g a1) in (arity g
+d u TMP_21))))) in (let TMP_23 \def (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (a1: A).(arity g d2 u2 a1)))) in (let TMP_24 \def (ex4_3 C T A
+TMP_19 TMP_20 TMP_22 TMP_23) in (let TMP_25 \def (TLRef i) in (let TMP_26
+\def (arity g c2 TMP_25 a0) in (let TMP_35 \def (\lambda (H5: (ex2 C (\lambda
+(d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d
+d2)))).(let TMP_29 \def (\lambda (d2: C).(let TMP_27 \def (Bind Abst) in (let
+TMP_28 \def (CHead d2 TMP_27 u) in (getl i c2 TMP_28)))) in (let TMP_30 \def
+(\lambda (d2: C).(csuba g d d2)) in (let TMP_31 \def (TLRef i) in (let TMP_32
+\def (arity g c2 TMP_31 a0) in (let TMP_34 \def (\lambda (x: C).(\lambda (H6:
+(getl i c2 (CHead x (Bind Abst) u))).(\lambda (H7: (csuba g d x)).(let TMP_33
+\def (H2 x H7) in (arity_abst g c2 x u i H6 a0 TMP_33))))) in (ex2_ind C
+TMP_29 TMP_30 TMP_32 TMP_34 H5))))))) in (let TMP_52 \def (\lambda (H5:
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity
+g d u (asucc g a1))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1:
+A).(arity g d2 u2 a1)))))).(let TMP_38 \def (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(let TMP_36 \def (Bind Abbr) in (let TMP_37 \def (CHead d2
+TMP_36 u2) in (getl i c2 TMP_37)))))) in (let TMP_39 \def (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d d2)))) in (let TMP_41 \def
+(\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(let TMP_40 \def (asucc g
+a1) in (arity g d u TMP_40))))) in (let TMP_42 \def (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (a1: A).(arity g d2 u2 a1)))) in (let TMP_43 \def (TLRef i)
+in (let TMP_44 \def (arity g c2 TMP_43 a0) in (let TMP_51 \def (\lambda (x0:
+C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H6: (getl i c2 (CHead x0 (Bind
+Abbr) x1))).(\lambda (_: (csuba g d x0)).(\lambda (H8: (arity g d u (asucc g
+x2))).(\lambda (H9: (arity g x0 x1 x2)).(let TMP_45 \def (TLRef i) in (let
+TMP_46 \def (arity_abbr g c2 x0 x1 i H6 x2 H9) in (let TMP_47 \def (asucc g
+x2) in (let TMP_48 \def (asucc g a0) in (let TMP_49 \def (arity_mono g d u
+TMP_47 H8 TMP_48 H1) in (let TMP_50 \def (asucc_inj g x2 a0 TMP_49) in
+(arity_repl g c2 TMP_45 x2 TMP_46 a0 TMP_50)))))))))))))) in (ex4_3_ind C T A
+TMP_38 TMP_39 TMP_41 TMP_42 TMP_44 TMP_51 H5))))))))) in (or_ind TMP_16
+TMP_24 TMP_26 TMP_35 TMP_52 H4)))))))))))))))))))))))) in (let TMP_60 \def
+(\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda
+(u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2:
((\forall (c2: C).((csuba g c c2) \to (arity g c2 u a1))))).(\lambda (t0:
-T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3:
-((\forall (c2: C).((csuba g c c2) \to (arity g c2 t0 (AHead a1
-a2)))))).(\lambda (c2: C).(\lambda (H4: (csuba g c c2)).(arity_appl g c2 u a1
-(H1 c2 H4) t0 a2 (H3 c2 H4))))))))))))) (\lambda (c: C).(\lambda (u:
+T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind b) u) t0
+a2)).(\lambda (H4: ((\forall (c2: C).((csuba g (CHead c (Bind b) u) c2) \to
+(arity g c2 t0 a2))))).(\lambda (c2: C).(\lambda (H5: (csuba g c c2)).(let
+TMP_54 \def (H2 c2 H5) in (let TMP_55 \def (Bind b) in (let TMP_56 \def
+(CHead c2 TMP_55 u) in (let TMP_57 \def (Bind b) in (let TMP_58 \def
+(csuba_head g c c2 H5 TMP_57 u) in (let TMP_59 \def (H4 TMP_56 TMP_58) in
+(arity_bind g b H0 c2 u a1 TMP_54 t0 a2 TMP_59)))))))))))))))))))) in (let
+TMP_67 \def (\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_:
+(arity g c u (asucc g a1))).(\lambda (H1: ((\forall (c2: C).((csuba g c c2)
+\to (arity g c2 u (asucc g a1)))))).(\lambda (t0: T).(\lambda (a2:
+A).(\lambda (_: (arity g (CHead c (Bind Abst) u) t0 a2)).(\lambda (H3:
+((\forall (c2: C).((csuba g (CHead c (Bind Abst) u) c2) \to (arity g c2 t0
+a2))))).(\lambda (c2: C).(\lambda (H4: (csuba g c c2)).(let TMP_61 \def (H1
+c2 H4) in (let TMP_62 \def (Bind Abst) in (let TMP_63 \def (CHead c2 TMP_62
+u) in (let TMP_64 \def (Bind Abst) in (let TMP_65 \def (csuba_head g c c2 H4
+TMP_64 u) in (let TMP_66 \def (H3 TMP_63 TMP_65) in (arity_head g c2 u a1
+TMP_61 t0 a2 TMP_66)))))))))))))))))) in (let TMP_70 \def (\lambda (c:
+C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda
+(H1: ((\forall (c2: C).((csuba g c c2) \to (arity g c2 u a1))))).(\lambda
+(t0: T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda
+(H3: ((\forall (c2: C).((csuba g c c2) \to (arity g c2 t0 (AHead a1
+a2)))))).(\lambda (c2: C).(\lambda (H4: (csuba g c c2)).(let TMP_68 \def (H1
+c2 H4) in (let TMP_69 \def (H3 c2 H4) in (arity_appl g c2 u a1 TMP_68 t0 a2
+TMP_69)))))))))))))) in (let TMP_73 \def (\lambda (c: C).(\lambda (u:
T).(\lambda (a0: A).(\lambda (_: (arity g c u (asucc g a0))).(\lambda (H1:
((\forall (c2: C).((csuba g c c2) \to (arity g c2 u (asucc g
a0)))))).(\lambda (t0: T).(\lambda (_: (arity g c t0 a0)).(\lambda (H3:
((\forall (c2: C).((csuba g c c2) \to (arity g c2 t0 a0))))).(\lambda (c2:
-C).(\lambda (H4: (csuba g c c2)).(arity_cast g c2 u a0 (H1 c2 H4) t0 (H3 c2
-H4)))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (_:
-(arity g c t0 a1)).(\lambda (H1: ((\forall (c2: C).((csuba g c c2) \to (arity
-g c2 t0 a1))))).(\lambda (a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c2:
-C).(\lambda (H3: (csuba g c c2)).(arity_repl g c2 t0 a1 (H1 c2 H3) a2
-H2)))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 1505
-END *)
+C).(\lambda (H4: (csuba g c c2)).(let TMP_71 \def (H1 c2 H4) in (let TMP_72
+\def (H3 c2 H4) in (arity_cast g c2 u a0 TMP_71 t0 TMP_72))))))))))))) in
+(let TMP_75 \def (\lambda (c: C).(\lambda (t0: T).(\lambda (a1: A).(\lambda
+(_: (arity g c t0 a1)).(\lambda (H1: ((\forall (c2: C).((csuba g c c2) \to
+(arity g c2 t0 a1))))).(\lambda (a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda
+(c2: C).(\lambda (H3: (csuba g c c2)).(let TMP_74 \def (H1 c2 H3) in
+(arity_repl g c2 t0 a1 TMP_74 a2 H2))))))))))) in (arity_ind g TMP_1 TMP_2
+TMP_11 TMP_53 TMP_60 TMP_67 TMP_70 TMP_73 TMP_75 c1 t a H)))))))))))))).
theorem csuba_arity_rev:
\forall (g: G).(\forall (c1: C).(\forall (t: T).(\forall (a: A).((arity g c1
t a))))))))
\def
\lambda (g: G).(\lambda (c1: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
-(arity g c1 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
-A).(\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0
-a0))))))) (\lambda (c: C).(\lambda (n: nat).(\lambda (c2: C).(\lambda (_:
-(csuba g c2 c)).(\lambda (_: (csubv c2 c)).(arity_sort g c2 n)))))) (\lambda
-(c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl
-i c (CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (H1: (arity g d u
-a0)).(\lambda (H2: ((\forall (c2: C).((csuba g c2 d) \to ((csubv c2 d) \to
-(arity g c2 u a0)))))).(\lambda (c2: C).(\lambda (H3: (csuba g c2
-c)).(\lambda (H4: (csubv c2 c)).(let H_x \def (csuba_getl_abbr_rev g c d u i
-H0 c2 H3) in (let H5 \def H_x in (or3_ind (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d2 d))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
-Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
-d)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2
-(asucc g a1))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d
-u a1))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d)))) (arity
-g c2 (TLRef i) a0) (\lambda (H6: (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2
-(Bind Abbr) u))) (\lambda (d2: C).(csuba g d2 d)))).(ex2_ind C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d2 d))
-(arity g c2 (TLRef i) a0) (\lambda (x: C).(\lambda (H7: (getl i c2 (CHead x
-(Bind Abbr) u))).(\lambda (H8: (csuba g x d)).(let H_x0 \def (csubv_getl_conf
-c2 c H4 Abbr x u i H7) in (let H9 \def H_x0 in (ex2_3_ind B C T (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csubv x d2)))) (\lambda (b2: B).(\lambda
-(d2: C).(\lambda (v2: T).(getl i c (CHead d2 (Bind b2) v2))))) (arity g c2
-(TLRef i) a0) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda
-(H10: (csubv x x1)).(\lambda (H11: (getl i c (CHead x1 (Bind x0) x2))).(let
-H12 \def (eq_ind C (CHead d (Bind Abbr) u) (\lambda (c0: C).(getl i c c0)) H0
-(CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abbr) u) i H0 (CHead x1
-(Bind x0) x2) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e in
-C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _)
-\Rightarrow c0])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono
-c (CHead d (Bind Abbr) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H14
-\def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B)
-with [(CSort _) \Rightarrow Abbr | (CHead _ k _) \Rightarrow (match k in K
-return (\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
-Abbr])])) (CHead d (Bind Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead
-d (Bind Abbr) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H15 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind
-Abbr) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abbr) u) i H0
-(CHead x1 (Bind x0) x2) H11)) in (\lambda (H16: (eq B Abbr x0)).(\lambda
-(H17: (eq C d x1)).(let H18 \def (eq_ind_r T x2 (\lambda (t0: T).(getl i c
-(CHead x1 (Bind x0) t0))) H12 u H15) in (let H19 \def (eq_ind_r C x1 (\lambda
-(c0: C).(getl i c (CHead c0 (Bind x0) u))) H18 d H17) in (let H20 \def
-(eq_ind_r C x1 (\lambda (c0: C).(csubv x c0)) H10 d H17) in (let H21 \def
-(eq_ind_r B x0 (\lambda (b: B).(getl i c (CHead d (Bind b) u))) H19 Abbr H16)
-in (arity_abbr g c2 x u i H7 a0 (H2 x H8 H20))))))))) H14)) H13))))))))
-H9)))))) H6)) (\lambda (H6: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d)))) (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2 (asucc g a1))))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d u a1)))))).(ex4_3_ind C T
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2
-(Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d2 d)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1: A).(arity g d2 u2
-(asucc g a1))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d
-u a1)))) (arity g c2 (TLRef i) a0) (\lambda (x0: C).(\lambda (x1: T).(\lambda
-(x2: A).(\lambda (H7: (getl i c2 (CHead x0 (Bind Abst) x1))).(\lambda (_:
-(csuba g x0 d)).(\lambda (H9: (arity g x0 x1 (asucc g x2))).(\lambda (H10:
-(arity g d u x2)).(arity_repl g c2 (TLRef i) x2 (arity_abst g c2 x0 x1 i H7
-x2 H9) a0 (arity_mono g d u x2 H10 a0 H1))))))))) H6)) (\lambda (H6: (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))))).(ex2_2_ind C T (\lambda
-(d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d))) (arity g c2 (TLRef i) a0) (\lambda
-(x0: C).(\lambda (x1: T).(\lambda (H7: (getl i c2 (CHead x0 (Bind Void)
-x1))).(\lambda (_: (csuba g x0 d)).(let H_x0 \def (csubv_getl_conf_void c2 c
-H4 x0 x1 i H7) in (let H9 \def H_x0 in (ex2_2_ind C T (\lambda (d2:
-C).(\lambda (_: T).(csubv x0 d2))) (\lambda (d2: C).(\lambda (v2: T).(getl i
-c (CHead d2 (Bind Void) v2)))) (arity g c2 (TLRef i) a0) (\lambda (x2:
-C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda (H11: (getl i c
-(CHead x2 (Bind Void) x3))).(let H12 \def (eq_ind C (CHead d (Bind Abbr) u)
-(\lambda (c0: C).(getl i c c0)) H0 (CHead x2 (Bind Void) x3) (getl_mono c
-(CHead d (Bind Abbr) u) i H0 (CHead x2 (Bind Void) x3) H11)) in (let H13 \def
-(eq_ind C (CHead d (Bind Abbr) u) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _)
-\Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
-True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat _)
-\Rightarrow False])])) I (CHead x2 (Bind Void) x3) (getl_mono c (CHead d
-(Bind Abbr) u) i H0 (CHead x2 (Bind Void) x3) H11)) in (False_ind (arity g c2
-(TLRef i) a0) H13))))))) H9))))))) H6)) H5)))))))))))))) (\lambda (c:
-C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c
-(CHead d (Bind Abst) u))).(\lambda (a0: A).(\lambda (_: (arity g d u (asucc g
-a0))).(\lambda (H2: ((\forall (c2: C).((csuba g c2 d) \to ((csubv c2 d) \to
-(arity g c2 u (asucc g a0))))))).(\lambda (c2: C).(\lambda (H3: (csuba g c2
-c)).(\lambda (H4: (csubv c2 c)).(let H_x \def (csuba_getl_abst_rev g c d u i
-H0 c2 H3) in (let H5 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d))) (ex2_2 C T
+(arity g c1 t a)).(let TMP_1 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
+(a0: A).(\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0
+a0))))))) in (let TMP_2 \def (\lambda (c: C).(\lambda (n: nat).(\lambda (c2:
+C).(\lambda (_: (csuba g c2 c)).(\lambda (_: (csubv c2 c)).(arity_sort g c2
+n)))))) in (let TMP_142 \def (\lambda (c: C).(\lambda (d: C).(\lambda (u:
+T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr)
+u))).(\lambda (a0: A).(\lambda (H1: (arity g d u a0)).(\lambda (H2: ((\forall
+(c2: C).((csuba g c2 d) \to ((csubv c2 d) \to (arity g c2 u a0)))))).(\lambda
+(c2: C).(\lambda (H3: (csuba g c2 c)).(\lambda (H4: (csubv c2 c)).(let H_x
+\def (csuba_getl_abbr_rev g c d u i H0 c2 H3) in (let H5 \def H_x in (let
+TMP_5 \def (\lambda (d2: C).(let TMP_3 \def (Bind Abbr) in (let TMP_4 \def
+(CHead d2 TMP_3 u) in (getl i c2 TMP_4)))) in (let TMP_6 \def (\lambda (d2:
+C).(csuba g d2 d)) in (let TMP_7 \def (ex2 C TMP_5 TMP_6) in (let TMP_10 \def
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(let TMP_8 \def (Bind Abst)
+in (let TMP_9 \def (CHead d2 TMP_8 u2) in (getl i c2 TMP_9)))))) in (let
+TMP_11 \def (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
+d)))) in (let TMP_13 \def (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1:
+A).(let TMP_12 \def (asucc g a1) in (arity g d2 u2 TMP_12))))) in (let TMP_14
+\def (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(arity g d u a1)))) in
+(let TMP_15 \def (ex4_3 C T A TMP_10 TMP_11 TMP_13 TMP_14) in (let TMP_18
+\def (\lambda (d2: C).(\lambda (u2: T).(let TMP_16 \def (Bind Void) in (let
+TMP_17 \def (CHead d2 TMP_16 u2) in (getl i c2 TMP_17))))) in (let TMP_19
+\def (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))) in (let TMP_20 \def
+(ex2_2 C T TMP_18 TMP_19) in (let TMP_21 \def (TLRef i) in (let TMP_22 \def
+(arity g c2 TMP_21 a0) in (let TMP_90 \def (\lambda (H6: (ex2 C (\lambda (d2:
+C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d2
+d)))).(let TMP_25 \def (\lambda (d2: C).(let TMP_23 \def (Bind Abbr) in (let
+TMP_24 \def (CHead d2 TMP_23 u) in (getl i c2 TMP_24)))) in (let TMP_26 \def
+(\lambda (d2: C).(csuba g d2 d)) in (let TMP_27 \def (TLRef i) in (let TMP_28
+\def (arity g c2 TMP_27 a0) in (let TMP_89 \def (\lambda (x: C).(\lambda (H7:
+(getl i c2 (CHead x (Bind Abbr) u))).(\lambda (H8: (csuba g x d)).(let H_x0
+\def (csubv_getl_conf c2 c H4 Abbr x u i H7) in (let H9 \def H_x0 in (let
+TMP_29 \def (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv x d2))))
+in (let TMP_32 \def (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(let
+TMP_30 \def (Bind b2) in (let TMP_31 \def (CHead d2 TMP_30 v2) in (getl i c
+TMP_31)))))) in (let TMP_33 \def (TLRef i) in (let TMP_34 \def (arity g c2
+TMP_33 a0) in (let TMP_88 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda
+(x2: T).(\lambda (H10: (csubv x x1)).(\lambda (H11: (getl i c (CHead x1 (Bind
+x0) x2))).(let TMP_35 \def (Bind Abbr) in (let TMP_36 \def (CHead d TMP_35 u)
+in (let TMP_37 \def (\lambda (c0: C).(getl i c c0)) in (let TMP_38 \def (Bind
+x0) in (let TMP_39 \def (CHead x1 TMP_38 x2) in (let TMP_40 \def (Bind Abbr)
+in (let TMP_41 \def (CHead d TMP_40 u) in (let TMP_42 \def (Bind x0) in (let
+TMP_43 \def (CHead x1 TMP_42 x2) in (let TMP_44 \def (getl_mono c TMP_41 i H0
+TMP_43 H11) in (let H12 \def (eq_ind C TMP_36 TMP_37 H0 TMP_39 TMP_44) in
+(let TMP_45 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow d |
+(CHead c0 _ _) \Rightarrow c0])) in (let TMP_46 \def (Bind Abbr) in (let
+TMP_47 \def (CHead d TMP_46 u) in (let TMP_48 \def (Bind x0) in (let TMP_49
+\def (CHead x1 TMP_48 x2) in (let TMP_50 \def (Bind Abbr) in (let TMP_51 \def
+(CHead d TMP_50 u) in (let TMP_52 \def (Bind x0) in (let TMP_53 \def (CHead
+x1 TMP_52 x2) in (let TMP_54 \def (getl_mono c TMP_51 i H0 TMP_53 H11) in
+(let H13 \def (f_equal C C TMP_45 TMP_47 TMP_49 TMP_54) in (let TMP_55 \def
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow Abbr | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
+Abbr])])) in (let TMP_56 \def (Bind Abbr) in (let TMP_57 \def (CHead d TMP_56
+u) in (let TMP_58 \def (Bind x0) in (let TMP_59 \def (CHead x1 TMP_58 x2) in
+(let TMP_60 \def (Bind Abbr) in (let TMP_61 \def (CHead d TMP_60 u) in (let
+TMP_62 \def (Bind x0) in (let TMP_63 \def (CHead x1 TMP_62 x2) in (let TMP_64
+\def (getl_mono c TMP_61 i H0 TMP_63 H11) in (let H14 \def (f_equal C B
+TMP_55 TMP_57 TMP_59 TMP_64) in (let TMP_65 \def (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let
+TMP_66 \def (Bind Abbr) in (let TMP_67 \def (CHead d TMP_66 u) in (let TMP_68
+\def (Bind x0) in (let TMP_69 \def (CHead x1 TMP_68 x2) in (let TMP_70 \def
+(Bind Abbr) in (let TMP_71 \def (CHead d TMP_70 u) in (let TMP_72 \def (Bind
+x0) in (let TMP_73 \def (CHead x1 TMP_72 x2) in (let TMP_74 \def (getl_mono c
+TMP_71 i H0 TMP_73 H11) in (let H15 \def (f_equal C T TMP_65 TMP_67 TMP_69
+TMP_74) in (let TMP_86 \def (\lambda (H16: (eq B Abbr x0)).(\lambda (H17: (eq
+C d x1)).(let TMP_77 \def (\lambda (t0: T).(let TMP_75 \def (Bind x0) in (let
+TMP_76 \def (CHead x1 TMP_75 t0) in (getl i c TMP_76)))) in (let H18 \def
+(eq_ind_r T x2 TMP_77 H12 u H15) in (let TMP_80 \def (\lambda (c0: C).(let
+TMP_78 \def (Bind x0) in (let TMP_79 \def (CHead c0 TMP_78 u) in (getl i c
+TMP_79)))) in (let H19 \def (eq_ind_r C x1 TMP_80 H18 d H17) in (let TMP_81
+\def (\lambda (c0: C).(csubv x c0)) in (let H20 \def (eq_ind_r C x1 TMP_81
+H10 d H17) in (let TMP_84 \def (\lambda (b: B).(let TMP_82 \def (Bind b) in
+(let TMP_83 \def (CHead d TMP_82 u) in (getl i c TMP_83)))) in (let H21 \def
+(eq_ind_r B x0 TMP_84 H19 Abbr H16) in (let TMP_85 \def (H2 x H8 H20) in
+(arity_abbr g c2 x u i H7 a0 TMP_85)))))))))))) in (let TMP_87 \def (TMP_86
+H14) in (TMP_87 H13)))))))))))))))))))))))))))))))))))))))))))))))))))) in
+(ex2_3_ind B C T TMP_29 TMP_32 TMP_34 TMP_88 H9))))))))))) in (ex2_ind C
+TMP_25 TMP_26 TMP_28 TMP_89 H6))))))) in (let TMP_104 \def (\lambda (H6:
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d2 d)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a1:
+A).(arity g d2 u2 (asucc g a1))))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a1: A).(arity g d u a1)))))).(let TMP_93 \def (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(let TMP_91 \def (Bind Abst) in (let TMP_92 \def (CHead d2
+TMP_91 u2) in (getl i c2 TMP_92)))))) in (let TMP_94 \def (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d)))) in (let TMP_96 \def
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a1: A).(let TMP_95 \def (asucc g
+a1) in (arity g d2 u2 TMP_95))))) in (let TMP_97 \def (\lambda (_:
+C).(\lambda (_: T).(\lambda (a1: A).(arity g d u a1)))) in (let TMP_98 \def
+(TLRef i) in (let TMP_99 \def (arity g c2 TMP_98 a0) in (let TMP_103 \def
