1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "Basic-1/csuba/fwd.ma".
19 include "Basic-1/drop/fwd.ma".
21 theorem csuba_drop_abbr:
22 \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop i
23 O c1 (CHead d1 (Bind Abbr) u)) \to (\forall (g: G).(\forall (c2: C).((csuba g
24 c1 c2) \to (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u)))
25 (\lambda (d2: C).(csuba g d1 d2))))))))))
27 \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (d1:
28 C).(\forall (u: T).((drop n O c1 (CHead d1 (Bind Abbr) u)) \to (\forall (g:
29 G).(\forall (c2: C).((csuba g c1 c2) \to (ex2 C (\lambda (d2: C).(drop n O c2
30 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))))))))
31 (\lambda (c1: C).(\lambda (d1: C).(\lambda (u: T).(\lambda (H: (drop O O c1
32 (CHead d1 (Bind Abbr) u))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H0:
33 (csuba g c1 c2)).(let H1 \def (eq_ind C c1 (\lambda (c: C).(csuba g c c2)) H0
34 (CHead d1 (Bind Abbr) u) (drop_gen_refl c1 (CHead d1 (Bind Abbr) u) H)) in
35 (let H_x \def (csuba_gen_abbr g d1 c2 u H1) in (let H2 \def H_x in (ex2_ind C
36 (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba
37 g d1 d2)) (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abbr) u)))
38 (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H3: (eq C c2
39 (CHead x (Bind Abbr) u))).(\lambda (H4: (csuba g d1 x)).(eq_ind_r C (CHead x
40 (Bind Abbr) u) (\lambda (c: C).(ex2 C (\lambda (d2: C).(drop O O c (CHead d2
41 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (ex_intro2 C (\lambda
42 (d2: C).(drop O O (CHead x (Bind Abbr) u) (CHead d2 (Bind Abbr) u))) (\lambda
43 (d2: C).(csuba g d1 d2)) x (drop_refl (CHead x (Bind Abbr) u)) H4) c2 H3))))
44 H2))))))))))) (\lambda (n: nat).(\lambda (H: ((\forall (c1: C).(\forall (d1:
45 C).(\forall (u: T).((drop n O c1 (CHead d1 (Bind Abbr) u)) \to (\forall (g:
46 G).(\forall (c2: C).((csuba g c1 c2) \to (ex2 C (\lambda (d2: C).(drop n O c2
47 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
48 d2)))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1:
49 C).(\forall (u: T).((drop (S n) O c (CHead d1 (Bind Abbr) u)) \to (\forall
50 (g: G).(\forall (c2: C).((csuba g c c2) \to (ex2 C (\lambda (d2: C).(drop (S
51 n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))))))))
52 (\lambda (n0: nat).(\lambda (d1: C).(\lambda (u: T).(\lambda (H0: (drop (S n)
53 O (CSort n0) (CHead d1 (Bind Abbr) u))).(\lambda (g: G).(\lambda (c2:
54 C).(\lambda (_: (csuba g (CSort n0) c2)).(and3_ind (eq C (CHead d1 (Bind
55 Abbr) u) (CSort n0)) (eq nat (S n) O) (eq nat O O) (ex2 C (\lambda (d2:
56 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
57 d2))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u) (CSort n0))).(\lambda (H3:
58 (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n)
59 (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
60 \Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (ex2 C
61 (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
62 C).(csuba g d1 d2))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr)
63 u) H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u:
64 T).((drop (S n) O c (CHead d1 (Bind Abbr) u)) \to (\forall (g: G).(\forall
65 (c2: C).((csuba g c c2) \to (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead
66 d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))))))))).(\lambda (k:
67 K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop (S n)
68 O (CHead c k t) (CHead d1 (Bind Abbr) u))).(\lambda (g: G).(\lambda (c2:
69 C).(\lambda (H2: (csuba g (CHead c k t) c2)).(K_ind (\lambda (k0: K).((csuba
70 g (CHead c k0 t) c2) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr) u)) \to
71 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda
72 (d2: C).(csuba g d1 d2)))))) (\lambda (b: B).(\lambda (H3: (csuba g (CHead c
73 (Bind b) t) c2)).(\lambda (H4: (drop (r (Bind b) n) O c (CHead d1 (Bind Abbr)
74 u))).(B_ind (\lambda (b0: B).((csuba g (CHead c (Bind b0) t) c2) \to ((drop
75 (r (Bind b0) n) O c (CHead d1 (Bind Abbr) u)) \to (ex2 C (\lambda (d2:
76 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
77 d2)))))) (\lambda (H5: (csuba g (CHead c (Bind Abbr) t) c2)).(\lambda (H6:
78 (drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abbr) u))).(let H_x \def
79 (csuba_gen_abbr g c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda (d2:
80 C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g c d2)) (ex2
81 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
82 C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x (Bind
83 Abbr) t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C (CHead x (Bind Abbr) t)
84 (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
85 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H10 \def (H c d1 u H6 g x
86 H9) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u)))
87 (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O
88 (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g
89 d1 d2))) (\lambda (x0: C).(\lambda (H11: (drop n O x (CHead x0 (Bind Abbr)
90 u))).(\lambda (H12: (csuba g d1 x0)).(let H13 \def (refl_equal nat (r (Bind
91 Abbr) n)) in (let H14 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x
92 (CHead x0 (Bind Abbr) u))) H11 (r (Bind Abbr) n) H13) in (ex_intro2 C
93 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr)
94 u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abbr) n x (CHead
95 x0 (Bind Abbr) u) H14 t) H12)))))) H10)) c2 H8)))) H7))))) (\lambda (H5:
96 (csuba g (CHead c (Bind Abst) t) c2)).(\lambda (H6: (drop (r (Bind Abst) n) O
97 c (CHead d1 (Bind Abbr) u))).(let H_x \def (csuba_gen_abst g c c2 t H5) in
98 (let H7 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
99 Abst) t))) (\lambda (d2: C).(csuba g c d2))) (ex4_3 C T A (\lambda (d2:
100 C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2)))))
101 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g c d2)))) (\lambda
102 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t (asucc g a))))) (\lambda