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H7: (getl i c2
+(CHead x0 (Bind Abst) x1))).(\lambda (_: (csuba g x0 d)).(\lambda (H9: (arity
+g x0 x1 (asucc g x2))).(\lambda (H10: (arity g d u x2)).(let TMP_100 \def
+(TLRef i) in (let TMP_101 \def (arity_abst g c2 x0 x1 i H7 x2 H9) in (let
+TMP_102 \def (arity_mono g d u x2 H10 a0 H1) in (arity_repl g c2 TMP_100 x2
+TMP_101 a0 TMP_102))))))))))) in (ex4_3_ind C T A TMP_93 TMP_94 TMP_96 TMP_97
+TMP_99 TMP_103 H6))))))))) in (let TMP_141 \def (\lambda (H6: (ex2_2 C T
(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d)))) (arity g c2 (TLRef i) a0)
-(\lambda (H6: (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
-(\lambda (d2: C).(csuba g d2 d)))).(ex2_ind C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d)) (arity g c2
-(TLRef i) a0) (\lambda (x: C).(\lambda (H7: (getl i c2 (CHead x (Bind Abst)
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))))).(let TMP_107 \def
+(\lambda (d2: C).(\lambda (u2: T).(let TMP_105 \def (Bind Void) in (let
+TMP_106 \def (CHead d2 TMP_105 u2) in (getl i c2 TMP_106))))) in (let TMP_108
+\def (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))) in (let TMP_109 \def
+(TLRef i) in (let TMP_110 \def (arity g c2 TMP_109 a0) in (let TMP_140 \def
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (H7: (getl i c2 (CHead x0 (Bind
+Void) x1))).(\lambda (_: (csuba g x0 d)).(let H_x0 \def (csubv_getl_conf_void
+c2 c H4 x0 x1 i H7) in (let H9 \def H_x0 in (let TMP_111 \def (\lambda (d2:
+C).(\lambda (_: T).(csubv x0 d2))) in (let TMP_114 \def (\lambda (d2:
+C).(\lambda (v2: T).(let TMP_112 \def (Bind Void) in (let TMP_113 \def (CHead
+d2 TMP_112 v2) in (getl i c TMP_113))))) in (let TMP_115 \def (TLRef i) in
+(let TMP_116 \def (arity g c2 TMP_115 a0) in (let TMP_139 \def (\lambda (x2:
+C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda (H11: (getl i c
+(CHead x2 (Bind Void) x3))).(let TMP_117 \def (Bind Abbr) in (let TMP_118
+\def (CHead d TMP_117 u) in (let TMP_119 \def (\lambda (c0: C).(getl i c c0))
+in (let TMP_120 \def (Bind Void) in (let TMP_121 \def (CHead x2 TMP_120 x3)
+in (let TMP_122 \def (Bind Abbr) in (let TMP_123 \def (CHead d TMP_122 u) in
+(let TMP_124 \def (Bind Void) in (let TMP_125 \def (CHead x2 TMP_124 x3) in
+(let TMP_126 \def (getl_mono c TMP_123 i H0 TMP_125 H11) in (let H12 \def
+(eq_ind C TMP_118 TMP_119 H0 TMP_121 TMP_126) in (let TMP_127 \def (Bind
+Abbr) in (let TMP_128 \def (CHead d TMP_127 u) in (let TMP_129 \def (\lambda
+(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) in (let TMP_130 \def (Bind Void) in (let TMP_131
+\def (CHead x2 TMP_130 x3) in (let TMP_132 \def (Bind Abbr) in (let TMP_133
+\def (CHead d TMP_132 u) in (let TMP_134 \def (Bind Void) in (let TMP_135
+\def (CHead x2 TMP_134 x3) in (let TMP_136 \def (getl_mono c TMP_133 i H0
+TMP_135 H11) in (let H13 \def (eq_ind C TMP_128 TMP_129 I TMP_131 TMP_136) in
+(let TMP_137 \def (TLRef i) in (let TMP_138 \def (arity g c2 TMP_137 a0) in
+(False_ind TMP_138 H13))))))))))))))))))))))))))))) in (ex2_2_ind C T TMP_111
+TMP_114 TMP_116 TMP_139 H9)))))))))))) in (ex2_2_ind C T TMP_107 TMP_108
+TMP_110 TMP_140 H6))))))) in (or3_ind TMP_7 TMP_15 TMP_20 TMP_22 TMP_90
+TMP_104 TMP_141 H5)))))))))))))))))))))))))))))) in (let TMP_260 \def
+(\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda
+(H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0: A).(\lambda (_: (arity
+g d u (asucc g a0))).(\lambda (H2: ((\forall (c2: C).((csuba g c2 d) \to
+((csubv c2 d) \to (arity g c2 u (asucc g a0))))))).(\lambda (c2: C).(\lambda
+(H3: (csuba g c2 c)).(\lambda (H4: (csubv c2 c)).(let H_x \def
+(csuba_getl_abst_rev g c d u i H0 c2 H3) in (let H5 \def H_x in (let TMP_145
+\def (\lambda (d2: C).(let TMP_143 \def (Bind Abst) in (let TMP_144 \def
+(CHead d2 TMP_143 u) in (getl i c2 TMP_144)))) in (let TMP_146 \def (\lambda
+(d2: C).(csuba g d2 d)) in (let TMP_147 \def (ex2 C TMP_145 TMP_146) in (let
+TMP_150 \def (\lambda (d2: C).(\lambda (u2: T).(let TMP_148 \def (Bind Void)
+in (let TMP_149 \def (CHead d2 TMP_148 u2) in (getl i c2 TMP_149))))) in (let
+TMP_151 \def (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))) in (let
+TMP_152 \def (ex2_2 C T TMP_150 TMP_151) in (let TMP_153 \def (TLRef i) in
+(let TMP_154 \def (arity g c2 TMP_153 a0) in (let TMP_222 \def (\lambda (H6:
+(ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d)))).(let TMP_157 \def (\lambda (d2: C).(let TMP_155 \def
+(Bind Abst) in (let TMP_156 \def (CHead d2 TMP_155 u) in (getl i c2
+TMP_156)))) in (let TMP_158 \def (\lambda (d2: C).(csuba g d2 d)) in (let
+TMP_159 \def (TLRef i) in (let TMP_160 \def (arity g c2 TMP_159 a0) in (let
+TMP_221 \def (\lambda (x: C).(\lambda (H7: (getl i c2 (CHead x (Bind Abst)
u))).(\lambda (H8: (csuba g x d)).(let H_x0 \def (csubv_getl_conf c2 c H4
-Abst x u i H7) in (let H9 \def H_x0 in (ex2_3_ind B C T (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csubv x d2)))) (\lambda (b2: B).(\lambda
-(d2: C).(\lambda (v2: T).(getl i c (CHead d2 (Bind b2) v2))))) (arity g c2
-(TLRef i) a0) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda
+Abst x u i H7) in (let H9 \def H_x0 in (let TMP_161 \def (\lambda (_:
+B).(\lambda (d2: C).(\lambda (_: T).(csubv x d2)))) in (let TMP_164 \def
+(\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(let TMP_162 \def (Bind
+b2) in (let TMP_163 \def (CHead d2 TMP_162 v2) in (getl i c TMP_163)))))) in
+(let TMP_165 \def (TLRef i) in (let TMP_166 \def (arity g c2 TMP_165 a0) in
+(let TMP_220 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda
(H10: (csubv x x1)).(\lambda (H11: (getl i c (CHead x1 (Bind x0) x2))).(let
-H12 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0
-(CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abst) u) i H0 (CHead x1
-(Bind x0) x2) H11)) in (let H13 \def (f_equal C C (\lambda (e: C).(match e in
-C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d | (CHead c0 _ _)
-\Rightarrow c0])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) (getl_mono
-c (CHead d (Bind Abst) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H14
-\def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B)
-with [(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k in K
-return (\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
-Abst])])) (CHead d (Bind Abst) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead
-d (Bind Abst) u) i H0 (CHead x1 (Bind x0) x2) H11)) in ((let H15 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d (Bind
-Abst) u) (CHead x1 (Bind x0) x2) (getl_mono c (CHead d (Bind Abst) u) i H0
-(CHead x1 (Bind x0) x2) H11)) in (\lambda (H16: (eq B Abst x0)).(\lambda
-(H17: (eq C d x1)).(let H18 \def (eq_ind_r T x2 (\lambda (t0: T).(getl i c
-(CHead x1 (Bind x0) t0))) H12 u H15) in (let H19 \def (eq_ind_r C x1 (\lambda
-(c0: C).(getl i c (CHead c0 (Bind x0) u))) H18 d H17) in (let H20 \def
-(eq_ind_r C x1 (\lambda (c0: C).(csubv x c0)) H10 d H17) in (let H21 \def
-(eq_ind_r B x0 (\lambda (b: B).(getl i c (CHead d (Bind b) u))) H19 Abst H16)
-in (arity_abst g c2 x u i H7 a0 (H2 x H8 H20))))))))) H14)) H13))))))))
-H9)))))) H6)) (\lambda (H6: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(getl
-i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
-d2 d))) (arity g c2 (TLRef i) a0) (\lambda (x0: C).(\lambda (x1: T).(\lambda
-(H7: (getl i c2 (CHead x0 (Bind Void) x1))).(\lambda (_: (csuba g x0 d)).(let
-H_x0 \def (csubv_getl_conf_void c2 c H4 x0 x1 i H7) in (let H9 \def H_x0 in
-(ex2_2_ind C T (\lambda (d2: C).(\lambda (_: T).(csubv x0 d2))) (\lambda (d2:
-C).(\lambda (v2: T).(getl i c (CHead d2 (Bind Void) v2)))) (arity g c2 (TLRef
-i) a0) (\lambda (x2: C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda
-(H11: (getl i c (CHead x2 (Bind Void) x3))).(let H12 \def (eq_ind C (CHead d
-(Bind Abst) u) (\lambda (c0: C).(getl i c c0)) H0 (CHead x2 (Bind Void) x3)
-(getl_mono c (CHead d (Bind Abst) u) i H0 (CHead x2 (Bind Void) x3) H11)) in
-(let H13 \def (eq_ind C (CHead d (Bind Abst) u) (\lambda (ee: C).(match ee in
-C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k
-_) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
-\Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
-False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat _)
-\Rightarrow False])])) I (CHead x2 (Bind Void) x3) (getl_mono c (CHead d
-(Bind Abst) u) i H0 (CHead x2 (Bind Void) x3) H11)) in (False_ind (arity g c2
-(TLRef i) a0) H13))))))) H9))))))) H6)) H5)))))))))))))) (\lambda (b:
-B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda (u:
-T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2: ((\forall
-(c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 u a1)))))).(\lambda
-(t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c (Bind b) u) t0
-a2)).(\lambda (H4: ((\forall (c2: C).((csuba g c2 (CHead c (Bind b) u)) \to
-((csubv c2 (CHead c (Bind b) u)) \to (arity g c2 t0 a2)))))).(\lambda (c2:
-C).(\lambda (H5: (csuba g c2 c)).(\lambda (H6: (csubv c2 c)).(arity_bind g b
-H0 c2 u a1 (H2 c2 H5 H6) t0 a2 (H4 (CHead c2 (Bind b) u) (csuba_head g c2 c
-H5 (Bind b) u) (csubv_bind_same c2 c H6 b u u))))))))))))))))) (\lambda (c:
-C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u (asucc g
-a1))).(\lambda (H1: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to
-(arity g c2 u (asucc g a1))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda
-(_: (arity g (CHead c (Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (c2:
-C).((csuba g c2 (CHead c (Bind Abst) u)) \to ((csubv c2 (CHead c (Bind Abst)
-u)) \to (arity g c2 t0 a2)))))).(\lambda (c2: C).(\lambda (H4: (csuba g c2
-c)).(\lambda (H5: (csubv c2 c)).(arity_head g c2 u a1 (H1 c2 H4 H5) t0 a2 (H3
-(CHead c2 (Bind Abst) u) (csuba_head g c2 c H4 (Bind Abst) u)
-(csubv_bind_same c2 c H5 Abst u u))))))))))))))) (\lambda (c: C).(\lambda (u:
+TMP_167 \def (Bind Abst) in (let TMP_168 \def (CHead d TMP_167 u) in (let
+TMP_169 \def (\lambda (c0: C).(getl i c c0)) in (let TMP_170 \def (Bind x0)
+in (let TMP_171 \def (CHead x1 TMP_170 x2) in (let TMP_172 \def (Bind Abst)
+in (let TMP_173 \def (CHead d TMP_172 u) in (let TMP_174 \def (Bind x0) in
+(let TMP_175 \def (CHead x1 TMP_174 x2) in (let TMP_176 \def (getl_mono c
+TMP_173 i H0 TMP_175 H11) in (let H12 \def (eq_ind C TMP_168 TMP_169 H0
+TMP_171 TMP_176) in (let TMP_177 \def (\lambda (e: C).(match e with [(CSort
+_) \Rightarrow d | (CHead c0 _ _) \Rightarrow c0])) in (let TMP_178 \def
+(Bind Abst) in (let TMP_179 \def (CHead d TMP_178 u) in (let TMP_180 \def
+(Bind x0) in (let TMP_181 \def (CHead x1 TMP_180 x2) in (let TMP_182 \def
+(Bind Abst) in (let TMP_183 \def (CHead d TMP_182 u) in (let TMP_184 \def
+(Bind x0) in (let TMP_185 \def (CHead x1 TMP_184 x2) in (let TMP_186 \def
+(getl_mono c TMP_183 i H0 TMP_185 H11) in (let H13 \def (f_equal C C TMP_177
+TMP_179 TMP_181 TMP_186) in (let TMP_187 \def (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow (match k with [(Bind
+b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) in (let TMP_188 \def (Bind
+Abst) in (let TMP_189 \def (CHead d TMP_188 u) in (let TMP_190 \def (Bind x0)
+in (let TMP_191 \def (CHead x1 TMP_190 x2) in (let TMP_192 \def (Bind Abst)
+in (let TMP_193 \def (CHead d TMP_192 u) in (let TMP_194 \def (Bind x0) in
+(let TMP_195 \def (CHead x1 TMP_194 x2) in (let TMP_196 \def (getl_mono c
+TMP_193 i H0 TMP_195 H11) in (let H14 \def (f_equal C B TMP_187 TMP_189
+TMP_191 TMP_196) in (let TMP_197 \def (\lambda (e: C).(match e with [(CSort
+_) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_198 \def
+(Bind Abst) in (let TMP_199 \def (CHead d TMP_198 u) in (let TMP_200 \def
+(Bind x0) in (let TMP_201 \def (CHead x1 TMP_200 x2) in (let TMP_202 \def
+(Bind Abst) in (let TMP_203 \def (CHead d TMP_202 u) in (let TMP_204 \def
+(Bind x0) in (let TMP_205 \def (CHead x1 TMP_204 x2) in (let TMP_206 \def
+(getl_mono c TMP_203 i H0 TMP_205 H11) in (let H15 \def (f_equal C T TMP_197
+TMP_199 TMP_201 TMP_206) in (let TMP_218 \def (\lambda (H16: (eq B Abst
+x0)).(\lambda (H17: (eq C d x1)).(let TMP_209 \def (\lambda (t0: T).(let
+TMP_207 \def (Bind x0) in (let TMP_208 \def (CHead x1 TMP_207 t0) in (getl i
+c TMP_208)))) in (let H18 \def (eq_ind_r T x2 TMP_209 H12 u H15) in (let
+TMP_212 \def (\lambda (c0: C).(let TMP_210 \def (Bind x0) in (let TMP_211
+\def (CHead c0 TMP_210 u) in (getl i c TMP_211)))) in (let H19 \def (eq_ind_r
+C x1 TMP_212 H18 d H17) in (let TMP_213 \def (\lambda (c0: C).(csubv x c0))
+in (let H20 \def (eq_ind_r C x1 TMP_213 H10 d H17) in (let TMP_216 \def
+(\lambda (b: B).(let TMP_214 \def (Bind b) in (let TMP_215 \def (CHead d
+TMP_214 u) in (getl i c TMP_215)))) in (let H21 \def (eq_ind_r B x0 TMP_216
+H19 Abst H16) in (let TMP_217 \def (H2 x H8 H20) in (arity_abst g c2 x u i H7
+a0 TMP_217)))))))))))) in (let TMP_219 \def (TMP_218 H14) in (TMP_219
+H13)))))))))))))))))))))))))))))))))))))))))))))))))))) in (ex2_3_ind B C T
+TMP_161 TMP_164 TMP_166 TMP_220 H9))))))))))) in (ex2_ind C TMP_157 TMP_158
+TMP_160 TMP_221 H6))))))) in (let TMP_259 \def (\lambda (H6: (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))))).(let TMP_225 \def
+(\lambda (d2: C).(\lambda (u2: T).(let TMP_223 \def (Bind Void) in (let
+TMP_224 \def (CHead d2 TMP_223 u2) in (getl i c2 TMP_224))))) in (let TMP_226
+\def (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d))) in (let TMP_227 \def
+(TLRef i) in (let TMP_228 \def (arity g c2 TMP_227 a0) in (let TMP_258 \def
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (H7: (getl i c2 (CHead x0 (Bind
+Void) x1))).(\lambda (_: (csuba g x0 d)).(let H_x0 \def (csubv_getl_conf_void
+c2 c H4 x0 x1 i H7) in (let H9 \def H_x0 in (let TMP_229 \def (\lambda (d2:
+C).(\lambda (_: T).(csubv x0 d2))) in (let TMP_232 \def (\lambda (d2:
+C).(\lambda (v2: T).(let TMP_230 \def (Bind Void) in (let TMP_231 \def (CHead
+d2 TMP_230 v2) in (getl i c TMP_231))))) in (let TMP_233 \def (TLRef i) in
+(let TMP_234 \def (arity g c2 TMP_233 a0) in (let TMP_257 \def (\lambda (x2:
+C).(\lambda (x3: T).(\lambda (_: (csubv x0 x2)).(\lambda (H11: (getl i c
+(CHead x2 (Bind Void) x3))).(let TMP_235 \def (Bind Abst) in (let TMP_236
+\def (CHead d TMP_235 u) in (let TMP_237 \def (\lambda (c0: C).(getl i c c0))
+in (let TMP_238 \def (Bind Void) in (let TMP_239 \def (CHead x2 TMP_238 x3)
+in (let TMP_240 \def (Bind Abst) in (let TMP_241 \def (CHead d TMP_240 u) in
+(let TMP_242 \def (Bind Void) in (let TMP_243 \def (CHead x2 TMP_242 x3) in
+(let TMP_244 \def (getl_mono c TMP_241 i H0 TMP_243 H11) in (let H12 \def
+(eq_ind C TMP_236 TMP_237 H0 TMP_239 TMP_244) in (let TMP_245 \def (Bind
+Abst) in (let TMP_246 \def (CHead d TMP_245 u) in (let TMP_247 \def (\lambda
+(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) in (let TMP_248 \def (Bind Void) in (let TMP_249
+\def (CHead x2 TMP_248 x3) in (let TMP_250 \def (Bind Abst) in (let TMP_251
+\def (CHead d TMP_250 u) in (let TMP_252 \def (Bind Void) in (let TMP_253
+\def (CHead x2 TMP_252 x3) in (let TMP_254 \def (getl_mono c TMP_251 i H0
+TMP_253 H11) in (let H13 \def (eq_ind C TMP_246 TMP_247 I TMP_249 TMP_254) in
+(let TMP_255 \def (TLRef i) in (let TMP_256 \def (arity g c2 TMP_255 a0) in
+(False_ind TMP_256 H13))))))))))))))))))))))))))))) in (ex2_2_ind C T TMP_229
+TMP_232 TMP_234 TMP_257 H9)))))))))))) in (ex2_2_ind C T TMP_225 TMP_226
+TMP_228 TMP_258 H6))))))) in (or_ind TMP_147 TMP_152 TMP_154 TMP_222 TMP_259
+H5)))))))))))))))))))))))) in (let TMP_268 \def (\lambda (b: B).(\lambda (H0:
+(not (eq B b Abst))).(\lambda (c: C).(\lambda (u: T).(\lambda (a1:
+A).(\lambda (_: (arity g c u a1)).(\lambda (H2: ((\forall (c2: C).((csuba g
+c2 c) \to ((csubv c2 c) \to (arity g c2 u a1)))))).(\lambda (t0: T).(\lambda
+(a2: A).(\lambda (_: (arity g (CHead c (Bind b) u) t0 a2)).(\lambda (H4:
+((\forall (c2: C).((csuba g c2 (CHead c (Bind b) u)) \to ((csubv c2 (CHead c
+(Bind b) u)) \to (arity g c2 t0 a2)))))).(\lambda (c2: C).(\lambda (H5:
+(csuba g c2 c)).(\lambda (H6: (csubv c2 c)).(let TMP_261 \def (H2 c2 H5 H6)
+in (let TMP_262 \def (Bind b) in (let TMP_263 \def (CHead c2 TMP_262 u) in
+(let TMP_264 \def (Bind b) in (let TMP_265 \def (csuba_head g c2 c H5 TMP_264
+u) in (let TMP_266 \def (csubv_bind_same c2 c H6 b u u) in (let TMP_267 \def
+(H4 TMP_263 TMP_265 TMP_266) in (arity_bind g b H0 c2 u a1 TMP_261 t0 a2
+TMP_267)))))))))))))))))))))) in (let TMP_276 \def (\lambda (c: C).(\lambda
+(u: T).(\lambda (a1: A).(\lambda (_: (arity g c u (asucc g a1))).(\lambda
+(H1: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 u
+(asucc g a1))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g
+(CHead c (Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (c2: C).((csuba g c2
+(CHead c (Bind Abst) u)) \to ((csubv c2 (CHead c (Bind Abst) u)) \to (arity g
+c2 t0 a2)))))).(\lambda (c2: C).(\lambda (H4: (csuba g c2 c)).(\lambda (H5:
+(csubv c2 c)).(let TMP_269 \def (H1 c2 H4 H5) in (let TMP_270 \def (Bind
+Abst) in (let TMP_271 \def (CHead c2 TMP_270 u) in (let TMP_272 \def (Bind
+Abst) in (let TMP_273 \def (csuba_head g c2 c H4 TMP_272 u) in (let TMP_274
+\def (csubv_bind_same c2 c H5 Abst u u) in (let TMP_275 \def (H3 TMP_271
+TMP_273 TMP_274) in (arity_head g c2 u a1 TMP_269 t0 a2
+TMP_275)))))))))))))))))))) in (let TMP_279 \def (\lambda (c: C).(\lambda (u:
T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H1: ((\forall
(c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 u a1)))))).(\lambda
(t0: T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda
(H3: ((\forall (c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0
(AHead a1 a2))))))).(\lambda (c2: C).(\lambda (H4: (csuba g c2 c)).(\lambda
-(H5: (csubv c2 c)).(arity_appl g c2 u a1 (H1 c2 H4 H5) t0 a2 (H3 c2 H4
-H5)))))))))))))) (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda
+(H5: (csubv c2 c)).(let TMP_277 \def (H1 c2 H4 H5) in (let TMP_278 \def (H3
+c2 H4 H5) in (arity_appl g c2 u a1 TMP_277 t0 a2 TMP_278))))))))))))))) in
+(let TMP_282 \def (\lambda (c: C).(\lambda (u: T).(\lambda (a0: A).(\lambda
(_: (arity g c u (asucc g a0))).(\lambda (H1: ((\forall (c2: C).((csuba g c2
c) \to ((csubv c2 c) \to (arity g c2 u (asucc g a0))))))).(\lambda (t0:
T).(\lambda (_: (arity g c t0 a0)).(\lambda (H3: ((\forall (c2: C).((csuba g
c2 c) \to ((csubv c2 c) \to (arity g c2 t0 a0)))))).(\lambda (c2: C).(\lambda
-(H4: (csuba g c2 c)).(\lambda (H5: (csubv c2 c)).(arity_cast g c2 u a0 (H1 c2
-H4 H5) t0 (H3 c2 H4 H5))))))))))))) (\lambda (c: C).(\lambda (t0: T).(\lambda
-(a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall (c2:
-C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0 a1)))))).(\lambda
-(a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c2: C).(\lambda (H3: (csuba g
-c2 c)).(\lambda (H4: (csubv c2 c)).(arity_repl g c2 t0 a1 (H1 c2 H3 H4) a2
-H2))))))))))) c1 t a H))))).