103 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex2 C
104 (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
105 C).(csuba g d1 d2))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
106 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)))).(ex2_ind C (\lambda (d2:
107 C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)) (ex2
108 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
109 C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H9: (eq C c2 (CHead x (Bind
110 Abst) t))).(\lambda (H10: (csuba g c x)).(eq_ind_r C (CHead x (Bind Abst) t)
111 (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
112 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H11 \def (H c d1 u H6 g x
113 H10) in (ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u)))
114 (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O
115 (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g
116 d1 d2))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abbr)
117 u))).(\lambda (H13: (csuba g d1 x0)).(let H14 \def (refl_equal nat (r (Bind
118 Abbr) n)) in (let H15 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x
119 (CHead x0 (Bind Abbr) u))) H12 (r (Bind Abbr) n) H14) in (ex_intro2 C
120 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr)
121 u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abst) n x (CHead
122 x0 (Bind Abbr) u) H15 t) H13)))))) H11)) c2 H9)))) H8)) (\lambda (H8: (ex4_3
123 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2
124 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
125 c d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t (asucc
126 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
127 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
128 A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
129 T).(\lambda (_: A).(csuba g c d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda
130 (a: A).(arity g c t (asucc g a))))) (\lambda (d2: C).(\lambda (u2:
131 T).(\lambda (a: A).(arity g d2 u2 a)))) (ex2 C (\lambda (d2: C).(drop (S n) O
132 c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda
133 (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H9: (eq C c2 (CHead x0
134 (Bind Abbr) x1))).(\lambda (H10: (csuba g c x0)).(\lambda (_: (arity g c t
135 (asucc g x2))).(\lambda (_: (arity g x0 x1 x2)).(eq_ind_r C (CHead x0 (Bind
136 Abbr) x1) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2
137 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H13 \def (H c d1 u
138 H6 g x0 H10) in (ex2_ind C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind
139 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S
140 n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2:
141 C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H14: (drop n O x0 (CHead x
142 (Bind Abbr) u))).(\lambda (H15: (csuba g d1 x)).(let H16 \def (refl_equal nat
143 (r (Bind Abbr) n)) in (let H17 \def (eq_ind nat n (\lambda (n0: nat).(drop n0
144 O x0 (CHead x (Bind Abbr) u))) H14 (r (Bind Abbr) n) H16) in (ex_intro2 C
145 (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind
146 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind Abbr) n x0
147 (CHead x (Bind Abbr) u) H17 x1) H15)))))) H13)) c2 H9)))))))) H8)) H7)))))
148 (\lambda (H5: (csuba g (CHead c (Bind Void) t) c2)).(\lambda (H6: (drop (r
149 (Bind Void) n) O c (CHead d1 (Bind Abbr) u))).(let H_x \def (csuba_gen_void g
150 c c2 t H5) in (let H7 \def H_x in (ex2_3_ind B C T (\lambda (b0: B).(\lambda
151 (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind b0) u2))))) (\lambda (_:
152 B).(\lambda (d2: C).(\lambda (_: T).(csuba g c d2)))) (ex2 C (\lambda (d2:
153 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
154 d2))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H8: (eq C
155 c2 (CHead x1 (Bind x0) x2))).(\lambda (H9: (csuba g c x1)).(eq_ind_r C (CHead
156 x1 (Bind x0) x2) (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0
157 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H10 \def
158 (H c d1 u H6 g x1 H9) in (ex2_ind C (\lambda (d2: C).(drop n O x1 (CHead d2
159 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2:
160 C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abbr) u))) (\lambda
161 (d2: C).(csuba g d1 d2))) (\lambda (x: C).(\lambda (H11: (drop n O x1 (CHead
162 x (Bind Abbr) u))).(\lambda (H12: (csuba g d1 x)).(let H13 \def (refl_equal
163 nat (r (Bind Abbr) n)) in (let H14 \def (eq_ind nat n (\lambda (n0:
164 nat).(drop n0 O x1 (CHead x (Bind Abbr) u))) H11 (r (Bind Abbr) n) H13) in
165 (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2
166 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind x0) n
167 x1 (CHead x (Bind Abbr) u) H14 x2) H12)))))) H10)) c2 H8)))))) H7))))) b H3
168 H4)))) (\lambda (f: F).(\lambda (H3: (csuba g (CHead c (Flat f) t)
169 c2)).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abbr) u))).(let
170 H_x \def (csuba_gen_flat g c c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T
171 (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda
172 (d2: C).(\lambda (_: T).(csuba g c d2))) (ex2 C (\lambda (d2: C).(drop (S n)
173 O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda
174 (x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f)
175 x1))).(\lambda (H7: (csuba g c x0)).(eq_ind_r C (CHead x0 (Flat f) x1)
176 (\lambda (c0: C).(ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
177 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))) (let H8 \def (H0 d1 u H4 g x0
178 H7) in (ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr)
179 u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(drop (S n) O
180 (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g
181 d1 d2))) (\lambda (x: C).(\lambda (H9: (drop (S n) O x0 (CHead x (Bind Abbr)
182 u))).(\lambda (H10: (csuba g d1 x)).(ex_intro2 C (\lambda (d2: C).(drop (S n)
183 O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g
184 d1 d2)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abbr) u) H9 x1) H10))))
185 H8)) c2 H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u) t n
186 H1)))))))))))) c1)))) i).
191 theorem csuba_drop_abst:
192 \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop i
193 O c1 (CHead d1 (Bind Abst) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba
194 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst)
195 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
196 C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr)
197 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
198 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
199 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
202 \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (d1:
203 C).(\forall (u1: T).((drop n O c1 (CHead d1 (Bind Abst) u1)) \to (\forall (g:
204 G).(\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C (\lambda (d2: C).(drop n
205 O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C
206 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O c2 (CHead d2
207 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
208 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
209 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
210 u2 a)))))))))))))) (\lambda (c1: C).(\lambda (d1: C).(\lambda (u1:
211 T).(\lambda (H: (drop O O c1 (CHead d1 (Bind Abst) u1))).(\lambda (g:
212 G).(\lambda (c2: C).(\lambda (H0: (csuba g c1 c2)).(let H1 \def (eq_ind C c1
213 (\lambda (c: C).(csuba g c c2)) H0 (CHead d1 (Bind Abst) u1) (drop_gen_refl
214 c1 (CHead d1 (Bind Abst) u1) H)) in (let H_x \def (csuba_gen_abst g d1 c2 u1
215 H1) in (let H2 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2
216 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
217 (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr)
218 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
219 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
220 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
221 a))))) (or (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) u1)))
222 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
223 (u2: T).(\lambda (_: A).(drop O O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
224 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
225 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
226 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H3:
227 (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
228 C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
229 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2:
230 C).(drop O O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
231 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O
232 O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
233 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
234 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
235 (a: A).(arity g d2 u2 a)))))) (\lambda (x: C).(\lambda (H4: (eq C c2 (CHead x
236 (Bind Abst) u1))).(\lambda (H5: (csuba g d1 x)).(eq_ind_r C (CHead x (Bind
237 Abst) u1) (\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (CHead d2
238 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
239 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O c (CHead d2 (Bind Abbr)
240 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
241 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
242 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
243 a))))))) (or_introl (ex2 C (\lambda (d2: C).(drop O O (CHead x (Bind Abst)
244 u1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
245 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O (CHead x (Bind
246 Abst) u1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
247 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
248 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
249 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2:
250 C).(drop O O (CHead x (Bind Abst) u1) (CHead d2 (Bind Abst) u1))) (\lambda
251 (d2: C).(csuba g d1 d2)) x (drop_refl (CHead x (Bind Abst) u1)) H5)) c2
252 H4)))) H3)) (\lambda (H3: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
253 T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
254 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
255 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
256 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C
257 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2
258 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
259 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
260 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
261 u2 a)))) (or (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) u1)))
262 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
263 (u2: T).(\lambda (_: A).(drop O O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
264 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
265 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
266 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x0:
267 C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H4: (eq C c2 (CHead x0 (Bind
268 Abbr) x1))).(\lambda (H5: (csuba g d1 x0)).(\lambda (H6: (arity g d1 u1
269 (asucc g x2))).(\lambda (H7: (arity g x0 x1 x2)).(eq_ind_r C (CHead x0 (Bind
270 Abbr) x1) (\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (CHead d2
271 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
272 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O c (CHead d2 (Bind Abbr)
273 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
274 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
275 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
276 a))))))) (or_intror (ex2 C (\lambda (d2: C).(drop O O (CHead x0 (Bind Abbr)
277 x1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
278 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O (CHead x0 (Bind
279 Abbr) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
280 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
281 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
282 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda
283 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O (CHead x0 (Bind Abbr) x1)
284 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
285 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
286 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
287 A).(arity g d2 u2 a)))) x0 x1 x2 (drop_refl (CHead x0 (Bind Abbr) x1)) H5 H6
288 H7)) c2 H4)))))))) H3)) H2))))))))))) (\lambda (n: nat).(\lambda (H:
289 ((\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop n O c1 (CHead d1
290 (Bind Abst) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c1 c2) \to
291 (or (ex2 C (\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abst) u1))) (\lambda
292 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
293 T).(\lambda (_: A).(drop n O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
294 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
295 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
296 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
297 a))))))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1:
298 C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abst) u1)) \to (\forall
299 (g: G).(\forall (c2: C).((csuba g c c2) \to (or (ex2 C (\lambda (d2: C).(drop
300 (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
301 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
302 c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
303 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
304 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
305 (a: A).(arity g d2 u2 a))))))))))))) (\lambda (n0: nat).(\lambda (d1:
306 C).(\lambda (u1: T).(\lambda (H0: (drop (S n) O (CSort n0) (CHead d1 (Bind
307 Abst) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (_: (csuba g (CSort n0)
308 c2)).(and3_ind (eq C (CHead d1 (Bind Abst) u1) (CSort n0)) (eq nat (S n) O)
309 (eq nat O O) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
310 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
311 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr)
312 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
313 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
314 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
315 a)))))) (\lambda (_: (eq C (CHead d1 (Bind Abst) u1) (CSort n0))).(\lambda
316 (H3: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S
317 n) (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
318 \Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2
319 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
320 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
321 (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
322 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
323 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
324 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) H5)))))
325 (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u1) H0))))))))) (\lambda (c:
326 C).(\lambda (H0: ((\forall (d1: C).(\forall (u1: T).((drop (S n) O c (CHead
327 d1 (Bind Abst) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c c2) \to
328 (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1)))
329 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
330 (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr) u2)))))
331 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
332 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
333 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
334 a)))))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda
335 (u1: T).(\lambda (H1: (drop (S n) O (CHead c k t) (CHead d1 (Bind Abst)
336 u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H2: (csuba g (CHead c k t)
337 c2)).(K_ind (\lambda (k0: K).((csuba g (CHead c k0 t) c2) \to ((drop (r k0 n)
338 O c (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O
339 c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
340 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead
341 d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
342 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
343 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
344 A).(arity g d2 u2 a))))))))) (\lambda (b: B).(\lambda (H3: (csuba g (CHead c