-(* COMMENTS
-Initial nodes: 3597
-END *)
+(H4: (csuba g c2 c)).(\lambda (H5: (csubv c2 c)).(let TMP_280 \def (H1 c2 H4
+H5) in (let TMP_281 \def (H3 c2 H4 H5) in (arity_cast g c2 u a0 TMP_280 t0
+TMP_281)))))))))))))) in (let TMP_284 \def (\lambda (c: C).(\lambda (t0:
+T).(\lambda (a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda (H1: ((\forall
+(c2: C).((csuba g c2 c) \to ((csubv c2 c) \to (arity g c2 t0
+a1)))))).(\lambda (a2: A).(\lambda (H2: (leq g a1 a2)).(\lambda (c2:
+C).(\lambda (H3: (csuba g c2 c)).(\lambda (H4: (csubv c2 c)).(let TMP_283
+\def (H1 c2 H3 H4) in (arity_repl g c2 t0 a1 TMP_283 a2 H2)))))))))))) in
+(arity_ind g TMP_1 TMP_2 TMP_142 TMP_260 TMP_268 TMP_276 TMP_279 TMP_282
+TMP_284 c1 t a H)))))))))))))).
theorem arity_appls_appl:
\forall (g: G).(\forall (c: C).(\forall (v: T).(\forall (a1: A).((arity g c
\def
\lambda (g: G).(\lambda (c: C).(\lambda (v: T).(\lambda (a1: A).(\lambda (H:
(arity g c v a1)).(\lambda (u: T).(\lambda (H0: (arity g c u (asucc g
-a1))).(\lambda (t: T).(\lambda (vs: TList).(TList_ind (\lambda (t0:
+a1))).(\lambda (t: T).(\lambda (vs: TList).(let TMP_7 \def (\lambda (t0:
TList).(\forall (a2: A).((arity g c (THeads (Flat Appl) t0 (THead (Bind Abbr)
-v t)) a2) \to (arity g c (THeads (Flat Appl) t0 (THead (Flat Appl) v (THead
-(Bind Abst) u t))) a2)))) (\lambda (a2: A).(\lambda (H1: (arity g c (THead
-(Bind Abbr) v t) a2)).(let H_x \def (arity_gen_bind Abbr (\lambda (H2: (eq B
-Abbr Abst)).(not_abbr_abst H2)) g c v t a2 H1) in (let H2 \def H_x in
-(ex2_ind A (\lambda (a3: A).(arity g c v a3)) (\lambda (_: A).(arity g (CHead
-c (Bind Abbr) v) t a2)) (arity g c (THead (Flat Appl) v (THead (Bind Abst) u
-t)) a2) (\lambda (x: A).(\lambda (_: (arity g c v x)).(\lambda (H4: (arity g
-(CHead c (Bind Abbr) v) t a2)).(arity_appl g c v a1 H (THead (Bind Abst) u t)
-a2 (arity_head g c u a1 H0 t a2 (csuba_arity_rev g (CHead c (Bind Abbr) v) t
-a2 H4 (CHead c (Bind Abst) u) (csuba_abst g c c (csuba_refl g c) u a1 H0 v H)
-(csubv_bind c c (csubv_refl c) Abst (sym_not_eq B Void Abst not_void_abst)
-Abbr u v))))))) H2))))) (\lambda (t0: T).(\lambda (t1: TList).(\lambda (H1:
-((\forall (a2: A).((arity g c (THeads (Flat Appl) t1 (THead (Bind Abbr) v t))
-a2) \to (arity g c (THeads (Flat Appl) t1 (THead (Flat Appl) v (THead (Bind
-Abst) u t))) a2))))).(\lambda (a2: A).(\lambda (H2: (arity g c (THead (Flat
-Appl) t0 (THeads (Flat Appl) t1 (THead (Bind Abbr) v t))) a2)).(let H3 \def
-(arity_gen_appl g c t0 (THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) a2 H2)
-in (ex2_ind A (\lambda (a3: A).(arity g c t0 a3)) (\lambda (a3: A).(arity g c
-(THeads (Flat Appl) t1 (THead (Bind Abbr) v t)) (AHead a3 a2))) (arity g c
-(THead (Flat Appl) t0 (THeads (Flat Appl) t1 (THead (Flat Appl) v (THead
-(Bind Abst) u t)))) a2) (\lambda (x: A).(\lambda (H4: (arity g c t0
-x)).(\lambda (H5: (arity g c (THeads (Flat Appl) t1 (THead (Bind Abbr) v t))
-(AHead x a2))).(arity_appl g c t0 x H4 (THeads (Flat Appl) t1 (THead (Flat
-Appl) v (THead (Bind Abst) u t))) a2 (H1 (AHead x a2) H5))))) H3)))))))
-vs))))))))).
-(* COMMENTS
-Initial nodes: 687
-END *)
+v t)) a2) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def (Flat Appl) in
+(let TMP_3 \def (Bind Abst) in (let TMP_4 \def (THead TMP_3 u t) in (let
+TMP_5 \def (THead TMP_2 v TMP_4) in (let TMP_6 \def (THeads TMP_1 t0 TMP_5)
+in (arity g c TMP_6 a2)))))))))) in (let TMP_30 \def (\lambda (a2:
+A).(\lambda (H1: (arity g c (THead (Bind Abbr) v t) a2)).(let H_x \def
+(arity_gen_bind Abbr not_abbr_abst g c v t a2 H1) in (let H2 \def H_x in (let
+TMP_8 \def (\lambda (a3: A).(arity g c v a3)) in (let TMP_11 \def (\lambda
+(_: A).(let TMP_9 \def (Bind Abbr) in (let TMP_10 \def (CHead c TMP_9 v) in
+(arity g TMP_10 t a2)))) in (let TMP_12 \def (Flat Appl) in (let TMP_13 \def
+(Bind Abst) in (let TMP_14 \def (THead TMP_13 u t) in (let TMP_15 \def (THead
+TMP_12 v TMP_14) in (let TMP_16 \def (arity g c TMP_15 a2) in (let TMP_29
+\def (\lambda (x: A).(\lambda (_: (arity g c v x)).(\lambda (H4: (arity g
+(CHead c (Bind Abbr) v) t a2)).(let TMP_17 \def (Bind Abst) in (let TMP_18
+\def (THead TMP_17 u t) in (let TMP_19 \def (Bind Abbr) in (let TMP_20 \def
+(CHead c TMP_19 v) in (let TMP_21 \def (Bind Abst) in (let TMP_22 \def (CHead
+c TMP_21 u) in (let TMP_23 \def (csuba_refl g c) in (let TMP_24 \def
+(csuba_abst g c c TMP_23 u a1 H0 v H) in (let TMP_25 \def (csubv_refl c) in
+(let TMP_26 \def (csubv_bind c c TMP_25 Abst not_abst_void Abbr u v) in (let
+TMP_27 \def (csuba_arity_rev g TMP_20 t a2 H4 TMP_22 TMP_24 TMP_26) in (let
+TMP_28 \def (arity_head g c u a1 H0 t a2 TMP_27) in (arity_appl g c v a1 H
+TMP_18 a2 TMP_28)))))))))))))))) in (ex2_ind A TMP_8 TMP_11 TMP_16 TMP_29
+H2))))))))))))) in (let TMP_60 \def (\lambda (t0: T).(\lambda (t1:
+TList).(\lambda (H1: ((\forall (a2: A).((arity g c (THeads (Flat Appl) t1
+(THead (Bind Abbr) v t)) a2) \to (arity g c (THeads (Flat Appl) t1 (THead
+(Flat Appl) v (THead (Bind Abst) u t))) a2))))).(\lambda (a2: A).(\lambda
+(H2: (arity g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1 (THead (Bind
+Abbr) v t))) a2)).(let TMP_31 \def (Flat Appl) in (let TMP_32 \def (Bind
+Abbr) in (let TMP_33 \def (THead TMP_32 v t) in (let TMP_34 \def (THeads
+TMP_31 t1 TMP_33) in (let H3 \def (arity_gen_appl g c t0 TMP_34 a2 H2) in
+(let TMP_35 \def (\lambda (a3: A).(arity g c t0 a3)) in (let TMP_41 \def
+(\lambda (a3: A).(let TMP_36 \def (Flat Appl) in (let TMP_37 \def (Bind Abbr)
+in (let TMP_38 \def (THead TMP_37 v t) in (let TMP_39 \def (THeads TMP_36 t1
+TMP_38) in (let TMP_40 \def (AHead a3 a2) in (arity g c TMP_39 TMP_40)))))))
+in (let TMP_42 \def (Flat Appl) in (let TMP_43 \def (Flat Appl) in (let
+TMP_44 \def (Flat Appl) in (let TMP_45 \def (Bind Abst) in (let TMP_46 \def
+(THead TMP_45 u t) in (let TMP_47 \def (THead TMP_44 v TMP_46) in (let TMP_48
+\def (THeads TMP_43 t1 TMP_47) in (let TMP_49 \def (THead TMP_42 t0 TMP_48)
+in (let TMP_50 \def (arity g c TMP_49 a2) in (let TMP_59 \def (\lambda (x:
+A).(\lambda (H4: (arity g c t0 x)).(\lambda (H5: (arity g c (THeads (Flat
+Appl) t1 (THead (Bind Abbr) v t)) (AHead x a2))).(let TMP_51 \def (Flat Appl)
+in (let TMP_52 \def (Flat Appl) in (let TMP_53 \def (Bind Abst) in (let
+TMP_54 \def (THead TMP_53 u t) in (let TMP_55 \def (THead TMP_52 v TMP_54) in
+(let TMP_56 \def (THeads TMP_51 t1 TMP_55) in (let TMP_57 \def (AHead x a2)
+in (let TMP_58 \def (H1 TMP_57 H5) in (arity_appl g c t0 x H4 TMP_56 a2
+TMP_58)))))))))))) in (ex2_ind A TMP_35 TMP_41 TMP_50 TMP_59
+H3))))))))))))))))))))))) in (TList_ind TMP_7 TMP_30 TMP_60 vs)))))))))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/defs.ma".
+include "basic_1/csuba/fwd.ma".
-include "Basic-1/clear/fwd.ma".
+include "basic_1/clear/fwd.ma".
theorem csuba_clear_conf:
\forall (g: G).(\forall (c1: C).(\forall (c2: C).((csuba g c1 c2) \to
(\lambda (e2: C).(clear c2 e2))))))))
\def
\lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csuba g c1
-c2)).(csuba_ind g (\lambda (c: C).(\lambda (c0: C).(\forall (e1: C).((clear c
-e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c0
-e2))))))) (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear (CSort n)
-e1)).(clear_gen_sort e1 n H0 (ex2 C (\lambda (e2: C).(csuba g e1 e2))
-(\lambda (e2: C).(clear (CSort n) e2))))))) (\lambda (c3: C).(\lambda (c4:
-C).(\lambda (H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c3
-e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c4
+c2)).(let TMP_3 \def (\lambda (c: C).(\lambda (c0: C).(\forall (e1:
+C).((clear c e1) \to (let TMP_1 \def (\lambda (e2: C).(csuba g e1 e2)) in
+(let TMP_2 \def (\lambda (e2: C).(clear c0 e2)) in (ex2 C TMP_1 TMP_2)))))))
+in (let TMP_8 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear
+(CSort n) e1)).(let TMP_4 \def (\lambda (e2: C).(csuba g e1 e2)) in (let
+TMP_6 \def (\lambda (e2: C).(let TMP_5 \def (CSort n) in (clear TMP_5 e2)))
+in (let TMP_7 \def (ex2 C TMP_4 TMP_6) in (clear_gen_sort e1 n H0
+TMP_7))))))) in (let TMP_49 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda
+(H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c3 e1) \to (ex2
+C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c4
e2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (e1: C).(\lambda (H2:
-(clear (CHead c3 k u) e1)).(K_ind (\lambda (k0: K).((clear (CHead c3 k0 u)
-e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear
-(CHead c4 k0 u) e2))))) (\lambda (b: B).(\lambda (H3: (clear (CHead c3 (Bind
-b) u) e1)).(eq_ind_r C (CHead c3 (Bind b) u) (\lambda (c: C).(ex2 C (\lambda
-(e2: C).(csuba g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b) u) e2))))
-(ex_intro2 C (\lambda (e2: C).(csuba g (CHead c3 (Bind b) u) e2)) (\lambda
-(e2: C).(clear (CHead c4 (Bind b) u) e2)) (CHead c4 (Bind b) u) (csuba_head g
-c3 c4 H0 (Bind b) u) (clear_bind b c4 u)) e1 (clear_gen_bind b c3 e1 u H3))))
-(\lambda (f: F).(\lambda (H3: (clear (CHead c3 (Flat f) u) e1)).(let H4 \def
-(H1 e1 (clear_gen_flat f c3 e1 u H3)) in (ex2_ind C (\lambda (e2: C).(csuba g
-e1 e2)) (\lambda (e2: C).(clear c4 e2)) (ex2 C (\lambda (e2: C).(csuba g e1
-e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f) u) e2))) (\lambda (x:
-C).(\lambda (H5: (csuba g e1 x)).(\lambda (H6: (clear c4 x)).(ex_intro2 C
-(\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f)
-u) e2)) x H5 (clear_flat c4 x H6 f u))))) H4)))) k H2))))))))) (\lambda (c3:
+(clear (CHead c3 k u) e1)).(let TMP_12 \def (\lambda (k0: K).((clear (CHead
+c3 k0 u) e1) \to (let TMP_9 \def (\lambda (e2: C).(csuba g e1 e2)) in (let
+TMP_11 \def (\lambda (e2: C).(let TMP_10 \def (CHead c4 k0 u) in (clear
+TMP_10 e2))) in (ex2 C TMP_9 TMP_11))))) in (let TMP_33 \def (\lambda (b:
+B).(\lambda (H3: (clear (CHead c3 (Bind b) u) e1)).(let TMP_13 \def (Bind b)
+in (let TMP_14 \def (CHead c3 TMP_13 u) in (let TMP_19 \def (\lambda (c:
+C).(let TMP_15 \def (\lambda (e2: C).(csuba g c e2)) in (let TMP_18 \def
+(\lambda (e2: C).(let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead c4
+TMP_16 u) in (clear TMP_17 e2)))) in (ex2 C TMP_15 TMP_18)))) in (let TMP_22
+\def (\lambda (e2: C).(let TMP_20 \def (Bind b) in (let TMP_21 \def (CHead c3
+TMP_20 u) in (csuba g TMP_21 e2)))) in (let TMP_25 \def (\lambda (e2: C).(let
+TMP_23 \def (Bind b) in (let TMP_24 \def (CHead c4 TMP_23 u) in (clear TMP_24
+e2)))) in (let TMP_26 \def (Bind b) in (let TMP_27 \def (CHead c4 TMP_26 u)
+in (let TMP_28 \def (Bind b) in (let TMP_29 \def (csuba_head g c3 c4 H0
+TMP_28 u) in (let TMP_30 \def (clear_bind b c4 u) in (let TMP_31 \def
+(ex_intro2 C TMP_22 TMP_25 TMP_27 TMP_29 TMP_30) in (let TMP_32 \def
+(clear_gen_bind b c3 e1 u H3) in (eq_ind_r C TMP_14 TMP_19 TMP_31 e1
+TMP_32))))))))))))))) in (let TMP_48 \def (\lambda (f: F).(\lambda (H3:
+(clear (CHead c3 (Flat f) u) e1)).(let TMP_34 \def (clear_gen_flat f c3 e1 u
+H3) in (let H4 \def (H1 e1 TMP_34) in (let TMP_35 \def (\lambda (e2:
+C).(csuba g e1 e2)) in (let TMP_36 \def (\lambda (e2: C).(clear c4 e2)) in
+(let TMP_37 \def (\lambda (e2: C).(csuba g e1 e2)) in (let TMP_40 \def
+(\lambda (e2: C).(let TMP_38 \def (Flat f) in (let TMP_39 \def (CHead c4
+TMP_38 u) in (clear TMP_39 e2)))) in (let TMP_41 \def (ex2 C TMP_37 TMP_40)
+in (let TMP_47 \def (\lambda (x: C).(\lambda (H5: (csuba g e1 x)).(\lambda
+(H6: (clear c4 x)).(let TMP_42 \def (\lambda (e2: C).(csuba g e1 e2)) in (let
+TMP_45 \def (\lambda (e2: C).(let TMP_43 \def (Flat f) in (let TMP_44 \def
+(CHead c4 TMP_43 u) in (clear TMP_44 e2)))) in (let TMP_46 \def (clear_flat
+c4 x H6 f u) in (ex_intro2 C TMP_42 TMP_45 x H5 TMP_46))))))) in (ex2_ind C
+TMP_35 TMP_36 TMP_41 TMP_47 H4))))))))))) in (K_ind TMP_12 TMP_33 TMP_48 k
+H2)))))))))))) in (let TMP_69 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda
+(H0: (csuba g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear c3 e1) \to (ex2
+C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c4
+e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1:
+T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: (clear (CHead c3 (Bind
+Void) u1) e1)).(let TMP_50 \def (Bind Void) in (let TMP_51 \def (CHead c3
+TMP_50 u1) in (let TMP_56 \def (\lambda (c: C).(let TMP_52 \def (\lambda (e2:
+C).(csuba g c e2)) in (let TMP_55 \def (\lambda (e2: C).(let TMP_53 \def
+(Bind b) in (let TMP_54 \def (CHead c4 TMP_53 u2) in (clear TMP_54 e2)))) in
+(ex2 C TMP_52 TMP_55)))) in (let TMP_59 \def (\lambda (e2: C).(let TMP_57
+\def (Bind Void) in (let TMP_58 \def (CHead c3 TMP_57 u1) in (csuba g TMP_58
+e2)))) in (let TMP_62 \def (\lambda (e2: C).(let TMP_60 \def (Bind b) in (let
+TMP_61 \def (CHead c4 TMP_60 u2) in (clear TMP_61 e2)))) in (let TMP_63 \def
+(Bind b) in (let TMP_64 \def (CHead c4 TMP_63 u2) in (let TMP_65 \def
+(csuba_void g c3 c4 H0 b H2 u1 u2) in (let TMP_66 \def (clear_bind b c4 u2)
+in (let TMP_67 \def (ex_intro2 C TMP_59 TMP_62 TMP_64 TMP_65 TMP_66) in (let
+TMP_68 \def (clear_gen_bind Void c3 e1 u1 H3) in (eq_ind_r C TMP_51 TMP_56
+TMP_67 e1 TMP_68)))))))))))))))))))))) in (let TMP_89 \def (\lambda (c3:
C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: ((\forall
(e1: C).((clear c3 e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda
-(e2: C).(clear c4 e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b
-Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3:
-(clear (CHead c3 (Bind Void) u1) e1)).(eq_ind_r C (CHead c3 (Bind Void) u1)
-(\lambda (c: C).(ex2 C (\lambda (e2: C).(csuba g c e2)) (\lambda (e2:
-C).(clear (CHead c4 (Bind b) u2) e2)))) (ex_intro2 C (\lambda (e2: C).(csuba
-g (CHead c3 (Bind Void) u1) e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b)
-u2) e2)) (CHead c4 (Bind b) u2) (csuba_void g c3 c4 H0 b H2 u1 u2)
-(clear_bind b c4 u2)) e1 (clear_gen_bind Void c3 e1 u1 H3))))))))))))
-(\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_:
-((\forall (e1: C).((clear c3 e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2))
-(\lambda (e2: C).(clear c4 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda
-(H2: (arity g c3 t (asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u
-a)).(\lambda (e1: C).(\lambda (H4: (clear (CHead c3 (Bind Abst) t)
-e1)).(eq_ind_r C (CHead c3 (Bind Abst) t) (\lambda (c: C).(ex2 C (\lambda
-(e2: C).(csuba g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u)
-e2)))) (ex_intro2 C (\lambda (e2: C).(csuba g (CHead c3 (Bind Abst) t) e2))
-(\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u) e2)) (CHead c4 (Bind Abbr)
-u) (csuba_abst g c3 c4 H0 t a H2 u H3) (clear_bind Abbr c4 u)) e1
-(clear_gen_bind Abst c3 e1 t H4))))))))))))) c1 c2 H)))).
-(* COMMENTS
-Initial nodes: 937
-END *)
+(e2: C).(clear c4 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H2:
+(arity g c3 t (asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u
+a)).(\lambda (e1: C).(\lambda (H4: (clear (CHead c3 (Bind Abst) t) e1)).(let
+TMP_70 \def (Bind Abst) in (let TMP_71 \def (CHead c3 TMP_70 t) in (let
+TMP_76 \def (\lambda (c: C).(let TMP_72 \def (\lambda (e2: C).(csuba g c e2))
+in (let TMP_75 \def (\lambda (e2: C).(let TMP_73 \def (Bind Abbr) in (let
+TMP_74 \def (CHead c4 TMP_73 u) in (clear TMP_74 e2)))) in (ex2 C TMP_72
+TMP_75)))) in (let TMP_79 \def (\lambda (e2: C).(let TMP_77 \def (Bind Abst)
+in (let TMP_78 \def (CHead c3 TMP_77 t) in (csuba g TMP_78 e2)))) in (let
+TMP_82 \def (\lambda (e2: C).(let TMP_80 \def (Bind Abbr) in (let TMP_81 \def
+(CHead c4 TMP_80 u) in (clear TMP_81 e2)))) in (let TMP_83 \def (Bind Abbr)
+in (let TMP_84 \def (CHead c4 TMP_83 u) in (let TMP_85 \def (csuba_abst g c3
+c4 H0 t a H2 u H3) in (let TMP_86 \def (clear_bind Abbr c4 u) in (let TMP_87
+\def (ex_intro2 C TMP_79 TMP_82 TMP_84 TMP_85 TMP_86) in (let TMP_88 \def
+(clear_gen_bind Abst c3 e1 t H4) in (eq_ind_r C TMP_71 TMP_76 TMP_87 e1
+TMP_88))))))))))))))))))))))) in (csuba_ind g TMP_3 TMP_8 TMP_49 TMP_69
+TMP_89 c1 c2 H))))))))).
theorem csuba_clear_trans:
\forall (g: G).(\forall (c1: C).(\forall (c2: C).((csuba g c2 c1) \to
(\lambda (e2: C).(clear c2 e2))))))))
\def
\lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csuba g c2
-c1)).(csuba_ind g (\lambda (c: C).(\lambda (c0: C).(\forall (e1: C).((clear
-c0 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c
-e2))))))) (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear (CSort n)
-e1)).(clear_gen_sort e1 n H0 (ex2 C (\lambda (e2: C).(csuba g e2 e1))
-(\lambda (e2: C).(clear (CSort n) e2))))))) (\lambda (c3: C).(\lambda (c4:
-C).(\lambda (H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c4
-e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c3
+c1)).(let TMP_3 \def (\lambda (c: C).(\lambda (c0: C).(\forall (e1:
+C).((clear c0 e1) \to (let TMP_1 \def (\lambda (e2: C).(csuba g e2 e1)) in
+(let TMP_2 \def (\lambda (e2: C).(clear c e2)) in (ex2 C TMP_1 TMP_2)))))))
+in (let TMP_8 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear
+(CSort n) e1)).(let TMP_4 \def (\lambda (e2: C).(csuba g e2 e1)) in (let
+TMP_6 \def (\lambda (e2: C).(let TMP_5 \def (CSort n) in (clear TMP_5 e2)))
+in (let TMP_7 \def (ex2 C TMP_4 TMP_6) in (clear_gen_sort e1 n H0
+TMP_7))))))) in (let TMP_49 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda
+(H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c4 e1) \to (ex2
+C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c3
e2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (e1: C).(\lambda (H2:
-(clear (CHead c4 k u) e1)).(K_ind (\lambda (k0: K).((clear (CHead c4 k0 u)
-e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear
-(CHead c3 k0 u) e2))))) (\lambda (b: B).(\lambda (H3: (clear (CHead c4 (Bind
-b) u) e1)).(eq_ind_r C (CHead c4 (Bind b) u) (\lambda (c: C).(ex2 C (\lambda
-(e2: C).(csuba g e2 c)) (\lambda (e2: C).(clear (CHead c3 (Bind b) u) e2))))
-(ex_intro2 C (\lambda (e2: C).(csuba g e2 (CHead c4 (Bind b) u))) (\lambda
-(e2: C).(clear (CHead c3 (Bind b) u) e2)) (CHead c3 (Bind b) u) (csuba_head g
-c3 c4 H0 (Bind b) u) (clear_bind b c3 u)) e1 (clear_gen_bind b c4 e1 u H3))))
-(\lambda (f: F).(\lambda (H3: (clear (CHead c4 (Flat f) u) e1)).(let H4 \def
-(H1 e1 (clear_gen_flat f c4 e1 u H3)) in (ex2_ind C (\lambda (e2: C).(csuba g
-e2 e1)) (\lambda (e2: C).(clear c3 e2)) (ex2 C (\lambda (e2: C).(csuba g e2
-e1)) (\lambda (e2: C).(clear (CHead c3 (Flat f) u) e2))) (\lambda (x:
-C).(\lambda (H5: (csuba g x e1)).(\lambda (H6: (clear c3 x)).(ex_intro2 C
-(\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear (CHead c3 (Flat f)
-u) e2)) x H5 (clear_flat c3 x H6 f u))))) H4)))) k H2))))))))) (\lambda (c3:
-C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: ((\forall
-(e1: C).((clear c4 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda
-(e2: C).(clear c3 e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b
-Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3:
-(clear (CHead c4 (Bind b) u2) e1)).(eq_ind_r C (CHead c4 (Bind b) u2)
-(\lambda (c: C).(ex2 C (\lambda (e2: C).(csuba g e2 c)) (\lambda (e2:
-C).(clear (CHead c3 (Bind Void) u1) e2)))) (ex_intro2 C (\lambda (e2:
-C).(csuba g e2 (CHead c4 (Bind b) u2))) (\lambda (e2: C).(clear (CHead c3
-(Bind Void) u1) e2)) (CHead c3 (Bind Void) u1) (csuba_void g c3 c4 H0 b H2 u1
-u2) (clear_bind Void c3 u1)) e1 (clear_gen_bind b c4 e1 u2 H3))))))))))))
-(\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_:
-((\forall (e1: C).((clear c4 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1))
-(\lambda (e2: C).(clear c3 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda
-(H2: (arity g c3 t (asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u
-a)).(\lambda (e1: C).(\lambda (H4: (clear (CHead c4 (Bind Abbr) u)
-e1)).(eq_ind_r C (CHead c4 (Bind Abbr) u) (\lambda (c: C).(ex2 C (\lambda
-(e2: C).(csuba g e2 c)) (\lambda (e2: C).(clear (CHead c3 (Bind Abst) t)
-e2)))) (ex_intro2 C (\lambda (e2: C).(csuba g e2 (CHead c4 (Bind Abbr) u)))
-(\lambda (e2: C).(clear (CHead c3 (Bind Abst) t) e2)) (CHead c3 (Bind Abst)
-t) (csuba_abst g c3 c4 H0 t a H2 u H3) (clear_bind Abst c3 t)) e1
-(clear_gen_bind Abbr c4 e1 u H4))))))))))))) c2 c1 H)))).