345 (Bind b) t) c2)).(\lambda (H4: (drop (r (Bind b) n) O c (CHead d1 (Bind Abst)
346 u1))).(B_ind (\lambda (b0: B).((csuba g (CHead c (Bind b0) t) c2) \to ((drop
347 (r (Bind b0) n) O c (CHead d1 (Bind Abst) u1)) \to (or (ex2 C (\lambda (d2:
348 C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
349 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
350 n) O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
351 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
352 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
353 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))))) (\lambda (H5: (csuba g
354 (CHead c (Bind Abbr) t) c2)).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead
355 d1 (Bind Abst) u1))).(let H_x \def (csuba_gen_abbr g c c2 t H5) in (let H7
356 \def H_x in (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t)))
357 (\lambda (d2: C).(csuba g c d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2
358 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
359 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2
360 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
361 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
362 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
363 u2 a)))))) (\lambda (x: C).(\lambda (H8: (eq C c2 (CHead x (Bind Abbr)
364 t))).(\lambda (H9: (csuba g c x)).(eq_ind_r C (CHead x (Bind Abbr) t)
365 (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
366 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
367 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (CHead d2 (Bind Abbr)
368 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
369 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
370 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
371 a))))))) (let H10 \def (H c d1 u1 H6 g x H9) in (or_ind (ex2 C (\lambda (d2:
372 C).(drop n O x (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
373 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x
374 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
375 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
376 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
377 A).(arity g d2 u2 a))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x
378 (Bind Abbr) t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
379 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
380 (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
381 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
382 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
383 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
384 (H11: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u1)))
385 (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop n O x
386 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C
387 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst)
388 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
389 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr) t)
390 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
391 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
392 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
393 A).(arity g d2 u2 a)))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead
394 x0 (Bind Abst) u1))).(\lambda (H13: (csuba g d1 x0)).(let H14 \def
395 (refl_equal nat (r (Bind Abbr) n)) in (let H15 \def (eq_ind nat n (\lambda
396 (n0: nat).(drop n0 O x (CHead x0 (Bind Abst) u1))) H12 (r (Bind Abbr) n) H14)
397 in (or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t)
398 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
399 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x
400 (Bind Abbr) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
401 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
402 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
403 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2:
404 C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u1))) (\lambda
405 (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abbr) n x (CHead x0 (Bind Abst)
406 u1) H15 t) H13))))))) H11)) (\lambda (H11: (ex4_3 C T A (\lambda (d2:
407 C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abbr) u2)))))
408 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
409 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
410 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
411 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
412 A).(drop n O x (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
413 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
414 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
415 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C (\lambda (d2:
416 C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u1))) (\lambda
417 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
418 T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind
419 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
420 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
421 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
422 a)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H12:
423 (drop n O x (CHead x0 (Bind Abbr) x1))).(\lambda (H13: (csuba g d1
424 x0)).(\lambda (H14: (arity g d1 u1 (asucc g x2))).(\lambda (H15: (arity g x0
425 x1 x2)).(let H16 \def (refl_equal nat (r (Bind Abbr) n)) in (let H17 \def
426 (eq_ind nat n (\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abbr) x1))) H12
427 (r (Bind Abbr) n) H16) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n) O
428 (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g
429 d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop
430 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
431 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
432 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
433 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C
434 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x
435 (Bind Abbr) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
436 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
437 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
438 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x0 x1 x2 (drop_drop (Bind Abbr)
439 n x (CHead x0 (Bind Abbr) x1) H17 t) H13 H14 H15))))))))))) H11)) H10)) c2
440 H8)))) H7))))) (\lambda (H5: (csuba g (CHead c (Bind Abst) t) c2)).(\lambda
441 (H6: (drop (r (Bind Abst) n) O c (CHead d1 (Bind Abst) u1))).(let H_x \def
442 (csuba_gen_abst g c c2 t H5) in (let H7 \def H_x in (or_ind (ex2 C (\lambda
443 (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)))
444 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2
445 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
446 A).(csuba g c d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g
447 c t (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity
448 g d2 u2 a))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
449 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
450 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr)
451 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
452 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
453 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
454 a)))))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst)
455 t))) (\lambda (d2: C).(csuba g c d2)))).(ex2_ind C (\lambda (d2: C).(eq C c2
456 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g c d2)) (or (ex2 C
457 (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
458 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
459 (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
460 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
461 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
462 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x:
463 C).(\lambda (H9: (eq C c2 (CHead x (Bind Abst) t))).(\lambda (H10: (csuba g c
464 x)).(eq_ind_r C (CHead x (Bind Abst) t) (\lambda (c0: C).(or (ex2 C (\lambda
465 (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
466 g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
467 A).(drop (S n) O c0 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda
468 (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
469 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
470 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))) (let H11 \def (H c d1 u1 H6 g
471 x H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst)
472 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
473 C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abbr) u2)))))
474 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
475 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
476 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or
477 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind
478 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
479 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t)
480 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
481 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
482 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
483 A).(arity g d2 u2 a)))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x
484 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C
485 (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u1))) (\lambda (d2:
486 C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind
487 Abst) t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
488 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
489 (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
490 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
491 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
492 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x0:
493 C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abst) u1))).(\lambda (H14:
494 (csuba g d1 x0)).(let H15 \def (refl_equal nat (r (Bind Abbr) n)) in (let H16
495 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abst)
496 u1))) H13 (r (Bind Abbr) n) H15) in (or_introl (ex2 C (\lambda (d2: C).(drop
497 (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u1))) (\lambda (d2:
498 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
499 (_: A).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u2)))))
500 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
501 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
502 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
503 (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2
504 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x0 (drop_drop (Bind Abst)
505 n x (CHead x0 (Bind Abst) u1) H16 t) H14))))))) H12)) (\lambda (H12: (ex4_3 C
506 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2
507 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
508 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
509 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
510 u2 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
511 A).(drop n O x (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
512 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
513 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
514 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C (\lambda (d2:
515 C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u1))) (\lambda
516 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
517 T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind
518 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
519 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
520 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
521 a)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H13:
522 (drop n O x (CHead x0 (Bind Abbr) x1))).(\lambda (H14: (csuba g d1
523 x0)).(\lambda (H15: (arity g d1 u1 (asucc g x2))).(\lambda (H16: (arity g x0
524 x1 x2)).(let H17 \def (refl_equal nat (r (Bind Abbr) n)) in (let H18 \def
525 (eq_ind nat n (\lambda (n0: nat).(drop n0 O x (CHead x0 (Bind Abbr) x1))) H13
526 (r (Bind Abbr) n) H17) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n) O
527 (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g
528 d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop
529 (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
530 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
531 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
532 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C
533 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x
534 (Bind Abst) t) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
535 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
536 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
537 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x0 x1 x2 (drop_drop (Bind Abst)
538 n x (CHead x0 (Bind Abbr) x1) H18 t) H14 H15 H16))))))))))) H12)) H11)) c2
539 H9)))) H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
540 T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
541 C).(\lambda (_: T).(\lambda (_: A).(csuba g c d2)))) (\lambda (_: C).(\lambda
542 (_: T).(\lambda (a: A).(arity g c t (asucc g a))))) (\lambda (d2: C).(\lambda
543 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C T A (\lambda (d2:
544 C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abbr) u2)))))
545 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g c d2)))) (\lambda
546 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t (asucc g a))))) (\lambda
547 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C
548 (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
549 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
550 (_: A).(drop (S n) O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
551 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
552 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
553 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x0:
554 C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H9: (eq C c2 (CHead x0 (Bind
555 Abbr) x1))).(\lambda (H10: (csuba g c x0)).(\lambda (_: (arity g c t (asucc g
556 x2))).(\lambda (_: (arity g x0 x1 x2)).(eq_ind_r C (CHead x0 (Bind Abbr) x1)
557 (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
558 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
559 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (CHead d2 (Bind Abbr)
560 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
561 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
562 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
563 a))))))) (let H13 \def (H c d1 u1 H6 g x0 H10) in (or_ind (ex2 C (\lambda
564 (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
565 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n
566 O x0 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
567 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
568 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
569 (a: A).(arity g d2 u2 a))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead
570 x0 (Bind Abbr) x1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
571 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
572 n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
573 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
574 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
575 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
576 (H14: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u1)))
577 (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop n O x0
578 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C
579 (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind
580 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
581 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Abbr) x1)
582 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
583 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
584 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
585 A).(arity g d2 u2 a)))))) (\lambda (x: C).(\lambda (H15: (drop n O x0 (CHead
586 x (Bind Abst) u1))).(\lambda (H16: (csuba g d1 x)).(let H17 \def (refl_equal
587 nat (r (Bind Abbr) n)) in (let H18 \def (eq_ind nat n (\lambda (n0:
588 nat).(drop n0 O x0 (CHead x (Bind Abst) u1))) H15 (r (Bind Abbr) n) H17) in
589 (or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abbr) x1)
590 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
591 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
592 (Bind Abbr) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
593 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
594 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
595 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2:
596 C).(drop (S n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abst) u1)))
597 (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind Abbr) n x0 (CHead x
598 (Bind Abst) u1) H18 x1) H16))))))) H14)) (\lambda (H14: (ex4_3 C T A (\lambda
599 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (CHead d2 (Bind Abbr)
600 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
601 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
602 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
603 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
604 A).(drop n O x0 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
605 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
606 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
607 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C (\lambda (d2:
608 C).(drop (S n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abst) u1)))
609 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
610 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Abbr) x1) (CHead d2
611 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
612 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
613 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
614 u2 a)))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: A).(\lambda (H15:
615 (drop n O x0 (CHead x3 (Bind Abbr) x4))).(\lambda (H16: (csuba g d1
616 x3)).(\lambda (H17: (arity g d1 u1 (asucc g x5))).(\lambda (H18: (arity g x3
617 x4 x5)).(let H19 \def (refl_equal nat (r (Bind Abbr) n)) in (let H20 \def
618 (eq_ind nat n (\lambda (n0: nat).(drop n0 O x0 (CHead x3 (Bind Abbr) x4)))
619 H15 (r (Bind Abbr) n) H19) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n)
620 O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abst) u1))) (\lambda (d2:
621 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
622 (_: A).(drop (S n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abbr) u2)))))
623 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
624 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
625 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
626 (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
627 n) O (CHead x0 (Bind Abbr) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
628 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
629 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
630 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x3 x4 x5
631 (drop_drop (Bind Abbr) n x0 (CHead x3 (Bind Abbr) x4) H20 x1) H16 H17
632 H18))))))))))) H14)) H13)) c2 H9)))))))) H8)) H7))))) (\lambda (H5: (csuba g
633 (CHead c (Bind Void) t) c2)).(\lambda (H6: (drop (r (Bind Void) n) O c (CHead
634 d1 (Bind Abst) u1))).(let H_x \def (csuba_gen_void g c c2 t H5) in (let H7
635 \def H_x in (ex2_3_ind B C T (\lambda (b0: B).(\lambda (d2: C).(\lambda (u2:
636 T).(eq C c2 (CHead d2 (Bind b0) u2))))) (\lambda (_: B).(\lambda (d2:
637 C).(\lambda (_: T).(csuba g c d2)))) (or (ex2 C (\lambda (d2: C).(drop (S n)
638 O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C
639 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead
640 d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
641 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
642 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
643 A).(arity g d2 u2 a)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2:
644 T).(\lambda (H8: (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda (H9: (csuba g c
645 x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c0: C).(or (ex2 C (\lambda
646 (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
647 g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
648 A).(drop (S n) O c0 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda
649 (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
650 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