-(* COMMENTS
-Initial nodes: 937
-END *)
+(clear (CHead c4 k u) e1)).(let TMP_12 \def (\lambda (k0: K).((clear (CHead
+c4 k0 u) e1) \to (let TMP_9 \def (\lambda (e2: C).(csuba g e2 e1)) in (let
+TMP_11 \def (\lambda (e2: C).(let TMP_10 \def (CHead c3 k0 u) in (clear
+TMP_10 e2))) in (ex2 C TMP_9 TMP_11))))) in (let TMP_33 \def (\lambda (b:
+B).(\lambda (H3: (clear (CHead c4 (Bind b) u) e1)).(let TMP_13 \def (Bind b)
+in (let TMP_14 \def (CHead c4 TMP_13 u) in (let TMP_19 \def (\lambda (c:
+C).(let TMP_15 \def (\lambda (e2: C).(csuba g e2 c)) in (let TMP_18 \def
+(\lambda (e2: C).(let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead c3
+TMP_16 u) in (clear TMP_17 e2)))) in (ex2 C TMP_15 TMP_18)))) in (let TMP_22
+\def (\lambda (e2: C).(let TMP_20 \def (Bind b) in (let TMP_21 \def (CHead c4
+TMP_20 u) in (csuba g e2 TMP_21)))) in (let TMP_25 \def (\lambda (e2: C).(let
+TMP_23 \def (Bind b) in (let TMP_24 \def (CHead c3 TMP_23 u) in (clear TMP_24
+e2)))) in (let TMP_26 \def (Bind b) in (let TMP_27 \def (CHead c3 TMP_26 u)
+in (let TMP_28 \def (Bind b) in (let TMP_29 \def (csuba_head g c3 c4 H0
+TMP_28 u) in (let TMP_30 \def (clear_bind b c3 u) in (let TMP_31 \def
+(ex_intro2 C TMP_22 TMP_25 TMP_27 TMP_29 TMP_30) in (let TMP_32 \def
+(clear_gen_bind b c4 e1 u H3) in (eq_ind_r C TMP_14 TMP_19 TMP_31 e1
+TMP_32))))))))))))))) in (let TMP_48 \def (\lambda (f: F).(\lambda (H3:
+(clear (CHead c4 (Flat f) u) e1)).(let TMP_34 \def (clear_gen_flat f c4 e1 u
+H3) in (let H4 \def (H1 e1 TMP_34) in (let TMP_35 \def (\lambda (e2:
+C).(csuba g e2 e1)) in (let TMP_36 \def (\lambda (e2: C).(clear c3 e2)) in
+(let TMP_37 \def (\lambda (e2: C).(csuba g e2 e1)) in (let TMP_40 \def
+(\lambda (e2: C).(let TMP_38 \def (Flat f) in (let TMP_39 \def (CHead c3
+TMP_38 u) in (clear TMP_39 e2)))) in (let TMP_41 \def (ex2 C TMP_37 TMP_40)
+in (let TMP_47 \def (\lambda (x: C).(\lambda (H5: (csuba g x e1)).(\lambda
+(H6: (clear c3 x)).(let TMP_42 \def (\lambda (e2: C).(csuba g e2 e1)) in (let
+TMP_45 \def (\lambda (e2: C).(let TMP_43 \def (Flat f) in (let TMP_44 \def
+(CHead c3 TMP_43 u) in (clear TMP_44 e2)))) in (let TMP_46 \def (clear_flat
+c3 x H6 f u) in (ex_intro2 C TMP_42 TMP_45 x H5 TMP_46))))))) in (ex2_ind C
+TMP_35 TMP_36 TMP_41 TMP_47 H4))))))))))) in (K_ind TMP_12 TMP_33 TMP_48 k
+H2)))))))))))) in (let TMP_69 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda
+(H0: (csuba g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear c4 e1) \to (ex2
+C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c3
+e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1:
+T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: (clear (CHead c4 (Bind b)
+u2) e1)).(let TMP_50 \def (Bind b) in (let TMP_51 \def (CHead c4 TMP_50 u2)
+in (let TMP_56 \def (\lambda (c: C).(let TMP_52 \def (\lambda (e2: C).(csuba
+g e2 c)) in (let TMP_55 \def (\lambda (e2: C).(let TMP_53 \def (Bind Void) in
+(let TMP_54 \def (CHead c3 TMP_53 u1) in (clear TMP_54 e2)))) in (ex2 C
+TMP_52 TMP_55)))) in (let TMP_59 \def (\lambda (e2: C).(let TMP_57 \def (Bind
+b) in (let TMP_58 \def (CHead c4 TMP_57 u2) in (csuba g e2 TMP_58)))) in (let
+TMP_62 \def (\lambda (e2: C).(let TMP_60 \def (Bind Void) in (let TMP_61 \def
+(CHead c3 TMP_60 u1) in (clear TMP_61 e2)))) in (let TMP_63 \def (Bind Void)
+in (let TMP_64 \def (CHead c3 TMP_63 u1) in (let TMP_65 \def (csuba_void g c3
+c4 H0 b H2 u1 u2) in (let TMP_66 \def (clear_bind Void c3 u1) in (let TMP_67
+\def (ex_intro2 C TMP_59 TMP_62 TMP_64 TMP_65 TMP_66) in (let TMP_68 \def
+(clear_gen_bind b c4 e1 u2 H3) in (eq_ind_r C TMP_51 TMP_56 TMP_67 e1
+TMP_68)))))))))))))))))))))) in (let TMP_89 \def (\lambda (c3: C).(\lambda
+(c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear
+c4 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear
+c3 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H2: (arity g c3 t
+(asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u a)).(\lambda (e1:
+C).(\lambda (H4: (clear (CHead c4 (Bind Abbr) u) e1)).(let TMP_70 \def (Bind
+Abbr) in (let TMP_71 \def (CHead c4 TMP_70 u) in (let TMP_76 \def (\lambda
+(c: C).(let TMP_72 \def (\lambda (e2: C).(csuba g e2 c)) in (let TMP_75 \def
+(\lambda (e2: C).(let TMP_73 \def (Bind Abst) in (let TMP_74 \def (CHead c3
+TMP_73 t) in (clear TMP_74 e2)))) in (ex2 C TMP_72 TMP_75)))) in (let TMP_79
+\def (\lambda (e2: C).(let TMP_77 \def (Bind Abbr) in (let TMP_78 \def (CHead
+c4 TMP_77 u) in (csuba g e2 TMP_78)))) in (let TMP_82 \def (\lambda (e2:
+C).(let TMP_80 \def (Bind Abst) in (let TMP_81 \def (CHead c3 TMP_80 t) in
+(clear TMP_81 e2)))) in (let TMP_83 \def (Bind Abst) in (let TMP_84 \def
+(CHead c3 TMP_83 t) in (let TMP_85 \def (csuba_abst g c3 c4 H0 t a H2 u H3)
+in (let TMP_86 \def (clear_bind Abst c3 t) in (let TMP_87 \def (ex_intro2 C
+TMP_79 TMP_82 TMP_84 TMP_85 TMP_86) in (let TMP_88 \def (clear_gen_bind Abbr
+c4 e1 u H4) in (eq_ind_r C TMP_71 TMP_76 TMP_87 e1
+TMP_88))))))))))))))))))))))) in (csuba_ind g TMP_3 TMP_8 TMP_49 TMP_69
+TMP_89 c2 c1 H))))))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/arity/defs.ma".
+include "basic_1/arity/defs.ma".
inductive csuba (g: G): C \to (C \to Prop) \def
| csuba_sort: \forall (n: nat).(csuba g (CSort n) (CSort n))
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/fwd.ma".
+include "basic_1/csuba/fwd.ma".
-include "Basic-1/drop/fwd.ma".
+include "basic_1/drop/fwd.ma".
theorem csuba_drop_abbr:
\forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop i
C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
d2))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u) (CSort n0))).(\lambda (H3:
(eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n)
-(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (ex2 C
-(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
-C).(csuba g d1 d2))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr)
-u) H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u:
-T).((drop (S n) O c (CHead d1 (Bind Abbr) u)) \to (\forall (g: G).(\forall
-(c2: C).((csuba g c c2) \to (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead
-d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))))))))).(\lambda (k:
-K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop (S n)
-O (CHead c k t) (CHead d1 (Bind Abbr) u))).(\lambda (g: G).(\lambda (c2:
-C).(\lambda (H2: (csuba g (CHead c k t) c2)).(K_ind (\lambda (k0: K).((csuba
-g (CHead c k0 t) c2) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr) u)) \to
-(ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda
-(d2: C).(csuba g d1 d2)))))) (\lambda (b: B).(\lambda (H3: (csuba g (CHead c
-(Bind b) t) c2)).(\lambda (H4: (drop (r (Bind b) n) O c (CHead d1 (Bind Abbr)
-u))).(B_ind (\lambda (b0: B).((csuba g (CHead c (Bind b0) t) c2) \to ((drop
-(r (Bind b0) n) O c (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2:
+(\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _) \Rightarrow
+True])) I O H3) in (False_ind (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead
+d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H5))))) (drop_gen_sort
+n0 (S n) O (CHead d1 (Bind Abbr) u) H0))))))))) (\lambda (c: C).(\lambda (H0:
+((\forall (d1: C).(\forall (u: T).((drop (S n) O c (CHead d1 (Bind Abbr) u))
+\to (\forall (g: G).(\forall (c2: C).((csuba g c c2) \to (ex2 C (\lambda (d2:
C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2)))))) (\lambda (H5: (csuba g (CHead c (Bind Abbr) t) c2)).(\lambda (H6:
-(drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abbr) u))).(let H_x \def
-(csuba_gen_abbr g c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda (d2:
-C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g c d2)) (ex2
-C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
-C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x (Bind
-Abbr) t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C (CHead x (Bind Abbr) t)
-(\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
-Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H10 \def (H c d1 u H6 g x
-H9) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u)))
-(\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O
-(CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g
-d1 d2))) (\lambda (x0: C).(\lambda (H11: (drop n O x (CHead x0 (Bind Abbr)
-u))).(\lambda (H12: (csuba g d1 x0)).(let H13 \def (refl_equal nat (r (Bind
-Abbr) n)) in (let H14 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x
-(CHead x0 (Bind Abbr) u))) H11 (r (Bind Abbr) n) H13) in (ex_intro2 C
-(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr)
-u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abbr) n x (CHead
-x0 (Bind Abbr) u) H14 t) H12)))))) H10)) c2 H8)))) H7))))) (\lambda (H5:
-(csuba g (CHead c (Bind Abst) t) c2)).(\lambda (H6: (drop (r (Bind Abst) n) O
-c (CHead d1 (Bind Abbr) u))).(let H_x \def (csuba_gen_abst g c c2 t H5) in
-(let H7 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
-Abst) t))) (\lambda (d2: C).(csuba g c d2))) (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g c d2)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex2 C
-(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
-C).(csuba g d1 d2))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
-(Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)))).(ex2_ind C (\lambda (d2:
-C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)) (ex2
-C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
-C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H9: (eq C c2 (CHead x (Bind
-Abst) t))).(\lambda (H10: (csuba g c x)).(eq_ind_r C (CHead x (Bind Abst) t)
-(\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
-Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H11 \def (H c d1 u H6 g x
-H10) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u)))
-(\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O
-(CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g
-d1 d2))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abbr)
-u))).(\lambda (H13: (csuba g d1 x0)).(let H14 \def (refl_equal nat (r (Bind
-Abbr) n)) in (let H15 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x
-(CHead x0 (Bind Abbr) u))) H12 (r (Bind Abbr) n) H14) in (ex_intro2 C
-(\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr)
-u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abst) n x (CHead
-x0 (Bind Abbr) u) H15 t) H13)))))) H11)) c2 H9)))) H8)) (\lambda (H8: (ex4_3
-C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2
-(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-c d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t (asucc
-g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
-A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
+d2))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u:
+T).(\lambda (H1: (drop (S n) O (CHead c k t) (CHead d1 (Bind Abbr)
+u))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: (csuba g (CHead c k t)
+c2)).(K_ind (\lambda (k0: K).((csuba g (CHead c k0 t) c2) \to ((drop (r k0 n)
+O c (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(drop (S n) O c2
+(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))) (\lambda (b:
+B).(\lambda (H3: (csuba g (CHead c (Bind b) t) c2)).(\lambda (H4: (drop (r
+(Bind b) n) O c (CHead d1 (Bind Abbr) u))).(B_ind (\lambda (b0: B).((csuba g
+(CHead c (Bind b0) t) c2) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind
+Abbr) u)) \to (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr)
+u))) (\lambda (d2: C).(csuba g d1 d2)))))) (\lambda (H5: (csuba g (CHead c
+(Bind Abbr) t) c2)).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead d1 (Bind
+Abbr) u))).(let H_x \def (csuba_gen_abbr g c c2 t H5) in (let H7 \def H_x in
+(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2:
+C).(csuba g c d2)) (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
+Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H8:
+(eq C c2 (CHead x (Bind Abbr) t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C
+(CHead x (Bind Abbr) t) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n)
+O c0 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H10
+\def (H c d1 u H6 g x H9) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead
+d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2:
+C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u))) (\lambda
+(d2: C).(csuba g d1 d2))) (\lambda (x0: C).(\lambda (H11: (drop n O x (CHead
+x0 (Bind Abbr) u))).(\lambda (H12: (csuba g d1 x0)).(let H13 \def (refl_equal
+nat (r (Bind Abbr) n)) in (let H14 \def (eq_ind nat n (\lambda (n0:
+nat).(drop n0 O x (CHead x0 (Bind Abbr) u))) H11 (r (Bind Abbr) n) H13) in
+(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abbr)
+n x (CHead x0 (Bind Abbr) u) H14 t) H12)))))) H10)) c2 H8)))) H7)))))
+(\lambda (H5: (csuba g (CHead c (Bind Abst) t) c2)).(\lambda (H6: (drop (r
+(Bind Abst) n) O c (CHead d1 (Bind Abbr) u))).(let H_x \def (csuba_gen_abst g
+c c2 t H5) in (let H7 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C c2
+(CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2))) (ex4_3 C T A
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind
+Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g c
+d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t (asucc g
+a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
+a))))) (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq
+C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)))).(ex2_ind C
+(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba
+g c d2)) (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H9: (eq C c2
+(CHead x (Bind Abst) t))).(\lambda (H10: (csuba g c x)).(eq_ind_r C (CHead x
+(Bind Abst) t) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0
+(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H11 \def
+(H c d1 u H6 g x H10) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2:
+C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u))) (\lambda
+(d2: C).(csuba g d1 d2))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead
+x0 (Bind Abbr) u))).(\lambda (H13: (csuba g d1 x0)).(let H14 \def (refl_equal
+nat (r (Bind Abbr) n)) in (let H15 \def (eq_ind nat n (\lambda (n0:
+nat).(drop n0 O x (CHead x0 (Bind Abbr) u))) H12 (r (Bind Abbr) n) H14) in
+(ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abst)
+n x (CHead x0 (Bind Abbr) u) H15 t) H13)))))) H11)) c2 H9)))) H8)) (\lambda
+(H8: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2
+(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g c d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g
+c t (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity
+g d2 u2 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
+(_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (_: A).(csuba g c d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda
(a: A).(arity g c t (asucc g a))))) (\lambda (d2: C).(\lambda (u2:
T).(\lambda (a: A).(arity g d2 u2 a)))) (ex2 C (\lambda (d2: C).(drop (S n) O
d1 d2)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abbr) u) H9 x1) H10))))
H8)) c2 H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u) t n
H1)))))))))))) c1)))) i).
-(* COMMENTS
-Initial nodes: 3648
-END *)
theorem csuba_drop_abst:
\forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop i
a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
a)))))) (\lambda (_: (eq C (CHead d1 (Bind Abst) u1) (CSort n0))).(\lambda
(H3: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S
-n) (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2
-C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
-C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) H5)))))
-(drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u1) H0))))))))) (\lambda (c:
-C).(\lambda (H0: ((\forall (d1: C).(\forall (u1: T).((drop (S n) O c (CHead
-d1 (Bind Abst) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c c2) \to
-(or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1)))
-(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a)))))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda
+n) (\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _) \Rightarrow
+True])) I O H3) in (False_ind (or (ex2 C (\lambda (d2: C).(drop (S n) O c2
+(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2
+(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
+d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
+(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
+u2 a)))))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u1)
+H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u1:
+T).((drop (S n) O c (CHead d1 (Bind Abst) u1)) \to (\forall (g: G).(\forall
+(c2: C).((csuba g c c2) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O c2
+(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2
+(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
+d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
+(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
+u2 a)))))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda
(u1: T).(\lambda (H1: (drop (S n) O (CHead c k t) (CHead d1 (Bind Abst)
u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: (csuba g (CHead c k t)
c2)).(K_ind (\lambda (k0: K).((csuba g (CHead c k0 t) c2) \to ((drop (r k0 n)
A).(arity g d2 u2 a)))) x2 x3 x4 (drop_drop (Flat f) n x0 (CHead x2 (Bind
Abbr) x3) H10 x1) H11 H12 H13))))))))) H9)) H8)) c2 H6))))) H5)))))) k H2
(drop_gen_drop k c (CHead d1 (Bind Abst) u1) t n H1)))))))))))) c1)))) i).
-(* COMMENTS
-Initial nodes: 12528
-END *)
theorem csuba_drop_abst_rev:
\forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop i
(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
(\lambda (_: (eq C (CHead d1 (Bind Abst) u) (CSort n0))).(\lambda (H3: (eq
nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n)
-(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2
-C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
-O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
-d2 d1))))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u)
-H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u:
-T).((drop (S n) O c (CHead d1 (Bind Abst) u)) \to (\forall (g: G).(\forall
-(c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O c2
+(\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _) \Rightarrow
+True])) I O H3) in (False_ind (or (ex2 C (\lambda (d2: C).(drop (S n) O c2
(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda
-(k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop
-(S n) O (CHead c k t) (CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda
-(c2: C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0:
-K).((csuba g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abst)
-u)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst)
-u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
-(u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (b: B).(\lambda (H3:
-(csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop (r (Bind b) n) O c
-(CHead d1 (Bind Abst) u))).(B_ind (\lambda (b0: B).((csuba g c2 (CHead c
-(Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind Abst) u)) \to
-(or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u)))
-(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
-(_: T).(csuba g d2 d1)))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr)
-t))).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abst)
-u))).(let H_x \def (csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in
-(or3_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda
-(d2: C).(csuba g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) H5)))))
+(drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u) H0))))))))) (\lambda (c:
+C).(\lambda (H0: ((\forall (d1: C).(\forall (u: T).((drop (S n) O c (CHead d1
+(Bind Abst) u)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c) \to (or
+(ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda
+(d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop
+(S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (d1:
+C).(\lambda (u: T).(\lambda (H1: (drop (S n) O (CHead c k t) (CHead d1 (Bind
+Abst) u))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: (csuba g c2 (CHead
+c k t))).(K_ind (\lambda (k0: K).((csuba g c2 (CHead c k0 t)) \to ((drop (r
+k0 n) O c (CHead d1 (Bind Abst) u)) \to (or (ex2 C (\lambda (d2: C).(drop (S
+n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
+C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (b:
+B).(\lambda (H3: (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop (r
+(Bind b) n) O c (CHead d1 (Bind Abst) u))).(B_ind (\lambda (b0: B).((csuba g
+c2 (CHead c (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind
+Abst) u)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
+(d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (H5: (csuba g c2
+(CHead c (Bind Abbr) t))).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead d1
+(Bind Abst) u))).(let H_x \def (csuba_gen_abbr_rev g c c2 t H5) in (let H7
+\def H_x in (or3_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr)
+t))) (\lambda (d2: C).(csuba g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\lambda (d2:
C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
(_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t a))))) (ex2_2 C T
(drop_drop (Flat f) n x0 (CHead x2 (Bind Void) x3) H10 x1) H11)))))) H9))
H8)) c2 H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abst) u) t n
H1)))))))))))) c1)))) i).
-(* COMMENTS
-Initial nodes: 11438
-END *)
theorem csuba_drop_abbr_rev:
\forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop i
T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
(_: T).(csuba g d2 d1))))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u1)
(CSort n0))).(\lambda (H3: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let
-H5 \def (eq_ind nat (S n) (\lambda (ee: nat).(match ee in nat return (\lambda
-(_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True])) I O H3)
-in (False_ind (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
+H5 \def (eq_ind nat (S n) (\lambda (ee: nat).(match ee with [O \Rightarrow
+False | (S _) \Rightarrow True])) I O H3) in (False_ind (or3 (ex2 C (\lambda
+(d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
+g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
+A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
+(_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
+(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) H5))))) (drop_gen_sort n0 (S n) O
+(CHead d1 (Bind Abbr) u1) H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall
+(d1: C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abbr) u1)) \to
+(\forall (g: G).(\forall (c2: C).((csuba g c2 c) \to (or3 (ex2 C (\lambda
+(d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
+g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
+A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
+(_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
+(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda (k: K).(\lambda
+(t: T).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H1: (drop (S n) O (CHead c
+k t) (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda
+(H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0: K).((csuba g c2 (CHead
+c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C
+(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
+(_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (b:
+B).(\lambda (H3: (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop (r
+(Bind b) n) O c (CHead d1 (Bind Abbr) u1))).(B_ind (\lambda (b0: B).((csuba g
+c2 (CHead c (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind
+Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
-Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) H5)))))
-(drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr) u1) H0))))))))) (\lambda (c:
-C).(\lambda (H0: ((\forall (d1: C).(\forall (u1: T).((drop (S n) O c (CHead
-d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c) \to
-(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1)))
-(\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
-C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda
-(k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H1: (drop
-(S n) O (CHead c k t) (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda
-(c2: C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0:
-K).((csuba g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr)
-u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr)
-u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda
-(b: B).(\lambda (H3: (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop
-(r (Bind b) n) O c (CHead d1 (Bind Abbr) u1))).(B_ind (\lambda (b0:
-B).((csuba g c2 (CHead c (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead
-d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind
-Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
-d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-(asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
-u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr) t))).(\lambda (H6:
-(drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def
-(csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in (or3_ind (ex2 C
-(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba
-g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
-C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d2 c)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g c t a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C
-c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-c)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr)
-u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
+(H5: (csuba g c2 (CHead c (Bind Abbr) t))).(\lambda (H6: (drop (r (Bind Abbr)
+n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def (csuba_gen_abbr_rev g c c2 t
+H5) in (let H7 \def H_x in (or3_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead
+d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c))) (ex4_3 C T A (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst)
+u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c))))
(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
-Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
-(H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda
-(d2: C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2
-(Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or3 (ex2 C (\lambda (d2:
+a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t a)))))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c)))) (or3 (ex2 C
+(\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
+(_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H8:
+(ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2:
+C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
+Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or3 (ex2 C (\lambda (d2:
C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
(d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Flat f) n x0
(CHead x2 (Bind Void) x3) H10 x1) H11)))))) H9)) H8)) c2 H6))))) H5)))))) k
H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u1) t n H1)))))))))))) c1)))) i).