651 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))) (let H10 \def (H c d1 u1 H6 g
652 x1 H9) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x1 (CHead d2 (Bind Abst)
653 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
654 C).(\lambda (u2: T).(\lambda (_: A).(drop n O x1 (CHead d2 (Bind Abbr)
655 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
656 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
657 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
658 a))))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x1 (Bind x0) x2)
659 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
660 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x1
661 (Bind x0) x2) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
662 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
663 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
664 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H11: (ex2 C (\lambda
665 (d2: C).(drop n O x1 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
666 d2)))).(ex2_ind C (\lambda (d2: C).(drop n O x1 (CHead d2 (Bind Abst) u1)))
667 (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O
668 (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g
669 d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop
670 (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
671 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
672 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
673 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x:
674 C).(\lambda (H12: (drop n O x1 (CHead x (Bind Abst) u1))).(\lambda (H13:
675 (csuba g d1 x)).(let H14 \def (refl_equal nat (r (Bind Abbr) n)) in (let H15
676 \def (eq_ind nat n (\lambda (n0: nat).(drop n0 O x1 (CHead x (Bind Abst)
677 u1))) H12 (r (Bind Abbr) n) H14) in (or_introl (ex2 C (\lambda (d2: C).(drop
678 (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abst) u1))) (\lambda (d2:
679 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
680 (_: A).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abbr) u2)))))
681 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
682 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
683 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
684 (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2
685 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x (drop_drop (Bind x0) n
686 x1 (CHead x (Bind Abst) u1) H15 x2) H13))))))) H11)) (\lambda (H11: (ex4_3 C
687 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x1 (CHead d2
688 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
689 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
690 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
691 u2 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
692 A).(drop n O x1 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
693 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
694 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
695 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C (\lambda (d2:
696 C).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abst) u1))) (\lambda
697 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
698 T).(\lambda (_: A).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind
699 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
700 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
701 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
702 a)))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: A).(\lambda (H12:
703 (drop n O x1 (CHead x3 (Bind Abbr) x4))).(\lambda (H13: (csuba g d1
704 x3)).(\lambda (H14: (arity g d1 u1 (asucc g x5))).(\lambda (H15: (arity g x3
705 x4 x5)).(let H16 \def (refl_equal nat (r (Bind Abbr) n)) in (let H17 \def
706 (eq_ind nat n (\lambda (n0: nat).(drop n0 O x1 (CHead x3 (Bind Abbr) x4)))
707 H12 (r (Bind Abbr) n) H16) in (or_intror (ex2 C (\lambda (d2: C).(drop (S n)
708 O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
709 g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
710 A).(drop (S n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abbr) u2)))))
711 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
712 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
713 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
714 (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
715 n) O (CHead x1 (Bind x0) x2) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
716 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
717 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
718 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x3 x4 x5
719 (drop_drop (Bind x0) n x1 (CHead x3 (Bind Abbr) x4) H17 x2) H13 H14
720 H15))))))))))) H11)) H10)) c2 H8)))))) H7))))) b H3 H4)))) (\lambda (f:
721 F).(\lambda (H3: (csuba g (CHead c (Flat f) t) c2)).(\lambda (H4: (drop (r
722 (Flat f) n) O c (CHead d1 (Bind Abst) u1))).(let H_x \def (csuba_gen_flat g c
723 c2 t f H3) in (let H5 \def H_x in (ex2_2_ind C T (\lambda (d2: C).(\lambda
724 (u2: T).(eq C c2 (CHead d2 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_:
725 T).(csuba g c d2))) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2
726 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
727 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind
728 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
729 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
730 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
731 a)))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0
732 (Flat f) x1))).(\lambda (H7: (csuba g c x0)).(eq_ind_r C (CHead x0 (Flat f)
733 x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2
734 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
735 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (CHead d2 (Bind
736 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
737 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
738 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
739 a))))))) (let H8 \def (H0 d1 u1 H4 g x0 H7) in (or_ind (ex2 C (\lambda (d2:
740 C).(drop (S n) O x0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
741 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
742 n) O x0 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
743 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
744 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
745 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or (ex2 C (\lambda (d2:
746 C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u1))) (\lambda
747 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
748 T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr)
749 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
750 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
751 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
752 a)))))) (\lambda (H9: (ex2 C (\lambda (d2: C).(drop (S n) O x0 (CHead d2
753 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda
754 (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba
755 g d1 d2)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1)
756 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
757 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
758 (Flat f) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
759 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
760 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
761 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x: C).(\lambda (H10:
762 (drop (S n) O x0 (CHead x (Bind Abst) u1))).(\lambda (H11: (csuba g d1
763 x)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1)
764 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
765 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
766 (Flat f) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
767 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
768 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
769 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2:
770 C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u1))) (\lambda
771 (d2: C).(csuba g d1 d2)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abst) u1)
772 H10 x1) H11))))) H9)) (\lambda (H9: (ex4_3 C T A (\lambda (d2: C).(\lambda
773 (u2: T).(\lambda (_: A).(drop (S n) O x0 (CHead d2 (Bind Abbr) u2)))))
774 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
775 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
776 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
777 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
778 A).(drop (S n) O x0 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda
779 (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
780 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
781 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C (\lambda (d2:
782 C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u1))) (\lambda
783 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
784 T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr)
785 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
786 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
787 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
788 a)))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H10:
789 (drop (S n) O x0 (CHead x2 (Bind Abbr) x3))).(\lambda (H11: (csuba g d1
790 x2)).(\lambda (H12: (arity g d1 u1 (asucc g x4))).(\lambda (H13: (arity g x2
791 x3 x4)).(or_intror (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f)
792 x1) (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
793 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
794 (Flat f) x1) (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
795 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
796 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
797 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda
798 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1)
799 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
800 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
801 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
802 A).(arity g d2 u2 a)))) x2 x3 x4 (drop_drop (Flat f) n x0 (CHead x2 (Bind
803 Abbr) x3) H10 x1) H11 H12 H13))))))))) H9)) H8)) c2 H6))))) H5)))))) k H2
804 (drop_gen_drop k c (CHead d1 (Bind Abst) u1) t n H1)))))))))))) c1)))) i).
809 theorem csuba_drop_abst_rev:
810 \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop i
811 O c1 (CHead d1 (Bind Abst) u)) \to (\forall (g: G).(\forall (c2: C).((csuba g
812 c2 c1) \to (or (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst)
813 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
814 (u2: T).(drop i O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
815 (_: T).(csuba g d2 d1))))))))))))
817 \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (d1:
818 C).(\forall (u: T).((drop n O c1 (CHead d1 (Bind Abst) u)) \to (\forall (g:
819 G).(\forall (c2: C).((csuba g c2 c1) \to (or (ex2 C (\lambda (d2: C).(drop n
820 O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
821 (\lambda (d2: C).(\lambda (u2: T).(drop n O c2 (CHead d2 (Bind Void) u2))))
822 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))) (\lambda (c1:
823 C).(\lambda (d1: C).(\lambda (u: T).(\lambda (H: (drop O O c1 (CHead d1 (Bind
824 Abst) u))).(\lambda (g: G).(\lambda (c2: C).(\lambda (H0: (csuba g c2
825 c1)).(let H1 \def (eq_ind C c1 (\lambda (c: C).(csuba g c2 c)) H0 (CHead d1
826 (Bind Abst) u) (drop_gen_refl c1 (CHead d1 (Bind Abst) u) H)) in (let H_x
827 \def (csuba_gen_abst_rev g d1 c2 u H1) in (let H2 \def H_x in (or_ind (ex2 C
828 (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba
829 g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2
830 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or
831 (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
832 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O
833 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
834 d1))))) (\lambda (H3: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst)
835 u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(eq C c2
836 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C
837 (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
838 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O
839 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
840 d1))))) (\lambda (x: C).(\lambda (H4: (eq C c2 (CHead x (Bind Abst)
841 u))).(\lambda (H5: (csuba g x d1)).(eq_ind_r C (CHead x (Bind Abst) u)
842 (\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abst)
843 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
844 (u2: T).(drop O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
845 (_: T).(csuba g d2 d1)))))) (or_introl (ex2 C (\lambda (d2: C).(drop O O
846 (CHead x (Bind Abst) u) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g
847 d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x
848 (Bind Abst) u) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
849 T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop O O (CHead x (Bind
850 Abst) u) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x
851 (drop_refl (CHead x (Bind Abst) u)) H5)) c2 H4)))) H3)) (\lambda (H3: (ex2_2
852 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void) u2))))
853 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda
854 (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
855 C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop O O c2
856 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
857 (\lambda (d2: C).(\lambda (u2: T).(drop O O c2 (CHead d2 (Bind Void) u2))))
858 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
859 C).(\lambda (x1: T).(\lambda (H4: (eq C c2 (CHead x0 (Bind Void)
860 x1))).(\lambda (H5: (csuba g x0 d1)).(eq_ind_r C (CHead x0 (Bind Void) x1)
861 (\lambda (c: C).(or (ex2 C (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abst)
862 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
863 (u2: T).(drop O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
864 (_: T).(csuba g d2 d1)))))) (or_intror (ex2 C (\lambda (d2: C).(drop O O
865 (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba
866 g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x0
867 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
868 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
869 T).(drop O O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda
870 (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_refl (CHead x0 (Bind
871 Void) x1)) H5)) c2 H4))))) H3)) H2))))))))))) (\lambda (n: nat).(\lambda (H:
872 ((\forall (c1: C).(\forall (d1: C).(\forall (u: T).((drop n O c1 (CHead d1
873 (Bind Abst) u)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c1) \to (or
874 (ex2 C (\lambda (d2: C).(drop n O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
875 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O
876 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
877 d1)))))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1:
878 C).(\forall (u: T).((drop (S n) O c (CHead d1 (Bind Abst) u)) \to (\forall
879 (g: G).(\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop
880 (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
881 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
882 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))
883 (\lambda (n0: nat).(\lambda (d1: C).(\lambda (u: T).(\lambda (H0: (drop (S n)
884 O (CSort n0) (CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda (c2:
885 C).(\lambda (_: (csuba g c2 (CSort n0))).(and3_ind (eq C (CHead d1 (Bind
886 Abst) u) (CSort n0)) (eq nat (S n) O) (eq nat O O) (or (ex2 C (\lambda (d2:
887 C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
888 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2
889 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
890 (\lambda (_: (eq C (CHead d1 (Bind Abst) u) (CSort n0))).(\lambda (H3: (eq
891 nat (S n) O)).(\lambda (_: (eq nat O O)).(let H5 \def (eq_ind nat (S n)
892 (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
893 \Rightarrow False | (S _) \Rightarrow True])) I O H3) in (False_ind (or (ex2
894 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
895 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
896 O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
897 d2 d1))))) H5))))) (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abst) u)
898 H0))))))))) (\lambda (c: C).(\lambda (H0: ((\forall (d1: C).(\forall (u:
899 T).((drop (S n) O c (CHead d1 (Bind Abst) u)) \to (\forall (g: G).(\forall
900 (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O c2
901 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
902 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
903 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda
904 (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u: T).(\lambda (H1: (drop
905 (S n) O (CHead c k t) (CHead d1 (Bind Abst) u))).(\lambda (g: G).(\lambda
906 (c2: C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0:
907 K).((csuba g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abst)
908 u)) \to (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst)
909 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
910 (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
911 C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda (b: B).(\lambda (H3:
912 (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop (r (Bind b) n) O c
913 (CHead d1 (Bind Abst) u))).(B_ind (\lambda (b0: B).((csuba g c2 (CHead c
914 (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead d1 (Bind Abst) u)) \to
915 (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u)))
916 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
917 T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
918 (_: T).(csuba g d2 d1)))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr)
919 t))).(\lambda (H6: (drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abst)
920 u))).(let H_x \def (csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in
921 (or3_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda
922 (d2: C).(csuba g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
923 T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
924 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\lambda (d2:
925 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
926 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t a))))) (ex2_2 C T
927 (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void) u2))))