-(* COMMENTS
-Initial nodes: 23852
-END *)
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/defs.ma".
+include "basic_1/csuba/defs.ma".
+
+let rec csuba_ind (g: G) (P: (C \to (C \to Prop))) (f: (\forall (n: nat).(P
+(CSort n) (CSort n)))) (f0: (\forall (c1: C).(\forall (c2: C).((csuba g c1
+c2) \to ((P c1 c2) \to (\forall (k: K).(\forall (u: T).(P (CHead c1 k u)
+(CHead c2 k u))))))))) (f1: (\forall (c1: C).(\forall (c2: C).((csuba g c1
+c2) \to ((P c1 c2) \to (\forall (b: B).((not (eq B b Void)) \to (\forall (u1:
+T).(\forall (u2: T).(P (CHead c1 (Bind Void) u1) (CHead c2 (Bind b)
+u2))))))))))) (f2: (\forall (c1: C).(\forall (c2: C).((csuba g c1 c2) \to ((P
+c1 c2) \to (\forall (t: T).(\forall (a: A).((arity g c1 t (asucc g a)) \to
+(\forall (u: T).((arity g c2 u a) \to (P (CHead c1 (Bind Abst) t) (CHead c2
+(Bind Abbr) u)))))))))))) (c: C) (c0: C) (c1: csuba g c c0) on c1: P c c0
+\def match c1 with [(csuba_sort n) \Rightarrow (f n) | (csuba_head c2 c3 c4 k
+u) \Rightarrow (f0 c2 c3 c4 ((csuba_ind g P f f0 f1 f2) c2 c3 c4) k u) |
+(csuba_void c2 c3 c4 b n u1 u2) \Rightarrow (f1 c2 c3 c4 ((csuba_ind g P f f0
+f1 f2) c2 c3 c4) b n u1 u2) | (csuba_abst c2 c3 c4 t a a0 u a1) \Rightarrow
+(f2 c2 c3 c4 ((csuba_ind g P f f0 f1 f2) c2 c3 c4) t a a0 u a1)].
theorem csuba_gen_abbr:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u: T).((csuba g
(c1: C).((eq C c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C
c1 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))) (\lambda
(n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Abbr) u))).(let H2
-\def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Bind Abbr) u) H1) in (False_ind (ex2 C (\lambda (d2:
-C).(eq C (CSort n) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2)))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c1 k u0)
-(CHead d1 (Bind Abbr) u))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c1 k u0) (CHead d1 (Bind Abbr) u) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
+\def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1 (Bind Abbr)
+u) H1) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind
+Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H2)))) (\lambda (c1:
+C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
+(CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))).(\lambda (k:
+K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c1 k u0) (CHead d1 (Bind Abbr)
+u))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 k u0) (CHead d1
+(Bind Abbr) u) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e
with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
u0) (CHead d1 (Bind Abbr) u) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u0) (CHead d1 (Bind Abbr) u) H3)
-in (\lambda (H7: (eq K k (Bind Abbr))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r
-T u (\lambda (t: T).(ex2 C (\lambda (d2: C).(eq C (CHead c2 k t) (CHead d2
-(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (eq_ind_r K (Bind Abbr)
-(\lambda (k0: K).(ex2 C (\lambda (d2: C).(eq C (CHead c2 k0 u) (CHead d2
-(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H9 \def (eq_ind C
-c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2))))) H2 d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0
-c2)) H1 d1 H8) in (ex_intro2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abbr)
-u) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) c2
-(refl_equal C (CHead c2 (Bind Abbr) u)) H10))) k H7) u0 H6)))) H5))
-H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
-c2)).(\lambda (_: (((eq C c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
-d2)))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead d1
-(Bind Abbr) u))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u1) (\lambda
-(ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b0) \Rightarrow (match b0 in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False | Void
-\Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abbr)
-u) H4) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind b) u2)
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H5)))))))))))
-(\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_:
-(((eq C c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C c2
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))).(\lambda (t:
+C).(match e with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t]))
+(CHead c1 k u0) (CHead d1 (Bind Abbr) u) H3) in (\lambda (H7: (eq K k (Bind
+Abbr))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r T u (\lambda (t: T).(ex2 C
+(\lambda (d2: C).(eq C (CHead c2 k t) (CHead d2 (Bind Abbr) u))) (\lambda
+(d2: C).(csuba g d1 d2)))) (eq_ind_r K (Bind Abbr) (\lambda (k0: K).(ex2 C
+(\lambda (d2: C).(eq C (CHead c2 k0 u) (CHead d2 (Bind Abbr) u))) (\lambda
+(d2: C).(csuba g d1 d2)))) (let H9 \def (eq_ind C c1 (\lambda (c0: C).((eq C
+c0 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))) H2 d1 H8) in (let H10
+\def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in (ex_intro2 C
+(\lambda (d2: C).(eq C (CHead c2 (Bind Abbr) u) (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2)) c2 (refl_equal C (CHead c2 (Bind Abbr) u))
+H10))) k H7) u0 H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c2:
+C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c1 (CHead d1 (Bind
+Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2)))))).(\lambda (b: B).(\lambda (_: (not (eq B
+b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1
+(Bind Void) u1) (CHead d1 (Bind Abbr) u))).(let H5 \def (eq_ind C (CHead c1
+(Bind Void) u1) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False
+| (CHead _ k _) \Rightarrow (match k with [(Bind b0) \Rightarrow (match b0
+with [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow
+True]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abbr) u) H4) in
+(False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind b) u2) (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H5))))))))))) (\lambda
+(c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C
+c1 (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
+(Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))).(\lambda (t:
T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g a))).(\lambda (u0:
T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C (CHead c1 (Bind Abst)
t) (CHead d1 (Bind Abbr) u))).(let H6 \def (eq_ind C (CHead c1 (Bind Abst) t)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return (\lambda
-(_: K).Prop) with [(Bind b) \Rightarrow (match b in B return (\lambda (_:
-B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow True | Void
-\Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abbr)
-u) H5) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abbr) u0)
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) H6))))))))))))
-y c H0))) H))))).
-(* COMMENTS
-Initial nodes: 1117
-END *)
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) I (CHead d1 (Bind Abbr) u) H5) in (False_ind (ex2 C
+(\lambda (d2: C).(eq C (CHead c2 (Bind Abbr) u0) (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2))) H6)))))))))))) y c H0))) H))))).
theorem csuba_gen_void:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).((csuba g
(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind b)
u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
d2)))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind
-Void) u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C
-return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Bind Void) u1) H1) in (False_ind (ex2_3 B C
-T (\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2
-(Bind b) u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
-(CHead d1 (Bind Void) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match
-e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c1 k u) (CHead d1 (Bind Void) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
+Void) u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1
+(Bind Void) u1) H1) in (False_ind (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
+C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Bind b) u2))))) (\lambda (_:
+B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))) H2)))) (\lambda (c1:
+C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
+(CHead d1 (Bind Void) u1)) \to (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
+C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b) u2))))) (\lambda (_:
+B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))))).(\lambda (k:
+K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u) (CHead d1 (Bind Void)
+u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 k u) (CHead d1
+(Bind Void) u1) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e
with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
u) (CHead d1 (Bind Void) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead d1 (Bind Void) u1) H3)
-in (\lambda (H7: (eq K k (Bind Void))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r
-T u1 (\lambda (t: T).(ex2_3 B C T (\lambda (b: B).(\lambda (d2: C).(\lambda
-(u2: T).(eq C (CHead c2 k t) (CHead d2 (Bind b) u2))))) (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))) (eq_ind_r K (Bind
-Void) (\lambda (k0: K).(ex2_3 B C T (\lambda (b: B).(\lambda (d2: C).(\lambda
-(u2: T).(eq C (CHead c2 k0 u1) (CHead d2 (Bind b) u2))))) (\lambda (_:
-B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))) (let H9 \def (eq_ind
-C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))) H2 d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g
-c0 c2)) H1 d1 H8) in (ex2_3_intro B C T (\lambda (b: B).(\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c2 (Bind Void) u1) (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))
-Void c2 u1 (refl_equal C (CHead c2 (Bind Void) u1)) H10))) k H7) u H6))))
-H5)) H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Void) u1)) \to (ex2_3 B C T
-(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b)
-u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2)))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u0:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u0) (CHead d1
-(Bind Void) u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _ _)
-\Rightarrow c0])) (CHead c1 (Bind Void) u0) (CHead d1 (Bind Void) u1) H4) in
-((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead
-c1 (Bind Void) u0) (CHead d1 (Bind Void) u1) H4) in (\lambda (H7: (eq C c1
-d1)).(let H8 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind
-Void) u1)) \to (ex2_3 B C T (\lambda (b0: B).(\lambda (d2: C).(\lambda (u3:
-T).(eq C c2 (CHead d2 (Bind b0) u3))))) (\lambda (_: B).(\lambda (d2:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
+(CHead c1 k u) (CHead d1 (Bind Void) u1) H3) in (\lambda (H7: (eq K k (Bind
+Void))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r T u1 (\lambda (t: T).(ex2_3 B C
+T (\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2 k t)
+(CHead d2 (Bind b) u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_:
+T).(csuba g d1 d2)))))) (eq_ind_r K (Bind Void) (\lambda (k0: K).(ex2_3 B C T
+(\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2 k0 u1)
+(CHead d2 (Bind b) u2))))) (\lambda (_: B).(\lambda (d2: C).(\lambda (_:
+T).(csuba g d1 d2)))))) (let H9 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0
+(CHead d1 (Bind Void) u1)) \to (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
+C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b) u2))))) (\lambda (_:
+B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))))) H2 d1 H8) in (let
+H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in
+(ex2_3_intro B C T (\lambda (b: B).(\lambda (d2: C).(\lambda (u2: T).(eq C
+(CHead c2 (Bind Void) u1) (CHead d2 (Bind b) u2))))) (\lambda (_: B).(\lambda
+(d2: C).(\lambda (_: T).(csuba g d1 d2)))) Void c2 u1 (refl_equal C (CHead c2
+(Bind Void) u1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
+C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
+(CHead d1 (Bind Void) u1)) \to (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
+C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b) u2))))) (\lambda (_:
+B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))))).(\lambda (b:
+B).(\lambda (_: (not (eq B b Void))).(\lambda (u0: T).(\lambda (u2:
+T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u0) (CHead d1 (Bind Void)
+u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 (Bind Void) u0)
+(CHead d1 (Bind Void) u1) H4) in ((let H6 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t]))
+(CHead c1 (Bind Void) u0) (CHead d1 (Bind Void) u1) H4) in (\lambda (H7: (eq
+C c1 d1)).(let H8 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1
+(Bind Void) u1)) \to (ex2_3 B C T (\lambda (b0: B).(\lambda (d2: C).(\lambda
+(u3: T).(eq C c2 (CHead d2 (Bind b0) u3))))) (\lambda (_: B).(\lambda (d2:
C).(\lambda (_: T).(csuba g d1 d2))))))) H2 d1 H7) in (let H9 \def (eq_ind C
c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H7) in (ex2_3_intro B C T (\lambda
(b0: B).(\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c2 (Bind b) u2) (CHead
d2)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc
g a))).(\lambda (u: T).(\lambda (_: (arity g c2 u a)).(\lambda (H5: (eq C
(CHead c1 (Bind Abst) t) (CHead d1 (Bind Void) u1))).(let H6 \def (eq_ind C
-(CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
-return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow
-True | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d1
-(Bind Void) u1) H5) in (False_ind (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
+(CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind b)
+\Rightarrow (match b with [Abbr \Rightarrow False | Abst \Rightarrow True |
+Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind
+Void) u1) H5) in (False_ind (ex2_3 B C T (\lambda (b: B).(\lambda (d2:
C).(\lambda (u2: T).(eq C (CHead c2 (Bind Abbr) u) (CHead d2 (Bind b) u2)))))
(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))))
H6)))))))))))) y c H0))) H))))).
-(* COMMENTS
-Initial nodes: 1418
-END *)
theorem csuba_gen_abst:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).((csuba g
(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))))
(\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Abst)
-u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Bind Abst) u1) H1) in (False_ind (or (ex2 C
-(\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind Abst) u1))) (\lambda (d2:
-C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(_: A).(eq C (CSort n) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) H2))))
-(\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda
-(H2: (((eq C c1 (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2:
-C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2
-(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
-g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 a))))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3:
-(eq C (CHead c1 k u) (CHead d1 (Bind Abst) u1))).(let H4 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 k u) (CHead d1
-(Bind Abst) u1) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e in
-C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _)
-\Rightarrow k0])) (CHead c1 k u) (CHead d1 (Bind Abst) u1) H3) in ((let H6
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u)
-(CHead d1 (Bind Abst) u1) H3) in (\lambda (H7: (eq K k (Bind Abst))).(\lambda
-(H8: (eq C c1 d1)).(eq_ind_r T u1 (\lambda (t: T).(or (ex2 C (\lambda (d2:
-C).(eq C (CHead c2 k t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g
-d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C
-(CHead c2 k t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
-T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
-T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (a: A).(arity g d2 u2 a))))))) (eq_ind_r K (Bind Abst)
-(\lambda (k0: K).(or (ex2 C (\lambda (d2: C).(eq C (CHead c2 k0 u1) (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 k0 u1) (CHead d2
+u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1
+(Bind Abst) u1) H1) in (False_ind (or (ex2 C (\lambda (d2: C).(eq C (CSort n)
+(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CSort n) (CHead d2
(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
-u2 a))))))) (let H9 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1
-(Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
-Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))) H2
-d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1
-H8) in (or_introl (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abst) u1)
-(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 (Bind Abst)
-u1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
+u2 a)))))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
+c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Abst) u1)) \to (or (ex2 C
+(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
+g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
+C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
(_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2: C).(eq C (CHead c2
-(Bind Abst) u1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))
-c2 (refl_equal C (CHead c2 (Bind Abst) u1)) H10)))) k H7) u H6)))) H5))
+(a: A).(arity g d2 u2 a))))))))).(\lambda (k: K).(\lambda (u: T).(\lambda
+(H3: (eq C (CHead c1 k u) (CHead d1 (Bind Abst) u1))).(let H4 \def (f_equal C
+C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead c0 _ _)
+\Rightarrow c0])) (CHead c1 k u) (CHead d1 (Bind Abst) u1) H3) in ((let H5
+\def (f_equal C K (\lambda (e: C).(match e with [(CSort _) \Rightarrow k |
+(CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u) (CHead d1 (Bind Abst) u1) H3)
+in ((let H6 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead d1 (Bind
+Abst) u1) H3) in (\lambda (H7: (eq K k (Bind Abst))).(\lambda (H8: (eq C c1
+d1)).(eq_ind_r T u1 (\lambda (t: T).(or (ex2 C (\lambda (d2: C).(eq C (CHead
+c2 k t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3
+C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 k t)
+(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
+g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+A).(arity g d2 u2 a))))))) (eq_ind_r K (Bind Abst) (\lambda (k0: K).(or (ex2
+C (\lambda (d2: C).(eq C (CHead c2 k0 u1) (CHead d2 (Bind Abst) u1)))
+(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(eq C (CHead c2 k0 u1) (CHead d2 (Bind Abbr) u2)))))
+(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))
+(let H9 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abst)
+u1)) \to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1)))
+(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))) H2 d1 H8)
+in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in
+(or_introl (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abst) u1) (CHead d2
+(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 (Bind Abst) u1)
+(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
+g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2: C).(eq C (CHead c2 (Bind
+Abst) u1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) c2
+(refl_equal C (CHead c2 (Bind Abst) u1)) H10)))) k H7) u H6)))) H5))
H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
c2)).(\lambda (_: (((eq C c1 (CHead d1 (Bind Abst) u1)) \to (or (ex2 C
(\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
(a: A).(arity g d2 u2 a))))))))).(\lambda (b: B).(\lambda (_: (not (eq B b
Void))).(\lambda (u0: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind
Void) u0) (CHead d1 (Bind Abst) u1))).(let H5 \def (eq_ind C (CHead c1 (Bind
-Void) u0) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with
-[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).Prop) with [(Bind b0) \Rightarrow (match b0 in B return
-(\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False |
-Void \Rightarrow True]) | (Flat _) \Rightarrow False])])) I (CHead d1 (Bind
-Abst) u1) H4) in (False_ind (or (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind
-b) u2) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3
-C T A (\lambda (d2: C).(\lambda (u3: T).(\lambda (_: A).(eq C (CHead c2 (Bind
-b) u2) (CHead d2 (Bind Abbr) u3))))) (\lambda (d2: C).(\lambda (_:
+Void) u0) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False |
+(CHead _ k _) \Rightarrow (match k with [(Bind b0) \Rightarrow (match b0 with
+[Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]) |
+(Flat _) \Rightarrow False])])) I (CHead d1 (Bind Abst) u1) H4) in (False_ind
+(or (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind b) u2) (CHead d2 (Bind
+Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u3: T).(\lambda (_: A).(eq C (CHead c2 (Bind b) u2) (CHead d2
+(Bind Abbr) u3))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
+d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
+(asucc g a))))) (\lambda (d2: C).(\lambda (u3: T).(\lambda (a: A).(arity g d2
+u3 a)))))) H5))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1:
+(csuba g c1 c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Bind Abst) u1)) \to (or
+(ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
+C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
+(_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u3: T).(\lambda (a: A).(arity g d2 u3 a)))))) H5))))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
-(CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
-a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a))))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H3: (arity g c1 t (asucc
-g a))).(\lambda (u: T).(\lambda (H4: (arity g c2 u a)).(\lambda (H5: (eq C
-(CHead c1 (Bind Abst) t) (CHead d1 (Bind Abst) u1))).(let H6 \def (f_equal C
-C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 (Bind Abst) t)
-(CHead d1 (Bind Abst) u1) H5) in ((let H7 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow t |
-(CHead _ _ t0) \Rightarrow t0])) (CHead c1 (Bind Abst) t) (CHead d1 (Bind
-Abst) u1) H5) in (\lambda (H8: (eq C c1 d1)).(let H9 \def (eq_ind T t
-(\lambda (t0: T).(arity g c1 t0 (asucc g a))) H3 u1 H7) in (let H10 \def
-(eq_ind C c1 (\lambda (c0: C).(arity g c0 u1 (asucc g a))) H9 d1 H8) in (let
-H11 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abst) u1))
-\to (or (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda
-(d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1 (asucc g a0))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2 a0)))))))) H2 d1 H8)
-in (let H12 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in
-(or_intror (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind Abbr) u) (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
+(u2: T).(\lambda (a: A).(arity g d2 u2 a))))))))).(\lambda (t: T).(\lambda
+(a: A).(\lambda (H3: (arity g c1 t (asucc g a))).(\lambda (u: T).(\lambda
+(H4: (arity g c2 u a)).(\lambda (H5: (eq C (CHead c1 (Bind Abst) t) (CHead d1
+(Bind Abst) u1))).(let H6 \def (f_equal C C (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 (Bind
+Abst) t) (CHead d1 (Bind Abst) u1) H5) in ((let H7 \def (f_equal C T (\lambda
+(e: C).(match e with [(CSort _) \Rightarrow t | (CHead _ _ t0) \Rightarrow
+t0])) (CHead c1 (Bind Abst) t) (CHead d1 (Bind Abst) u1) H5) in (\lambda (H8:
+(eq C c1 d1)).(let H9 \def (eq_ind T t (\lambda (t0: T).(arity g c1 t0 (asucc
+g a))) H3 u1 H7) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(arity g c0
+u1 (asucc g a))) H9 d1 H8) in (let H11 \def (eq_ind C c1 (\lambda (c0:
+C).((eq C c0 (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(eq C
+c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
+A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind
+Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
+d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1 (asucc
+g a0))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2
+a0)))))))) H2 d1 H8) in (let H12 \def (eq_ind C c1 (\lambda (c0: C).(csuba g
+c0 c2)) H1 d1 H8) in (or_intror (ex2 C (\lambda (d2: C).(eq C (CHead c2 (Bind
+Abbr) u) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead
+c2 (Bind Abbr) u) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
+T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
+T).(\lambda (a0: A).(arity g d1 u1 (asucc g a0))))) (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (a0: A).(arity g d2 u2 a0))))) (ex4_3_intro C T A (\lambda
(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c2 (Bind Abbr) u)
(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity
g d1 u1 (asucc g a0))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0:
-A).(arity g d2 u2 a0))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(eq C (CHead c2 (Bind Abbr) u) (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1 (asucc g
-a0))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2
-a0)))) c2 u a (refl_equal C (CHead c2 (Bind Abbr) u)) H12 H10 H4))))))))
-H6)))))))))))) y c H0))) H))))).
-(* COMMENTS
-Initial nodes: 2550
-END *)
+A).(arity g d2 u2 a0)))) c2 u a (refl_equal C (CHead c2 (Bind Abbr) u)) H12
+H10 H4)))))))) H6)))))))))))) y c H0))) H))))).
theorem csuba_gen_flat:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).(\forall
(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
d2))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Flat f)
-u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Flat f) u1) H1) in (False_ind (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Flat f) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2)))) H2)))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c1
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
-(CHead d1 (Flat f) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c1 k u) (CHead d1 (Flat f) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k
-u) (CHead d1 (Flat f) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead d1 (Flat f) u1) H3) in
-(\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r T u1
-(\lambda (t: T).(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2
-k t) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))) (eq_ind_r K (Flat f) (\lambda (k0: K).(ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c2 k0 u1) (CHead d2 (Flat f) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d1 d2))))) (let H9 \def (eq_ind C c1
-(\lambda (c0: C).((eq C c0 (CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d1 d2)))))) H2 d1 H8) in (let H10 \def (eq_ind C
-c1 (\lambda (c0: C).(csuba g c0 c2)) H1 d1 H8) in (ex2_2_intro C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C (CHead c2 (Flat f) u1) (CHead d2 (Flat f)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))) c2 u1 (refl_equal C
-(CHead c2 (Flat f) u1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c1
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
-d2))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u0:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u0) (CHead d1
-(Flat f) u1))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u0) (\lambda (ee:
-C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop)
-with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1
-(Flat f) u1) H4) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u3:
-T).(eq C (CHead c2 (Bind b) u2) (CHead d2 (Flat f) u3)))) (\lambda (d2:
+u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1
+(Flat f) u1) H1) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
+T).(eq C (CSort n) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d1 d2)))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1:
+(csuba g c1 c2)).(\lambda (H2: (((eq C c1 (CHead d1 (Flat f) u1)) \to (ex2_2
+C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))))).(\lambda (k:
+K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u) (CHead d1 (Flat f)
+u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c0 _ _) \Rightarrow c0])) (CHead c1 k u) (CHead d1
+(Flat f) u1) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u)
+(CHead d1 (Flat f) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
+(CHead c1 k u) (CHead d1 (Flat f) u1) H3) in (\lambda (H7: (eq K k (Flat
+f))).(\lambda (H8: (eq C c1 d1)).(eq_ind_r T u1 (\lambda (t: T).(ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2 k t) (CHead d2 (Flat f)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))) (eq_ind_r K (Flat
+f) (\lambda (k0: K).(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead
+c2 k0 u1) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
+d1 d2))))) (let H9 \def (eq_ind C c1 (\lambda (c0: C).((eq C c0 (CHead d1
+(Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2
+(CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1
+d2)))))) H2 d1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c0: C).(csuba g c0
+c2)) H1 d1 H8) in (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(eq C
+(CHead c2 (Flat f) u1) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d1 d2))) c2 u1 (refl_equal C (CHead c2 (Flat f) u1)) H10))) k
+H7) u H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_:
+(csuba g c1 c2)).(\lambda (_: (((eq C c1 (CHead d1 (Flat f) u1)) \to (ex2_2 C
+T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))))).(\lambda (b:
+B).(\lambda (_: (not (eq B b Void))).(\lambda (u0: T).(\lambda (u2:
+T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u0) (CHead d1 (Flat f)
+u1))).(let H5 \def (eq_ind C (CHead c1 (Bind Void) u0) (\lambda (ee:
+C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow
+(match k with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I
+(CHead d1 (Flat f) u1) H4) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda
+(u3: T).(eq C (CHead c2 (Bind b) u2) (CHead d2 (Flat f) u3)))) (\lambda (d2:
C).(\lambda (_: T).(csuba g d1 d2)))) H5))))))))))) (\lambda (c1: C).(\lambda
(c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c1 (CHead d1 (Flat
f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2
d2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g
a))).(\lambda (u: T).(\lambda (_: (arity g c2 u a)).(\lambda (H5: (eq C
(CHead c1 (Bind Abst) t) (CHead d1 (Flat f) u1))).(let H6 \def (eq_ind C
-(CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat
-_) \Rightarrow False])])) I (CHead d1 (Flat f) u1) H5) in (False_ind (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c2 (Bind Abbr) u) (CHead d2
-(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d1 d2))))
-H6)))))))))))) y c H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1183
-END *)
+(CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1 (Flat f) u1)
+H5) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead
+c2 (Bind Abbr) u) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d1 d2)))) H6)))))))))))) y c H0))) H)))))).
theorem csuba_gen_bind:
\forall (g: G).(\forall (b1: B).(\forall (e1: C).(\forall (c2: C).(\forall
T).(eq C c0 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
C).(\lambda (_: T).(csuba g e1 e2)))))))) (\lambda (n: nat).(\lambda (H1: (eq
C (CSort n) (CHead e1 (Bind b1) v1))).(let H2 \def (eq_ind C (CSort n)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Bind b1)
-v1) H1) in (False_ind (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C (CSort n) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e1 e2))))) H2)))) (\lambda (c1: C).(\lambda
-(c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1
-(Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e1 e2)))))))).(\lambda (k: K).(\lambda (u:
-T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Bind b1) v1))).(let H4 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k u)
-(CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
-C).(match e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k |
-(CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u) (CHead e1 (Bind b1) v1) H3)
-in ((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
-(CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7: (eq K k (Bind
-b1))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v1 (\lambda (t: T).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k t)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))))) (eq_ind_r K (Bind b1) (\lambda (k0: K).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 k0 v1)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))))) (let H9 \def (eq_ind C c1 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1 H8) in (let
-H10 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H8) in
-(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
-(CHead c3 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e1 e2)))) b1 c3 v1 (refl_equal C (CHead c3
-(Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow True | (CHead _ _ _)
+\Rightarrow False])) I (CHead e1 (Bind b1) v1) H1) in (False_ind (ex2_3 B C T
+(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CSort n) (CHead e2
+(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
+e1 e2))))) H2)))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1: (csuba g c1
+c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T
+(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind
+b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1
+e2)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u)
+(CHead e1 (Bind b1) v1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 k
+u) (CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
+(CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in ((let H6 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t)
+\Rightarrow t])) (CHead c1 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7:
+(eq K k (Bind b1))).(\lambda (H8: (eq C c1 e1)).(eq_ind_r T v1 (\lambda (t:
+T).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c3 k t) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csuba g e1 e2)))))) (eq_ind_r K (Bind b1) (\lambda (k0:
+K).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c3 k0 v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csuba g e1 e2)))))) (let H9 \def (eq_ind C c1 (\lambda
+(c: C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
+B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2)))))
+(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1
+H8) in (let H10 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H8)
+in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq
+C (CHead c3 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2)))) b1 c3 v1 (refl_equal C
+(CHead c3 (Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
C).(\lambda (c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c1
(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2)))))))).(\lambda (b:
B).(\lambda (_: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2:
T).(\lambda (H4: (eq C (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1)
-v1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c]))
-(CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H6 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Void | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow
-Void])])) (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H7
-\def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T)
-with [(CSort _) \Rightarrow u1 | (CHead _ _ t) \Rightarrow t])) (CHead c1
-(Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in (\lambda (H8: (eq B Void
-b1)).(\lambda (H9: (eq C c1 e1)).(let H10 \def (eq_ind C c1 (\lambda (c:
-C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2)))))
-(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1
-H9) in (let H11 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H9)
-in (let H12 \def (eq_ind_r B b1 (\lambda (b0: B).((eq C e1 (CHead e1 (Bind
-b0) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
+v1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 (Bind Void) u1)
+(CHead e1 (Bind b1) v1) H4) in ((let H6 \def (f_equal C B (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow Void | (CHead _ k _) \Rightarrow
+(match k with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Void])]))
+(CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4) in ((let H7 \def
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u1 | (CHead
+_ _ t) \Rightarrow t])) (CHead c1 (Bind Void) u1) (CHead e1 (Bind b1) v1) H4)
+in (\lambda (H8: (eq B Void b1)).(\lambda (H9: (eq C c1 e1)).(let H10 \def
+(eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C
+T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind
+b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1
+e2))))))) H2 e1 H9) in (let H11 \def (eq_ind C c1 (\lambda (c: C).(csuba g c
+c3)) H1 e1 H9) in (let H12 \def (eq_ind_r B b1 (\lambda (b0: B).((eq C e1
+(CHead e1 (Bind b0) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
+C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H10 Void H8) in
+(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c3 (Bind b) u2) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
+(e2: C).(\lambda (_: T).(csuba g e1 e2)))) b c3 u2 (refl_equal C (CHead c3
+(Bind b) u2)) H11))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3:
+C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind
+b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e1 e2))))))) H10 Void H8) in (ex2_3_intro B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind b)
-u2) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2)))) b c3 u2 (refl_equal C (CHead c3 (Bind b) u2))
-H11))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csuba g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1 (Bind b1) v1)) \to (ex2_3
-B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
-e1 e2)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H3: (arity g c1 t
-(asucc g a))).(\lambda (u: T).(\lambda (_: (arity g c3 u a)).(\lambda (H5:
-(eq C (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1))).(let H6 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
+C).(\lambda (_: T).(csuba g e1 e2)))))))).(\lambda (t: T).(\lambda (a:
+A).(\lambda (H3: (arity g c1 t (asucc g a))).(\lambda (u: T).(\lambda (_:
+(arity g c3 u a)).(\lambda (H5: (eq C (CHead c1 (Bind Abst) t) (CHead e1
+(Bind b1) v1))).(let H6 \def (f_equal C C (\lambda (e: C).(match e with
[(CSort _) \Rightarrow c1 | (CHead c _ _) \Rightarrow c])) (CHead c1 (Bind
Abst) t) (CHead e1 (Bind b1) v1) H5) in ((let H7 \def (f_equal C B (\lambda
-(e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow
-Abst | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with
-[(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead c1 (Bind
-Abst) t) (CHead e1 (Bind b1) v1) H5) in ((let H8 \def (f_equal C T (\lambda
-(e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow t
-| (CHead _ _ t0) \Rightarrow t0])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind
-b1) v1) H5) in (\lambda (H9: (eq B Abst b1)).(\lambda (H10: (eq C c1
-e1)).(let H11 \def (eq_ind T t (\lambda (t0: T).(arity g c1 t0 (asucc g a)))
-H3 v1 H8) in (let H12 \def (eq_ind C c1 (\lambda (c: C).(arity g c v1 (asucc
-g a))) H11 e1 H10) in (let H13 \def (eq_ind C c1 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))))) H2 e1 H10) in (let
-H14 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c3)) H1 e1 H10) in (let H15
-\def (eq_ind_r B b1 (\lambda (b: B).((eq C e1 (CHead e1 (Bind b) v1)) \to
-(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e1 e2))))))) H13 Abst H9) in (ex2_3_intro B C T (\lambda (b2:
-B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c3 (Bind Abbr) u) (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
-e1 e2)))) Abbr c3 u (refl_equal C (CHead c3 (Bind Abbr) u)) H14))))))))) H7))
+(e: C).(match e with [(CSort _) \Rightarrow Abst | (CHead _ k _) \Rightarrow
+(match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abst])])) (CHead
+c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5) in ((let H8 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow t | (CHead _ _ t0)
+\Rightarrow t0])) (CHead c1 (Bind Abst) t) (CHead e1 (Bind b1) v1) H5) in
+(\lambda (H9: (eq B Abst b1)).(\lambda (H10: (eq C c1 e1)).(let H11 \def
+(eq_ind T t (\lambda (t0: T).(arity g c1 t0 (asucc g a))) H3 v1 H8) in (let
+H12 \def (eq_ind C c1 (\lambda (c: C).(arity g c v1 (asucc g a))) H11 e1 H10)
+in (let H13 \def (eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Bind b1)
+v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq
+C c3 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda
+(_: T).(csuba g e1 e2))))))) H2 e1 H10) in (let H14 \def (eq_ind C c1
+(\lambda (c: C).(csuba g c c3)) H1 e1 H10) in (let H15 \def (eq_ind_r B b1
+(\lambda (b: B).((eq C e1 (CHead e1 (Bind b) v1)) \to (ex2_3 B C T (\lambda
+(b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c3 (CHead e2 (Bind b2)
+v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1
+e2))))))) H13 Abst H9) in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2:
+C).(\lambda (v2: T).(eq C (CHead c3 (Bind Abbr) u) (CHead e2 (Bind b2)
+v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e1 e2))))
+Abbr c3 u (refl_equal C (CHead c3 (Bind Abbr) u)) H14))))))))) H7))
H6)))))))))))) y c2 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1889
-END *)
theorem csuba_gen_abst_rev:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u: T).((csuba g c
(\lambda (d2: C).(\lambda (u2: T).(eq C c0 (CHead d2 (Bind Void) u2))))
(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (n:
nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Abst) u))).(let H2 \def
-(eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Bind Abst) u) H1) in (False_ind (or (ex2 C (\lambda
-(d2: C).(eq C (CSort n) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g
-d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead
-d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
-H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Abst) u)) \to (or (ex2 C
-(\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba
-g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c2 k
-u0) (CHead d1 (Bind Abst) u))).(let H4 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 |
-(CHead c0 _ _) \Rightarrow c0])) (CHead c2 k u0) (CHead d1 (Bind Abst) u) H3)
-in ((let H5 \def (f_equal C K (\lambda (e: C).(match e in C return (\lambda
-(_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
-(CHead c2 k u0) (CHead d1 (Bind Abst) u) H3) in ((let H6 \def (f_equal C T
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _)
+(eq_ind C (CSort n) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow
+True | (CHead _ _ _) \Rightarrow False])) I (CHead d1 (Bind Abst) u) H1) in
+(False_ind (or (ex2 C (\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind Abst)
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(eq C (CSort n) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1))))) H2)))) (\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind
+Abst) u)) \to (or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u)))
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
+T).(eq C c1 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq
+C (CHead c2 k u0) (CHead d1 (Bind Abst) u))).(let H4 \def (f_equal C C
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _)
+\Rightarrow c0])) (CHead c2 k u0) (CHead d1 (Bind Abst) u) H3) in ((let H5
+\def (f_equal C K (\lambda (e: C).(match e with [(CSort _) \Rightarrow k |
+(CHead _ k0 _) \Rightarrow k0])) (CHead c2 k u0) (CHead d1 (Bind Abst) u) H3)
+in ((let H6 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
\Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead c2 k u0) (CHead d1
(Bind Abst) u) H3) in (\lambda (H7: (eq K k (Bind Abst))).(\lambda (H8: (eq C
c2 d1)).(eq_ind_r T u (\lambda (t: T).(or (ex2 C (\lambda (d2: C).(eq C
C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (b: B).(\lambda (H3: (not
(eq B b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead
c2 (Bind b) u2) (CHead d1 (Bind Abst) u))).(let H5 \def (f_equal C C (\lambda
-(e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2
-| (CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead d1 (Bind
-Abst) u) H4) in ((let H6 \def (f_equal C B (\lambda (e: C).(match e in C
-return (\lambda (_: C).B) with [(CSort _) \Rightarrow b | (CHead _ k _)
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b0)
-\Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c2 (Bind b) u2) (CHead d1
-(Bind Abst) u) H4) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e in
-C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t)
-\Rightarrow t])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abst) u) H4) in
-(\lambda (H8: (eq B b Abst)).(\lambda (H9: (eq C c2 d1)).(let H10 \def
-(eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 Abst H8) in (let H11
-\def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abst) u)) \to
-(or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C c1
-(CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))) H2 d1 H9) in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g
-c1 c0)) H1 d1 H9) in (or_intror (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind
-Void) u1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c1 (Bind Void) u1)
-(CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c1
-(Bind Void) u1) (CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))) c1 u1 (refl_equal C (CHead c1 (Bind Void) u1))
-H12)))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_:
-(csuba g c1 c2)).(\lambda (_: (((eq C c2 (CHead d1 (Bind Abst) u)) \to (or
-(ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc
-g a))).(\lambda (u0: T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C
-(CHead c2 (Bind Abbr) u0) (CHead d1 (Bind Abst) u))).(let H6 \def (eq_ind C
-(CHead c2 (Bind Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
-return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow
-False | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead
-d1 (Bind Abst) u) H5) in (False_ind (or (ex2 C (\lambda (d2: C).(eq C (CHead
-c1 (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
-d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 (Bind
-Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba
-g d2 d1))))) H6)))))))))))) c y H0))) H))))).
-(* COMMENTS
-Initial nodes: 1980
-END *)
+(e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow
+c0])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abst) u) H4) in ((let H6 \def
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow b | (CHead
+_ k _) \Rightarrow (match k with [(Bind b0) \Rightarrow b0 | (Flat _)
+\Rightarrow b])])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abst) u) H4) in
+((let H7 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c2 (Bind b) u2) (CHead
+d1 (Bind Abst) u) H4) in (\lambda (H8: (eq B b Abst)).(\lambda (H9: (eq C c2
+d1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 Abst
+H8) in (let H11 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind
+Abst) u)) \to (or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abst) u)))
+(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3:
+T).(eq C c1 (CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))))) H2 d1 H9) in (let H12 \def (eq_ind C c2 (\lambda
+(c0: C).(csuba g c1 c0)) H1 d1 H9) in (or_intror (ex2 C (\lambda (d2: C).(eq
+C (CHead c1 (Bind Void) u1) (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C
+(CHead c1 (Bind Void) u1) (CHead d2 (Bind Void) u3)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2:
+C).(\lambda (u3: T).(eq C (CHead c1 (Bind Void) u1) (CHead d2 (Bind Void)
+u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) c1 u1 (refl_equal C
+(CHead c1 (Bind Void) u1)) H12)))))))) H6)) H5))))))))))) (\lambda (c1:
+C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c2
+(CHead d1 (Bind Abst) u)) \to (or (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (t: T).(\lambda (a:
+A).(\lambda (_: (arity g c1 t (asucc g a))).(\lambda (u0: T).(\lambda (_:
+(arity g c2 u0 a)).(\lambda (H5: (eq C (CHead c2 (Bind Abbr) u0) (CHead d1
+(Bind Abst) u))).(let H6 \def (eq_ind C (CHead c2 (Bind Abbr) u0) (\lambda
+(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) I (CHead d1 (Bind Abst) u) H5) in (False_ind (or
+(ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Abst) t) (CHead d2 (Bind Abst)
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(eq C (CHead c1 (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda
+(d2: C).(\lambda (_: T).(csuba g d2 d1))))) H6)))))))))))) c y H0))) H))))).
theorem csuba_gen_void_rev:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u: T).((csuba g c
(c1: C).((eq C c1 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C
c0 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))))) (\lambda
(n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind Void) u))).(let H2
-\def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow
-False])) I (CHead d1 (Bind Void) u) H1) in (False_ind (ex2 C (\lambda (d2:
-C).(eq C (CSort n) (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1)))))).(\lambda (k: K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c2 k u0)
-(CHead d1 (Bind Void) u))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c2 k u0) (CHead d1 (Bind Void) u) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
+\def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1 (Bind Void)
+u) H1) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind
+Void) u))) (\lambda (d2: C).(csuba g d2 d1))) H2)))) (\lambda (c1:
+C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2
+(CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2
+(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))))).(\lambda (k:
+K).(\lambda (u0: T).(\lambda (H3: (eq C (CHead c2 k u0) (CHead d1 (Bind Void)
+u))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) (CHead c2 k u0) (CHead d1
+(Bind Void) u) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e
with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k
u0) (CHead d1 (Bind Void) u) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 |
-(CHead _ _ t) \Rightarrow t])) (CHead c2 k u0) (CHead d1 (Bind Void) u) H3)
-in (\lambda (H7: (eq K k (Bind Void))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r
-T u (\lambda (t: T).(ex2 C (\lambda (d2: C).(eq C (CHead c1 k t) (CHead d2
-(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) (eq_ind_r K (Bind Void)
-(\lambda (k0: K).(ex2 C (\lambda (d2: C).(eq C (CHead c1 k0 u) (CHead d2
-(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) (let H9 \def (eq_ind C
-c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1))))) H2 d1 H8) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1
-c0)) H1 d1 H8) in (ex_intro2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void)
-u) (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)) c1
-(refl_equal C (CHead c1 (Bind Void) u)) H10))) k H7) u0 H6)))) H5))
-H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
-c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1)))))).(\lambda (b: B).(\lambda (H3: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1
-(Bind Void) u))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _)
-\Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in
-((let H6 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_:
-C).B) with [(CSort _) \Rightarrow b | (CHead _ k _) \Rightarrow (match k in K
-return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
+C).(match e with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t]))
+(CHead c2 k u0) (CHead d1 (Bind Void) u) H3) in (\lambda (H7: (eq K k (Bind
+Void))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r T u (\lambda (t: T).(ex2 C
+(\lambda (d2: C).(eq C (CHead c1 k t) (CHead d2 (Bind Void) u))) (\lambda
+(d2: C).(csuba g d2 d1)))) (eq_ind_r K (Bind Void) (\lambda (k0: K).(ex2 C
+(\lambda (d2: C).(eq C (CHead c1 k0 u) (CHead d2 (Bind Void) u))) (\lambda
+(d2: C).(csuba g d2 d1)))) (let H9 \def (eq_ind C c2 (\lambda (c0: C).((eq C
+c0 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2
+(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1))))) H2 d1 H8) in (let H10
+\def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H8) in (ex_intro2 C
+(\lambda (d2: C).(eq C (CHead c1 (Bind Void) u) (CHead d2 (Bind Void) u)))
+(\lambda (d2: C).(csuba g d2 d1)) c1 (refl_equal C (CHead c1 (Bind Void) u))
+H10))) k H7) u0 H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind
+Void) u)) \to (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Void) u)))
+(\lambda (d2: C).(csuba g d2 d1)))))).(\lambda (b: B).(\lambda (H3: (not (eq
+B b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c2
+(Bind b) u2) (CHead d1 (Bind Void) u))).(let H5 \def (f_equal C C (\lambda
+(e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow
+c0])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in ((let H6 \def
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow b | (CHead
+_ k _) \Rightarrow (match k with [(Bind b0) \Rightarrow b0 | (Flat _)
\Rightarrow b])])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in
-((let H7 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
-C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead
-c2 (Bind b) u2) (CHead d1 (Bind Void) u) H4) in (\lambda (H8: (eq B b
-Void)).(\lambda (H9: (eq C c2 d1)).(let H10 \def (eq_ind B b (\lambda (b0:
-B).(not (eq B b0 Void))) H3 Void H8) in (let H11 \def (eq_ind C c2 (\lambda
-(c0: C).((eq C c0 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C
-c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1))))) H2 d1 H9)
-in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H9) in
-(let H13 \def (match (H10 (refl_equal B Void)) in False return (\lambda (_:
-False).(ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void) u1) (CHead d2
-(Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))) with []) in H13)))))))
-H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1
-c2)).(\lambda (_: (((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda
-(d2: C).(eq C c1 (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2
-d1)))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g
-a))).(\lambda (u0: T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C
-(CHead c2 (Bind Abbr) u0) (CHead d1 (Bind Void) u))).(let H6 \def (eq_ind C
-(CHead c2 (Bind Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B
-return (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow
-False | Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead
-d1 (Bind Void) u) H5) in (False_ind (ex2 C (\lambda (d2: C).(eq C (CHead c1
-(Bind Abst) t) (CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))
-H6)))))))))))) c y H0))) H))))).
-(* COMMENTS
-Initial nodes: 1326
-END *)
+((let H7 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c2 (Bind b) u2) (CHead
+d1 (Bind Void) u) H4) in (\lambda (H8: (eq B b Void)).(\lambda (H9: (eq C c2
+d1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 Void
+H8) in (let H11 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind
+Void) u)) \to (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Void) u)))
+(\lambda (d2: C).(csuba g d2 d1))))) H2 d1 H9) in (let H12 \def (eq_ind C c2
+(\lambda (c0: C).(csuba g c1 c0)) H1 d1 H9) in (let H13 \def (match (H10
+(refl_equal B Void)) in False with []) in H13))))))) H6)) H5)))))))))))
+(\lambda (c1: C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_:
+(((eq C c2 (CHead d1 (Bind Void) u)) \to (ex2 C (\lambda (d2: C).(eq C c1
+(CHead d2 (Bind Void) u))) (\lambda (d2: C).(csuba g d2 d1)))))).(\lambda (t:
+T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g a))).(\lambda (u0:
+T).(\lambda (_: (arity g c2 u0 a)).(\lambda (H5: (eq C (CHead c2 (Bind Abbr)
+u0) (CHead d1 (Bind Void) u))).(let H6 \def (eq_ind C (CHead c2 (Bind Abbr)
+u0) (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k
+_) \Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
+\Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat
+_) \Rightarrow False])])) I (CHead d1 (Bind Void) u) H5) in (False_ind (ex2 C
+(\lambda (d2: C).(eq C (CHead c1 (Bind Abst) t) (CHead d2 (Bind Void) u)))
+(\lambda (d2: C).(csuba g d2 d1))) H6)))))))))))) c y H0))) H))))).
theorem csuba_gen_abbr_rev:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).((csuba g c
(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
C c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
d2 d1)))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Bind
-Abbr) u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C
-return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Bind Abbr) u1) H1) in (False_ind (or3 (ex2
-C (\lambda (d2: C).(eq C (CSort n) (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
-(_: A).(eq C (CSort n) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) H2)))) (\lambda
-(c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C
-c2 (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1
-(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind
-Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
-d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
+Abbr) u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1
+(Bind Abbr) u1) H1) in (False_ind (or3 (ex2 C (\lambda (d2: C).(eq C (CSort
+n) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T
+A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CSort n) (CHead d2
+(Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
+d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
(asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
-u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c2 k u)
-(CHead d1 (Bind Abbr) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match
-e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c2 k u) (CHead d1 (Bind Abbr) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k
-u) (CHead d1 (Bind Abbr) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
+H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1: (csuba g c1
+c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C
+(\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
+g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
+C c1 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
+(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
+C c1 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
+d2 d1)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c2 k
+u) (CHead d1 (Bind Abbr) u1))).(let H4 \def (f_equal C C (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0]))
+(CHead c2 k u) (CHead d1 (Bind Abbr) u1) H3) in ((let H5 \def (f_equal C K
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow k | (CHead _ k0 _)
+\Rightarrow k0])) (CHead c2 k u) (CHead d1 (Bind Abbr) u1) H3) in ((let H6
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u |
(CHead _ _ t) \Rightarrow t])) (CHead c2 k u) (CHead d1 (Bind Abbr) u1) H3)
in (\lambda (H7: (eq K k (Bind Abbr))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r
T u1 (\lambda (t: T).(or3 (ex2 C (\lambda (d2: C).(eq C (CHead c1 k t) (CHead
u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (b:
B).(\lambda (H3: (not (eq B b Void))).(\lambda (u0: T).(\lambda (u2:
T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr)
-u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0]))
-(CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr) u1) H4) in ((let H6 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow b | (CHead _ k _) \Rightarrow (match k in K return
-(\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow
-b])])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr) u1) H4) in ((let H7 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c2 (Bind b)
-u2) (CHead d1 (Bind Abbr) u1) H4) in (\lambda (H8: (eq B b Abbr)).(\lambda
-(H9: (eq C c2 d1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0
-Void))) H3 Abbr H8) in (let H11 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u3: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u3))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u3: T).(\lambda (a: A).(arity g d2 u3 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C c1 (CHead d2 (Bind Void)
-u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))) H2 d1 H9) in
-(let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H9) in
-(or3_intro2 (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void) u0) (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u3: T).(\lambda (_: A).(eq C (CHead c1 (Bind Void) u0)
-(CHead d2 (Bind Abst) u3))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u3: T).(\lambda (a:
-A).(arity g d2 u3 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq
+u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind b) u2)
+(CHead d1 (Bind Abbr) u1) H4) in ((let H6 \def (f_equal C B (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow b | (CHead _ k _) \Rightarrow (match
+k with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c2
+(Bind b) u2) (CHead d1 (Bind Abbr) u1) H4) in ((let H7 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow u2 | (CHead _ _ t)
+\Rightarrow t])) (CHead c2 (Bind b) u2) (CHead d1 (Bind Abbr) u1) H4) in
+(\lambda (H8: (eq B b Abbr)).(\lambda (H9: (eq C c2 d1)).(let H10 \def
+(eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 Abbr H8) in (let H11
+\def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1 (Bind Abbr) u1)) \to
+(or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abbr) u1))) (\lambda
+(d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u3:
+T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst) u3))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+C).(\lambda (u3: T).(\lambda (a: A).(arity g d2 u3 (asucc g a))))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u3: T).(eq C c1 (CHead d2 (Bind Void) u3))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))) H2 d1 H9) in (let H12
+\def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H9) in (or3_intro2
+(ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Void) u0) (CHead d2 (Bind Abbr)
+u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u3: T).(\lambda (_: A).(eq C (CHead c1 (Bind Void) u0) (CHead d2
+(Bind Abst) u3))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
+d2 d1)))) (\lambda (d2: C).(\lambda (u3: T).(\lambda (a: A).(arity g d2 u3
+(asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
+u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C (CHead c1 (Bind
+Void) u0) (CHead d2 (Bind Void) u3)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u3: T).(eq
C (CHead c1 (Bind Void) u0) (CHead d2 (Bind Void) u3)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2:
-C).(\lambda (u3: T).(eq C (CHead c1 (Bind Void) u0) (CHead d2 (Bind Void)
-u3)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) c1 u0 (refl_equal C
-(CHead c1 (Bind Void) u0)) H12)))))))) H6)) H5))))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
-a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (t:
+C).(\lambda (_: T).(csuba g d2 d1))) c1 u0 (refl_equal C (CHead c1 (Bind
+Void) u0)) H12)))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c2:
+C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Bind
+Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead d2 (Bind Abbr)
+u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst) u2)))))
+(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
+(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
+C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))).(\lambda (t:
T).(\lambda (a: A).(\lambda (H3: (arity g c1 t (asucc g a))).(\lambda (u:
T).(\lambda (H4: (arity g c2 u a)).(\lambda (H5: (eq C (CHead c2 (Bind Abbr)
u) (CHead d1 (Bind Abbr) u1))).(let H6 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 |
-(CHead c0 _ _) \Rightarrow c0])) (CHead c2 (Bind Abbr) u) (CHead d1 (Bind
-Abbr) u1) H5) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e in C
-return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0)
-\Rightarrow t0])) (CHead c2 (Bind Abbr) u) (CHead d1 (Bind Abbr) u1) H5) in
-(\lambda (H8: (eq C c2 d1)).(let H9 \def (eq_ind T u (\lambda (t0: T).(arity
-g c2 t0 a)) H4 u1 H7) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(arity g
-c0 u1 a)) H9 d1 H8) in (let H11 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0
-(CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq C c1 (CHead
-d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2 (Bind Abst)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2 (asucc g
-a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1 u1
-a0))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Bind
-Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))) H2 d1 H8)
-in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H8) in
-(or3_intro1 (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Abst) t) (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c1 (Bind Abst) t)
-(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
-A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0:
+C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0]))
+(CHead c2 (Bind Abbr) u) (CHead d1 (Bind Abbr) u1) H5) in ((let H7 \def
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead
+_ _ t0) \Rightarrow t0])) (CHead c2 (Bind Abbr) u) (CHead d1 (Bind Abbr) u1)
+H5) in (\lambda (H8: (eq C c2 d1)).(let H9 \def (eq_ind T u (\lambda (t0:
+T).(arity g c2 t0 a)) H4 u1 H7) in (let H10 \def (eq_ind C c2 (\lambda (c0:
+C).(arity g c0 u1 a)) H9 d1 H8) in (let H11 \def (eq_ind C c2 (\lambda (c0:
+C).((eq C c0 (CHead d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(eq
+C c1 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C
+T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c1 (CHead d2
+(Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
+d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0: A).(arity g d2 u2
+(asucc g a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1
+u1 a0))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))) H2
+d1 H8) in (let H12 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1
+H8) in (or3_intro1 (ex2 C (\lambda (d2: C).(eq C (CHead c1 (Bind Abst) t)
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C (CHead c1 (Bind Abst)
+t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
+(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a0:
A).(arity g d2 u2 (asucc g a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda
(a0: A).(arity g d1 u1 a0))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
T).(eq C (CHead c1 (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
(asucc g a0))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a0: A).(arity g d1
u1 a0)))) c1 t a (refl_equal C (CHead c1 (Bind Abst) t)) H12 H3 H10))))))))
H6)))))))))))) c y H0))) H))))).
-(* COMMENTS
-Initial nodes: 3459
-END *)
theorem csuba_gen_flat_rev:
\forall (g: G).(\forall (d1: C).(\forall (c: C).(\forall (u1: T).(\forall
(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
C c0 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
d1))))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead d1 (Flat f)
-u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee in C return
-(\lambda (_: C).Prop) with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) I (CHead d1 (Flat f) u1) H1) in (False_ind (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(eq C (CSort n) (CHead d2 (Flat f) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) H2)))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (H1: (csuba g c1 c2)).(\lambda (H2: (((eq C c2
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c2 k u)
-(CHead d1 (Flat f) u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
-in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _
-_) \Rightarrow c0])) (CHead c2 k u) (CHead d1 (Flat f) u1) H3) in ((let H5
-\def (f_equal C K (\lambda (e: C).(match e in C return (\lambda (_: C).K)
-with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k
-u) (CHead d1 (Flat f) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u |
-(CHead _ _ t) \Rightarrow t])) (CHead c2 k u) (CHead d1 (Flat f) u1) H3) in
-(\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r T u1
-(\lambda (t: T).(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1
-k t) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))) (eq_ind_r K (Flat f) (\lambda (k0: K).(ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C (CHead c1 k0 u1) (CHead d2 (Flat f) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (let H9 \def (eq_ind C c2
-(\lambda (c0: C).((eq C c0 (CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))))) H2 d1 H8) in (let H10 \def (eq_ind C
-c2 (\lambda (c0: C).(csuba g c1 c0)) H1 d1 H8) in (ex2_2_intro C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C (CHead c1 (Flat f) u1) (CHead d2 (Flat f)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) c1 u1 (refl_equal C
-(CHead c1 (Flat f) u1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
-C).(\lambda (c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c2
-(CHead d1 (Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq
-C c1 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1))))))).(\lambda (b: B).(\lambda (_: (not (eq B b Void))).(\lambda (u0:
-T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1
-(Flat f) u1))).(let H5 \def (eq_ind C (CHead c2 (Bind b) u2) (\lambda (ee:
-C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow
-False | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop)
-with [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1
-(Flat f) u1) H4) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u3:
-T).(eq C (CHead c1 (Bind Void) u0) (CHead d2 (Flat f) u3)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) H5))))))))))) (\lambda (c1: C).(\lambda
-(c2: C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c2 (CHead d1 (Flat
-f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
+u1))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead d1
+(Flat f) u1) H1) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
+T).(eq C (CSort n) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))) H2)))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (H1:
+(csuba g c1 c2)).(\lambda (H2: (((eq C c2 (CHead d1 (Flat f) u1)) \to (ex2_2
+C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Flat f) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))).(\lambda (k:
+K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c2 k u) (CHead d1 (Flat f)
+u1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0])) (CHead c2 k u) (CHead d1
+(Flat f) u1) H3) in ((let H5 \def (f_equal C K (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c2 k u)
+(CHead d1 (Flat f) u1) H3) in ((let H6 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
+(CHead c2 k u) (CHead d1 (Flat f) u1) H3) in (\lambda (H7: (eq K k (Flat
+f))).(\lambda (H8: (eq C c2 d1)).(eq_ind_r T u1 (\lambda (t: T).(ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 k t) (CHead d2 (Flat f)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (eq_ind_r K (Flat
+f) (\lambda (k0: K).(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead
+c1 k0 u1) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
+d2 d1))))) (let H9 \def (eq_ind C c2 (\lambda (c0: C).((eq C c0 (CHead d1
+(Flat f) u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1
+(CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1)))))) H2 d1 H8) in (let H10 \def (eq_ind C c2 (\lambda (c0: C).(csuba g c1
+c0)) H1 d1 H8) in (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(eq C
+(CHead c1 (Flat f) u1) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d2 d1))) c1 u1 (refl_equal C (CHead c1 (Flat f) u1)) H10))) k
+H7) u H6)))) H5)) H4))))))))) (\lambda (c1: C).(\lambda (c2: C).(\lambda (_:
+(csuba g c1 c2)).(\lambda (_: (((eq C c2 (CHead d1 (Flat f) u1)) \to (ex2_2 C
+T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2 (Flat f) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))).(\lambda (b:
+B).(\lambda (_: (not (eq B b Void))).(\lambda (u0: T).(\lambda (u2:
+T).(\lambda (H4: (eq C (CHead c2 (Bind b) u2) (CHead d1 (Flat f) u1))).(let
+H5 \def (eq_ind C (CHead c2 (Bind b) u2) (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind
+_) \Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1 (Flat f)
+u1) H4) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u3: T).(eq C
+(CHead c1 (Bind Void) u0) (CHead d2 (Flat f) u3)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d2 d1)))) H5))))))))))) (\lambda (c1: C).(\lambda (c2:
+C).(\lambda (_: (csuba g c1 c2)).(\lambda (_: (((eq C c2 (CHead d1 (Flat f)
+u1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c1 (CHead d2
(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
d1))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g
a))).(\lambda (u: T).(\lambda (_: (arity g c2 u a)).(\lambda (H5: (eq C
(CHead c2 (Bind Abbr) u) (CHead d1 (Flat f) u1))).(let H6 \def (eq_ind C
-(CHead c2 (Bind Abbr) u) (\lambda (ee: C).(match ee in C return (\lambda (_:
-C).Prop) with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match
-k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat
-_) \Rightarrow False])])) I (CHead d1 (Flat f) u1) H5) in (False_ind (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead c1 (Bind Abst) t) (CHead d2
-(Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))
-H6)))))))))))) c y H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1183
-END *)
+(CHead c2 (Bind Abbr) u) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead d1 (Flat f) u1)
+H5) in (False_ind (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C (CHead
+c1 (Bind Abst) t) (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))) H6)))))))))))) c y H0))) H)))))).
theorem csuba_gen_bind_rev:
\forall (g: G).(\forall (b1: B).(\forall (e1: C).(\forall (c2: C).(\forall
T).(eq C c (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
C).(\lambda (_: T).(csuba g e2 e1)))))))) (\lambda (n: nat).(\lambda (H1: (eq
C (CSort n) (CHead e1 (Bind b1) v1))).(let H2 \def (eq_ind C (CSort n)
-(\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort _)
-\Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Bind b1)
-v1) H1) in (False_ind (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C (CSort n) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e2 e1))))) H2)))) (\lambda (c1: C).(\lambda
-(c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c3 (CHead e1
-(Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
-(v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e2 e1)))))))).(\lambda (k: K).(\lambda (u:
-T).(\lambda (H3: (eq C (CHead c3 k u) (CHead e1 (Bind b1) v1))).(let H4 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3 k u)
-(CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
-C).(match e in C return (\lambda (_: C).K) with [(CSort _) \Rightarrow k |
-(CHead _ k0 _) \Rightarrow k0])) (CHead c3 k u) (CHead e1 (Bind b1) v1) H3)
-in ((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t) \Rightarrow t]))
-(CHead c3 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7: (eq K k (Bind
-b1))).(\lambda (H8: (eq C c3 e1)).(eq_ind_r T v1 (\lambda (t: T).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c1 k t)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))))) (eq_ind_r K (Bind b1) (\lambda (k0: K).(ex2_3 B C T
-(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c1 k0 v1)
-(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))))) (let H9 \def (eq_ind C c3 (\lambda (c: C).((eq C c
-(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_:
-B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))))) H2 e1 H8) in (let
-H10 \def (eq_ind C c3 (\lambda (c: C).(csuba g c1 c)) H1 e1 H8) in
-(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
-(CHead c1 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda
-(e2: C).(\lambda (_: T).(csuba g e2 e1)))) b1 c1 v1 (refl_equal C (CHead c1
-(Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
+(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow True | (CHead _ _ _)
+\Rightarrow False])) I (CHead e1 (Bind b1) v1) H1) in (False_ind (ex2_3 B C T
+(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CSort n) (CHead e2
+(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
+e2 e1))))) H2)))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1: (csuba g c1
+c3)).(\lambda (H2: (((eq C c3 (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T
+(\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind
+b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2
+e1)))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c3 k u)
+(CHead e1 (Bind b1) v1))).(let H4 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3 k
+u) (CHead e1 (Bind b1) v1) H3) in ((let H5 \def (f_equal C K (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
+(CHead c3 k u) (CHead e1 (Bind b1) v1) H3) in ((let H6 \def (f_equal C T
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead _ _ t)
+\Rightarrow t])) (CHead c3 k u) (CHead e1 (Bind b1) v1) H3) in (\lambda (H7:
+(eq K k (Bind b1))).(\lambda (H8: (eq C c3 e1)).(eq_ind_r T v1 (\lambda (t:
+T).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c1 k t) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csuba g e2 e1)))))) (eq_ind_r K (Bind b1) (\lambda (k0:
+K).(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c1 k0 v1) (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csuba g e2 e1)))))) (let H9 \def (eq_ind C c3 (\lambda
+(c: C).((eq C c (CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2:
+B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2)))))
+(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))))) H2 e1
+H8) in (let H10 \def (eq_ind C c3 (\lambda (c: C).(csuba g c1 c)) H1 e1 H8)
+in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq
+C (CHead c1 (Bind b1) v1) (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1)))) b1 c1 v1 (refl_equal C
+(CHead c1 (Bind b1) v1)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
C).(\lambda (c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c3
(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_:
B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1)))))))).(\lambda (b:
B).(\lambda (H3: (not (eq B b Void))).(\lambda (u1: T).(\lambda (u2:
T).(\lambda (H4: (eq C (CHead c3 (Bind b) u2) (CHead e1 (Bind b1) v1))).(let
-H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C)
-with [(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3
-(Bind b) u2) (CHead e1 (Bind b1) v1) H4) in ((let H6 \def (f_equal C B
-(\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
-\Rightarrow b | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_:
-K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c3
-(Bind b) u2) (CHead e1 (Bind b1) v1) H4) in ((let H7 \def (f_equal C T
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _)
-\Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c3 (Bind b) u2) (CHead
-e1 (Bind b1) v1) H4) in (\lambda (H8: (eq B b b1)).(\lambda (H9: (eq C c3
-e1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0 Void))) H3 b1
-H8) in (let H11 \def (eq_ind C c3 (\lambda (c: C).((eq C c (CHead e1 (Bind
-b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
-T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
-C).(\lambda (_: T).(csuba g e2 e1))))))) H2 e1 H9) in (let H12 \def (eq_ind C
-c3 (\lambda (c: C).(csuba g c1 c)) H1 e1 H9) in (ex2_3_intro B C T (\lambda
-(b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C (CHead c1 (Bind Void) u1)
+H5 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c3
+| (CHead c _ _) \Rightarrow c])) (CHead c3 (Bind b) u2) (CHead e1 (Bind b1)
+v1) H4) in ((let H6 \def (f_equal C B (\lambda (e: C).(match e with [(CSort
+_) \Rightarrow b | (CHead _ k _) \Rightarrow (match k with [(Bind b0)
+\Rightarrow b0 | (Flat _) \Rightarrow b])])) (CHead c3 (Bind b) u2) (CHead e1
+(Bind b1) v1) H4) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e with
+[(CSort _) \Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c3 (Bind b)
+u2) (CHead e1 (Bind b1) v1) H4) in (\lambda (H8: (eq B b b1)).(\lambda (H9:
+(eq C c3 e1)).(let H10 \def (eq_ind B b (\lambda (b0: B).(not (eq B b0
+Void))) H3 b1 H8) in (let H11 \def (eq_ind C c3 (\lambda (c: C).((eq C c
+(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
+C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))))) H2 e1 H9) in (let
+H12 \def (eq_ind C c3 (\lambda (c: C).(csuba g c1 c)) H1 e1 H9) in
+(ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C
+(CHead c1 (Bind Void) u1) (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1)))) Void c1 u1 (refl_equal
+C (CHead c1 (Bind Void) u1)) H12))))))) H6)) H5))))))))))) (\lambda (c1:
+C).(\lambda (c3: C).(\lambda (H1: (csuba g c1 c3)).(\lambda (H2: (((eq C c3
+(CHead e1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2:
+C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_:
+B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1)))))))).(\lambda (t:
+T).(\lambda (a: A).(\lambda (_: (arity g c1 t (asucc g a))).(\lambda (u:
+T).(\lambda (H4: (arity g c3 u a)).(\lambda (H5: (eq C (CHead c3 (Bind Abbr)
+u) (CHead e1 (Bind b1) v1))).(let H6 \def (f_equal C C (\lambda (e: C).(match
+e with [(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3
+(Bind Abbr) u) (CHead e1 (Bind b1) v1) H5) in ((let H7 \def (f_equal C B
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow Abbr | (CHead _ k _)
+\Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
+Abbr])])) (CHead c3 (Bind Abbr) u) (CHead e1 (Bind b1) v1) H5) in ((let H8
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u |
+(CHead _ _ t0) \Rightarrow t0])) (CHead c3 (Bind Abbr) u) (CHead e1 (Bind b1)
+v1) H5) in (\lambda (H9: (eq B Abbr b1)).(\lambda (H10: (eq C c3 e1)).(let
+H11 \def (eq_ind T u (\lambda (t0: T).(arity g c3 t0 a)) H4 v1 H8) in (let
+H12 \def (eq_ind C c3 (\lambda (c: C).(arity g c v1 a)) H11 e1 H10) in (let
+H13 \def (eq_ind C c3 (\lambda (c: C).((eq C c (CHead e1 (Bind b1) v1)) \to
+(ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1
(CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
-T).(csuba g e2 e1)))) Void c1 u1 (refl_equal C (CHead c1 (Bind Void) u1))
-H12))))))) H6)) H5))))))))))) (\lambda (c1: C).(\lambda (c3: C).(\lambda (H1:
-(csuba g c1 c3)).(\lambda (H2: (((eq C c3 (CHead e1 (Bind b1) v1)) \to (ex2_3
-B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2
-(Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
-e2 e1)))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (_: (arity g c1 t
-(asucc g a))).(\lambda (u: T).(\lambda (H4: (arity g c3 u a)).(\lambda (H5:
-(eq C (CHead c3 (Bind Abbr) u) (CHead e1 (Bind b1) v1))).(let H6 \def
-(f_equal C C (\lambda (e: C).(match e in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3 (Bind
-Abbr) u) (CHead e1 (Bind b1) v1) H5) in ((let H7 \def (f_equal C B (\lambda
-(e: C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow
-Abbr | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with
-[(Bind b) \Rightarrow b | (Flat _) \Rightarrow Abbr])])) (CHead c3 (Bind
-Abbr) u) (CHead e1 (Bind b1) v1) H5) in ((let H8 \def (f_equal C T (\lambda
-(e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u
-| (CHead _ _ t0) \Rightarrow t0])) (CHead c3 (Bind Abbr) u) (CHead e1 (Bind
-b1) v1) H5) in (\lambda (H9: (eq B Abbr b1)).(\lambda (H10: (eq C c3
-e1)).(let H11 \def (eq_ind T u (\lambda (t0: T).(arity g c3 t0 a)) H4 v1 H8)
-in (let H12 \def (eq_ind C c3 (\lambda (c: C).(arity g c v1 a)) H11 e1 H10)
-in (let H13 \def (eq_ind C c3 (\lambda (c: C).((eq C c (CHead e1 (Bind b1)
-v1)) \to (ex2_3 B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq
-C c1 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda
-(_: T).(csuba g e2 e1))))))) H2 e1 H10) in (let H14 \def (eq_ind C c3
-(\lambda (c: C).(csuba g c1 c)) H1 e1 H10) in (let H15 \def (eq_ind_r B b1
-(\lambda (b: B).((eq C e1 (CHead e1 (Bind b) v1)) \to (ex2_3 B C T (\lambda
-(b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2)
-v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2
-e1))))))) H13 Abbr H9) in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2:
-C).(\lambda (v2: T).(eq C (CHead c1 (Bind Abst) t) (CHead e2 (Bind b2)
-v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))
-Abst c1 t (refl_equal C (CHead c1 (Bind Abst) t)) H14))))))))) H7))
-H6)))))))))))) c2 y H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1831
-END *)
+T).(csuba g e2 e1))))))) H2 e1 H10) in (let H14 \def (eq_ind C c3 (\lambda
+(c: C).(csuba g c1 c)) H1 e1 H10) in (let H15 \def (eq_ind_r B b1 (\lambda
+(b: B).((eq C e1 (CHead e1 (Bind b) v1)) \to (ex2_3 B C T (\lambda (b2:
+B).(\lambda (e2: C).(\lambda (v2: T).(eq C c1 (CHead e2 (Bind b2) v2)))))
+(\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1))))))) H13
+Abbr H9) in (ex2_3_intro B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda
+(v2: T).(eq C (CHead c1 (Bind Abst) t) (CHead e2 (Bind b2) v2))))) (\lambda
+(_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 e1)))) Abst c1 t
+(refl_equal C (CHead c1 (Bind Abst) t)) H14))))))))) H7)) H6)))))))))))) c2 y
+H0))) H)))))).
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/drop.ma".
+include "basic_1/csuba/drop.ma".
-include "Basic-1/csuba/clear.ma".
+include "basic_1/csuba/clear.ma".
-include "Basic-1/getl/clear.ma".
+include "basic_1/getl/clear.ma".
theorem csuba_getl_abbr:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).(\forall
Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))))) (\lambda (b: B).(\lambda
(H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear (CHead x0
(Bind b) t) (CHead d1 (Bind Abbr) u))).(let H7 \def (f_equal C C (\lambda (e:
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 |
-(CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t)
-(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H8 \def
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
-[(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 in K
-return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
-\Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t)
-(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H9 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
+C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c]))
+(CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1
+(Bind Abbr) u) t H6)) in ((let H8 \def (f_equal C B (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 with
+[(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind
Abbr) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u)
-t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda
-(c2: C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda
-(t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def
-(eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abbr
-H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c
-(Bind Abbr) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abbr i c1 d1 u H15
-g c2 H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr)
-u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x1:
+t H6)) in ((let H9 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abbr) u)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in
+(\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2:
+C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0:
+T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def (eq_ind_r
+B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abbr H10) in
+(let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind
+Abbr) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abbr i c1 d1 u H15 g c2
+H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u)))
+(\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl i c2 (CHead
+d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x1:
C).(\lambda (H17: (drop i O c2 (CHead x1 (Bind Abbr) u))).(\lambda (H18:
(csuba g d1 x1)).(ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x1 (getl_intro i c2 (CHead x1
(\lambda (d2: C).(csuba g d1 d2)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead
x9 (Bind Abbr) u) n H22) H23)))) H21)))))))) H17)))))) H14))))))) H11))))))))
i) H7))))) k H3 H4))))))) x H1 H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 2319
-END *)
theorem csuba_getl_abst:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
u2 a))))))))))) (\lambda (b: B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b)
t))).(\lambda (H6: (clear (CHead x0 (Bind b) t) (CHead d1 (Bind Abst)
-u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c]))
-(CHead d1 (Bind Abst) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead
-d1 (Bind Abst) u1) t H6)) in ((let H8 \def (f_equal C B (\lambda (e:
-C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abst |
-(CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with
-[(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abst])])) (CHead d1 (Bind
-Abst) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst)
-u1) t H6)) in ((let H9 \def (f_equal C T (\lambda (e: C).(match e in C return
-(\lambda (_: C).T) with [(CSort _) \Rightarrow u1 | (CHead _ _ t0)
-\Rightarrow t0])) (CHead d1 (Bind Abst) u1) (CHead x0 (Bind b) t)
-(clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6)) in (\lambda (H10: (eq B
-Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
-g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
-(Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r B b (\lambda (b0:
-B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abst H10) in (let H15 \def
-(eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind Abst) u1))) H14 d1
-H11) in (let H16 \def (csuba_drop_abst i c1 d1 u1 H15 g c2 H12) in (or_ind
-(ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1))) (\lambda
-(d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
-T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
-C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abst) u1)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6))
+in ((let H8 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0)
+\Rightarrow b0 | (Flat _) \Rightarrow Abst])])) (CHead d1 (Bind Abst) u1)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6))
+in ((let H9 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u1 | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abst) u1)
+(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6))
+in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2:
+C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0:
+T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r
+B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abst H10) in
+(let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind
+Abst) u1))) H14 d1 H11) in (let H16 \def (csuba_drop_abst i c1 d1 u1 H15 g c2
+H12) in (or_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst)
+u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr)
+u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
+(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
+a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
+a))))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
+(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
+(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or (ex2 C
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
+(H17: (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1)))
+(\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop i O c2
+(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C
(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
(_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H17: (ex2 C (\lambda
-(d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
-d2)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1)))
-(\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
-(\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
-Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
-d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
-g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-a)))))) (\lambda (x1: C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abst)
-u1))).(\lambda (H19: (csuba g d1 x1)).(or_introl (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1: C).(\lambda
+(H18: (drop i O c2 (CHead x1 (Bind Abst) u1))).(\lambda (H19: (csuba g d1
+x1)).(or_introl (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
+u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
+(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
+(ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda
+(d2: C).(csuba g d1 d2)) x1 (getl_intro i c2 (CHead x1 (Bind Abst) u1) (CHead
+x1 (Bind Abst) u1) H18 (clear_bind Abst x1 u1)) H19))))) H17)) (\lambda (H17:
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2
(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2
-(Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x1 (getl_intro i c2
-(CHead x1 (Bind Abst) u1) (CHead x1 (Bind Abst) u1) H18 (clear_bind Abst x1
-u1)) H19))))) H17)) (\lambda (H17: (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
-(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
-C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C
-T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2
-(Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
-(asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
-u2 a)))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
-(\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
-(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+A).(arity g d2 u2 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1:
-C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1
-(Bind Abbr) x2))).(\lambda (H19: (csuba g d1 x1)).(\lambda (H20: (arity g d1
-u1 (asucc g x3))).(\lambda (H21: (arity g x1 x2 x3)).(or_intror (ex2 C
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C
(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
(_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr)
-u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
-a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))
-x1 x2 x3 (getl_intro i c2 (CHead x1 (Bind Abbr) x2) (CHead x1 (Bind Abbr) x2)
-H18 (clear_bind Abbr x1 x2)) H19 H20 H21))))))))) H17)) H16)))))))))) H8))
+(u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1: C).(\lambda (x2:
+T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abbr)
+x2))).(\lambda (H19: (csuba g d1 x1)).(\lambda (H20: (arity g d1 u1 (asucc g
+x3))).(\lambda (H21: (arity g x1 x2 x3)).(or_intror (ex2 C (\lambda (d2:
+C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
+g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
+C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x1 x2 x3
+(getl_intro i c2 (CHead x1 (Bind Abbr) x2) (CHead x1 (Bind Abbr) x2) H18
+(clear_bind Abbr x1 x2)) H19 H20 H21))))))))) H17)) H16)))))))))) H8))
H7))))) (\lambda (f: F).(\lambda (H5: (drop i O c1 (CHead x0 (Flat f)
t))).(\lambda (H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abst)
u1))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop i O c (CHead x0
c2 x7 x8 H20 (CHead x9 (Bind Abbr) x10) n H23) H24 H25 H26))))))))) H22))
H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4))))))) x H1
H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 6437
-END *)
theorem csuba_getl_abst_rev:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).(\forall
u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))) (\lambda (b:
B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear
(CHead x0 (Bind b) t) (CHead d1 (Bind Abst) u))).(let H7 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abst) u)
-(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in
-((let H8 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_:
-C).B) with [(CSort _) \Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0
-in K return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
-\Rightarrow Abst])])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _)
+\Rightarrow c])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in ((let H8 \def
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow Abst |
+(CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0) \Rightarrow b0 | (Flat
+_) \Rightarrow Abst])])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
(clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in ((let H9 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
-Abst) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u)
-t H6)) in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda
-(c2: C).(\lambda (H12: (csuba g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda
-(t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def
-(eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abst
-H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c
-(Bind Abst) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abst_rev i c1 d1 u
-H15 g c2 H12) in (or_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u | (CHead
+_ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in (\lambda (H10: (eq B
+Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
+g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
+(Bind b) t0))) H5 u H9) in (let H14 \def (eq_ind_r B b (\lambda (b0: B).(drop
+i O c1 (CHead x0 (Bind b0) u))) H13 Abst H10) in (let H15 \def (eq_ind_r C x0
+(\lambda (c: C).(drop i O c1 (CHead c (Bind Abst) u))) H14 d1 H11) in (let
+H16 \def (csuba_drop_abst_rev i c1 d1 u H15 g c2 H12) in (or_ind (ex2 C
(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
-C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abst) u))).(\lambda (H19:
-(csuba g x1 d1)).(or_introl (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(getl i
-c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x1
-(getl_intro i c2 (CHead x1 (Bind Abst) u) (CHead x1 (Bind Abst) u) H18
-(clear_bind Abst x1 u)) H19))))) H17)) (\lambda (H17: (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2:
-C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(getl i c2
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
-C).(\lambda (x2: T).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Void)
-x2))).(\lambda (H19: (csuba g x1 d1)).(or_intror (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x1 x2 (getl_intro i c2
-(CHead x1 (Bind Void) x2) (CHead x1 (Bind Void) x2) H18 (clear_bind Void x1
-x2)) H19)))))) H17)) H16)))))))))) H8)) H7))))) (\lambda (f: F).(\lambda (H5:
-(drop i O c1 (CHead x0 (Flat f) t))).(\lambda (H6: (clear (CHead x0 (Flat f)
-t) (CHead d1 (Bind Abst) u))).(let H7 \def H5 in (unintro C c1 (\lambda (c:
-C).((drop i O c (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 c)
-\to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop i O
+c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1)))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))))))) (nat_ind (\lambda (n: nat).(\forall (x1: C).((drop
-n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 x1) \to (or
-(ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl n c2
+T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C (\lambda (d2: C).(drop i O c2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
+(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1: C).(\lambda (H18: (drop
+i O c2 (CHead x1 (Bind Abst) u))).(\lambda (H19: (csuba g x1 d1)).(or_introl
+(ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))))))))) (\lambda (x1: C).(\lambda (H8: (drop O O x1 (CHead x0 (Flat f)
-t))).(\lambda (c2: C).(\lambda (H9: (csuba g c2 x1)).(let H10 \def (eq_ind C
-x1 (\lambda (c: C).(csuba g c2 c)) H9 (CHead x0 (Flat f) t) (drop_gen_refl x1
-(CHead x0 (Flat f) t) H8)) in (let H_y \def (clear_flat x0 (CHead d1 (Bind
-Abst) u) (clear_gen_flat f x0 (CHead d1 (Bind Abst) u) t H6) f t) in (let H11
-\def (csuba_clear_trans g (CHead x0 (Flat f) t) c2 H10 (CHead d1 (Bind Abst)
-u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba g e2 (CHead d1 (Bind Abst) u)))
-(\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead
-d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (H12:
-(csuba g x2 (CHead d1 (Bind Abst) u))).(\lambda (H13: (clear c2 x2)).(let H_x
-\def (csuba_gen_abst_rev g d1 x2 u H12) in (let H14 \def H_x in (or_ind (ex2
-C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C x2
+d1)))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
+(\lambda (d2: C).(csuba g d2 d1)) x1 (getl_intro i c2 (CHead x1 (Bind Abst)
+u) (CHead x1 (Bind Abst) u) H18 (clear_bind Abst x1 u)) H19))))) H17))
+(\lambda (H17: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop i O c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
-(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (H15: (ex2 C (\lambda (d2: C).(eq C x2 (CHead
-d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda
-(d2: C).(eq C x2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))
-(or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda
-(d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl
-O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
-d2 d1))))) (\lambda (x3: C).(\lambda (H16: (eq C x2 (CHead x3 (Bind Abst)
-u))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def (eq_ind C x2 (\lambda (c:
-C).(clear c2 c)) H13 (CHead x3 (Bind Abst) u) H16) in (or_introl (ex2 C
-(\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2
+d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or
+(ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (ex_intro2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
-(\lambda (d2: C).(csuba g d2 d1)) x3 (getl_intro O c2 (CHead x3 (Bind Abst)
-u) c2 (drop_refl c2) H18) H17)))))) H15)) (\lambda (H15: (ex2_2 C T (\lambda
-(d2: C).(\lambda (u2: T).(eq C x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2:
-C).(\lambda (u2: T).(eq C x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(getl O c2
+d1))))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (H18: (drop i O c2 (CHead
+x1 (Bind Void) x2))).(\lambda (H19: (csuba g x1 d1)).(or_intror (ex2 C
+(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2
+(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead
+d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x1
+x2 (getl_intro i c2 (CHead x1 (Bind Void) x2) (CHead x1 (Bind Void) x2) H18
+(clear_bind Void x1 x2)) H19)))))) H17)) H16)))))))))) H8)) H7))))) (\lambda
+(f: F).(\lambda (H5: (drop i O c1 (CHead x0 (Flat f) t))).(\lambda (H6:
+(clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abst) u))).(let H7 \def H5 in
+(unintro C c1 (\lambda (c: C).((drop i O c (CHead x0 (Flat f) t)) \to
+(\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(getl i c2
(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x3:
-C).(\lambda (x4: T).(\lambda (H16: (eq C x2 (CHead x3 (Bind Void)
-x4))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def (eq_ind C x2 (\lambda (c:
-C).(clear c2 c)) H13 (CHead x3 (Bind Void) x4) H16) in (or_intror (ex2 C
+(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))) (nat_ind (\lambda
+(n: nat).(\forall (x1: C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall
+(c2: C).((csuba g c2 x1) \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2
+(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(getl n c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1)))))))))) (\lambda (x1: C).(\lambda (H8:
+(drop O O x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H9: (csuba g
+c2 x1)).(let H10 \def (eq_ind C x1 (\lambda (c: C).(csuba g c2 c)) H9 (CHead
+x0 (Flat f) t) (drop_gen_refl x1 (CHead x0 (Flat f) t) H8)) in (let H_y \def
+(clear_flat x0 (CHead d1 (Bind Abst) u) (clear_gen_flat f x0 (CHead d1 (Bind
+Abst) u) t H6) f t) in (let H11 \def (csuba_clear_trans g (CHead x0 (Flat f)
+t) c2 H10 (CHead d1 (Bind Abst) u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba
+g e2 (CHead d1 (Bind Abst) u))) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C
(\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2
(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead
-d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x3
-x4 (getl_intro O c2 (CHead x3 (Bind Void) x4) c2 (drop_refl c2) H18)
-H17))))))) H15)) H14)))))) H11)))))))) (\lambda (n: nat).(\lambda (H8:
-((\forall (x1: C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2:
-C).((csuba g c2 x1) \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl n c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))))))))).(\lambda (x1: C).(\lambda (H9:
-(drop (S n) O x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H10:
-(csuba g c2 x1)).(let H11 \def (drop_clear x1 (CHead x0 (Flat f) t) n H9) in
-(ex2_3_ind B C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear x1
-(CHead e (Bind b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_:
-T).(drop n O e (CHead x0 (Flat f) t))))) (or (ex2 C (\lambda (d2: C).(getl (S
-n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C
-T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x2:
-B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H12: (clear x1 (CHead x3 (Bind
-x2) x4))).(\lambda (H13: (drop n O x3 (CHead x0 (Flat f) t))).(let H14 \def
-(csuba_clear_trans g x1 c2 H10 (CHead x3 (Bind x2) x4) H12) in (ex2_ind C
-(\lambda (e2: C).(csuba g e2 (CHead x3 (Bind x2) x4))) (\lambda (e2:
-C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x5: C).(\lambda (H15: (csuba
-g x5 (CHead x3 (Bind x2) x4))).(\lambda (H16: (clear c2 x5)).(let H_x \def
-(csuba_gen_bind_rev g x2 x3 x5 x4 H15) in (let H17 \def H_x in (ex2_3_ind B C
-T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C x5 (CHead e2 (Bind
-b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2
-x3)))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u)))
+d1))))) (\lambda (x2: C).(\lambda (H12: (csuba g x2 (CHead d1 (Bind Abst)
+u))).(\lambda (H13: (clear c2 x2)).(let H_x \def (csuba_gen_abst_rev g d1 x2
+u H12) in (let H14 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C x2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(eq C x2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2:
+C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H15:
+(ex2 C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
+C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x3:
+C).(\lambda (H16: (eq C x2 (CHead x3 (Bind Abst) u))).(\lambda (H17: (csuba g
+x3 d1)).(let H18 \def (eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead
+x3 (Bind Abst) u) H16) in (or_introl (ex2 C (\lambda (d2: C).(getl O c2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl O c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda
+(d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
+d1)) x3 (getl_intro O c2 (CHead x3 (Bind Abst) u) c2 (drop_refl c2) H18)
+H17)))))) H15)) (\lambda (H15: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
+T).(eq C x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C
+x2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
+d1))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (x6: B).(\lambda (x7: C).(\lambda (x8:
-T).(\lambda (H18: (eq C x5 (CHead x7 (Bind x6) x8))).(\lambda (H19: (csuba g
-x7 x3)).(let H20 \def (eq_ind C x5 (\lambda (c: C).(clear c2 c)) H16 (CHead
-x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 H13 x7 H19) in (or_ind (ex2 C
-(\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl n x7
-(CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
-d1)))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u)))
+T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (H16: (eq C
+x2 (CHead x3 (Bind Void) x4))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def
+(eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 (Bind Void) x4) H16)
+in (or_intror (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u)))
(\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (H22: (ex2 C (\lambda (d2: C).(getl n x7
-(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
-(\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u))) (\lambda (d2:
-C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2
-(Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
-C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x9: C).(\lambda (H23: (getl
-n x7 (CHead x9 (Bind Abst) u))).(\lambda (H24: (csuba g x9 d1)).(or_introl
+T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
+T).(getl O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))) x3 x4 (getl_intro O c2 (CHead x3 (Bind Void) x4) c2
+(drop_refl c2) H18) H17))))))) H15)) H14)))))) H11)))))))) (\lambda (n:
+nat).(\lambda (H8: ((\forall (x1: C).((drop n O x1 (CHead x0 (Flat f) t)) \to
+(\forall (c2: C).((csuba g c2 x1) \to (or (ex2 C (\lambda (d2: C).(getl n c2
+(CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl n c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))).(\lambda (x1:
+C).(\lambda (H9: (drop (S n) O x1 (CHead x0 (Flat f) t))).(\lambda (c2:
+C).(\lambda (H10: (csuba g c2 x1)).(let H11 \def (drop_clear x1 (CHead x0
+(Flat f) t) n H9) in (ex2_3_ind B C T (\lambda (b: B).(\lambda (e:
+C).(\lambda (v: T).(clear x1 (CHead e (Bind b) v))))) (\lambda (_:
+B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead x0 (Flat f) t))))) (or
(ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u))) (\lambda
(d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl
(S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba
-g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
-Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x9 (getl_clear_bind x6 c2 x7 x8
-H20 (CHead x9 (Bind Abst) u) n H23) H24))))) H22)) (\lambda (H22: (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl n x7 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda
-(d2: C).(\lambda (u2: T).(getl n x7 (CHead d2 (Bind Void) u2)))) (\lambda
-(d2: C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(getl
-(S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
-C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void)
-u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x9:
-C).(\lambda (x10: T).(\lambda (H23: (getl n x7 (CHead x9 (Bind Void)
-x10))).(\lambda (H24: (csuba g x9 d1)).(or_intror (ex2 C (\lambda (d2:
+g d2 d1))))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda
+(H12: (clear x1 (CHead x3 (Bind x2) x4))).(\lambda (H13: (drop n O x3 (CHead
+x0 (Flat f) t))).(let H14 \def (csuba_clear_trans g x1 c2 H10 (CHead x3 (Bind
+x2) x4) H12) in (ex2_ind C (\lambda (e2: C).(csuba g e2 (CHead x3 (Bind x2)
+x4))) (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n)
+c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x5:
+C).(\lambda (H15: (csuba g x5 (CHead x3 (Bind x2) x4))).(\lambda (H16: (clear
+c2 x5)).(let H_x \def (csuba_gen_bind_rev g x2 x3 x5 x4 H15) in (let H17 \def
+H_x in (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
+T).(eq C x5 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
+C).(\lambda (_: T).(csuba g e2 x3)))) (or (ex2 C (\lambda (d2: C).(getl (S n)
+c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x6:
+B).(\lambda (x7: C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind
+x6) x8))).(\lambda (H19: (csuba g x7 x3)).(let H20 \def (eq_ind C x5 (\lambda
+(c: C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3
+H13 x7 H19) in (or_ind (ex2 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
+C).(\lambda (u2: T).(getl n x7 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
+C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(getl (S n)
+c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H22: (ex2 C
+(\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind
+Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
C).(getl (S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))
-(ex2_2_intro C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2
-(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x9 x10
-(getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Void) x10) n H23) H24))))))
-H22)) H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4)))))))
-x H1 H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 4703
-END *)
+(Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
+(\lambda (x9: C).(\lambda (H23: (getl n x7 (CHead x9 (Bind Abst)
+u))).(\lambda (H24: (csuba g x9 d1)).(or_introl (ex2 C (\lambda (d2: C).(getl
+(S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
+C T (\lambda (d2: C).(\lambda (u2: T).(getl (S n) c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C
+(\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
+C).(csuba g d2 d1)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abst)
+u) n H23) H24))))) H22)) (\lambda (H22: (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(getl n x7 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(getl
+n x7 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
+d2 d1))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d2 d1))))) (\lambda (x9: C).(\lambda (x10: T).(\lambda (H23:
+(getl n x7 (CHead x9 (Bind Void) x10))).(\lambda (H24: (csuba g x9
+d1)).(or_intror (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
+u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
+(u2: T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
+(_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
+T).(getl (S n) c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))) x9 x10 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind
+Void) x10) n H23) H24)))))) H22)) H21)))))))) H17)))))) H14)))))))
+H11)))))))) i) H7))))) k H3 H4))))))) x H1 H2)))) H0))))))).
theorem csuba_getl_abbr_rev:
\forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))) (\lambda (b:
B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear
(CHead x0 (Bind b) t) (CHead d1 (Bind Abbr) u1))).(let H7 \def (f_equal C C
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abbr) u1)
-(CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6))
-in ((let H8 \def (f_equal C B (\lambda (e: C).(match e in C return (\lambda
-(_: C).B) with [(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow
-(match k0 in K return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 |
-(Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b)
-t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in ((let H9 \def
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow u1 | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
-Abbr) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr)
-u1) t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1
-x0)).(\lambda (c2: C).(\lambda (H12: (csuba g c2 c1)).(let H13 \def (eq_ind_r
-T t (\lambda (t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u1 H9) in (let
-H14 \def (eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0)
-u1))) H13 Abbr H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O
-c1 (CHead c (Bind Abbr) u1))) H14 d1 H11) in (let H16 \def
-(csuba_drop_abbr_rev i c1 d1 u1 H15 g c2 H12) in (or3_ind (ex2 C (\lambda
-(d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
-d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i
-O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _)
+\Rightarrow c])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in ((let H8 \def
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow Abbr |
+(CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0) \Rightarrow b0 | (Flat
+_) \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in ((let H9 \def
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u1 | (CHead
+_ _ t0) \Rightarrow t0])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
+(clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in (\lambda (H10: (eq B
+Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
+g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
+(Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r B b (\lambda (b0:
+B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abbr H10) in (let H15 \def
+(eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind Abbr) u1))) H14 d1
+H11) in (let H16 \def (csuba_drop_abbr_rev i c1 d1 u1 H15 g c2 H12) in
+(or3_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1)))
+(\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
+(u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
+(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
+(\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2))))
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2:
+C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
+T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C (\lambda (d2: C).(drop i O c2
+(CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
+(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
+C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2)))))
(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H17: (ex2 C
-(\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
-C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2:
-C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
-(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
+C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abbr) u1))).(\lambda (H19:
+(csuba g x1 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2
+(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
+(d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst)
+u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
+(\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
+a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
+(ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void)
+u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C
+(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
+C).(csuba g d2 d1)) x1 (getl_intro i c2 (CHead x1 (Bind Abbr) u1) (CHead x1
+(Bind Abbr) u1) H18 (clear_bind Abbr x1 u1)) H19))))) H17)) (\lambda (H17:
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2
(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1))))) (\lambda (x1: C).(\lambda (H18: (drop i O c2 (CHead x1
-(Bind Abbr) u1))).(\lambda (H19: (csuba g x1 d1)).(or3_intro0 (ex2 C (\lambda
-(d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
-d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i
-c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
-(_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
-A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
-(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
-T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
-T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2
-(Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x1 (getl_intro i c2
-(CHead x1 (Bind Abbr) u1) (CHead x1 (Bind Abbr) u1) H18 (clear_bind Abbr x1
-u1)) H19))))) H17)) (\lambda (H17: (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
-(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T
-A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2
-(Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
-d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
-(asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
-u1 a)))) (or3 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1)))
-(\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
-(u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda
-(d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+(a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
-(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
-(\lambda (d2: C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2))))
-(\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1:
-C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1
-(Bind Abst) x2))).(\lambda (H19: (csuba g x1 d1)).(\lambda (H20: (arity g x1
-x2 (asucc g x3))).(\lambda (H21: (arity g d1 u1 x3)).(or3_intro1 (ex2 C
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C
(\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
(_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
(_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
C).(\lambda (u2: T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
-C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A (\lambda (d2:
-C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2)))))
-(\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
-(d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
-(\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x1 x2 x3
+C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x1: C).(\lambda (x2:
+T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abst)
+x2))).(\lambda (H19: (csuba g x1 d1)).(\lambda (H20: (arity g x1 x2 (asucc g
+x3))).(\lambda (H21: (arity g d1 u1 x3)).(or3_intro1 (ex2 C (\lambda (d2:
+C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
+(ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
+(CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
+A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
+A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
+T).(getl i c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
+T).(csuba g d2 d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2:
+T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
+C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
+C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x1 x2 x3
(getl_intro i c2 (CHead x1 (Bind Abst) x2) (CHead x1 (Bind Abst) x2) H18
(clear_bind Abst x1 x2)) H19 H20 H21))))))))) H17)) (\lambda (H17: (ex2_2 C T
(\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2))))
(getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Void) x10) n H23) H24))))))
H22)) H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4)))))))
x H1 H2)))) H0))))))).
-(* COMMENTS
-Initial nodes: 9091
-END *)
(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csuba/defs.ma".
+include "basic_1/csuba/defs.ma".
+
+include "basic_1/C/fwd.ma".
theorem csuba_refl:
\forall (g: G).(\forall (c: C).(csuba g c c))
\def
- \lambda (g: G).(\lambda (c: C).(C_ind (\lambda (c0: C).(csuba g c0 c0))
-(\lambda (n: nat).(csuba_sort g n)) (\lambda (c0: C).(\lambda (H: (csuba g c0
-c0)).(\lambda (k: K).(\lambda (t: T).(csuba_head g c0 c0 H k t))))) c)).
-(* COMMENTS
-Initial nodes: 53
-END *)
+ \lambda (g: G).(\lambda (c: C).(let TMP_1 \def (\lambda (c0: C).(csuba g c0
+c0)) in (let TMP_2 \def (\lambda (n: nat).(csuba_sort g n)) in (let TMP_3
+\def (\lambda (c0: C).(\lambda (H: (csuba g c0 c0)).(\lambda (k: K).(\lambda
+(t: T).(csuba_head g c0 c0 H k t))))) in (C_ind TMP_1 TMP_2 TMP_3 c))))).
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