928 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c)))) (or (ex2 C (\lambda (d2:
929 C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
930 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2
931 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
932 (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t)))
933 (\lambda (d2: C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2
934 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or (ex2 C
935 (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
936 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
937 O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
938 d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq C c2 (CHead x (Bind Abbr)
939 t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C (CHead x (Bind Abbr) t)
940 (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind
941 Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
942 C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda
943 (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H11 \def (H c d1 u H6 g x
944 H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst)
945 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
946 (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
947 (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x
948 (Bind Abbr) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
949 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind
950 Abbr) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba
951 g d2 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2
952 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2:
953 C).(drop n O x (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))
954 (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2
955 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
956 C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind
957 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
958 (x0: C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abst) u))).(\lambda (H14:
959 (csuba g x0 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x
960 (Bind Abbr) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
961 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind
962 Abbr) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba
963 g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr)
964 t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop
965 (Bind Abbr) n x (CHead x0 (Bind Abst) u) H13 t) H14))))) H12)) (\lambda (H12:
966 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind
967 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind
968 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void)
969 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda
970 (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u)))
971 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
972 T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2))))
973 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
974 C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead x0 (Bind Void)
975 x1))).(\lambda (H14: (csuba g x0 d1)).(or_intror (ex2 C (\lambda (d2:
976 C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u))) (\lambda
977 (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop
978 (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
979 C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2:
980 C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind
981 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1
982 (drop_drop (Bind Abbr) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12))
983 H11)) c2 H9)))) H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda
984 (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
985 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\lambda (d2:
986 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
987 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t a)))))).(ex4_3_ind C T A
988 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind
989 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
990 c)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc
991 g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t a))))
992 (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u)))
993 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
994 T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
995 (_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2:
996 A).(\lambda (H9: (eq C c2 (CHead x0 (Bind Abst) x1))).(\lambda (H10: (csuba g
997 x0 c)).(\lambda (_: (arity g x0 x1 (asucc g x2))).(\lambda (_: (arity g c t
998 x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1) (\lambda (c0: C).(or (ex2 C
999 (\lambda (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2:
1000 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
1001 O c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
1002 d2 d1)))))) (let H13 \def (H c d1 u H6 g x0 H10) in (or_ind (ex2 C (\lambda
1003 (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
1004 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2
1005 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or
1006 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2
1007 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1008 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1009 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1010 (H14: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u)))
1011 (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x0
1012 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C
1013 (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1014 Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1015 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1016 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1017 (x: C).(\lambda (H15: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H16:
1018 (csuba g x d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0
1019 (Bind Abst) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
1020 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind
1021 Abst) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1022 T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0
1023 (Bind Abst) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))
1024 x (drop_drop (Bind Abst) n x0 (CHead x (Bind Abst) u) H15 x1) H16))))) H14))
1025 (\lambda (H14: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0
1026 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1027 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead
1028 d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or
1029 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2
1030 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1031 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1032 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1033 (x3: C).(\lambda (x4: T).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Void)
1034 x4))).(\lambda (H16: (csuba g x3 d1)).(or_intror (ex2 C (\lambda (d2:
1035 C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u)))
1036 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1037 T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2))))
1038 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda
1039 (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2
1040 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x3 x4
1041 (drop_drop (Bind Abst) n x0 (CHead x3 (Bind Void) x4) H15 x1) H16)))))) H14))
1042 H13)) c2 H9)))))))) H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda
1043 (u2: T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1044 T).(csuba g d2 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C
1045 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1046 c))) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u)))
1047 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1048 T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1049 (_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H9:
1050 (eq C c2 (CHead x0 (Bind Void) x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r
1051 C (CHead x0 (Bind Void) x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2:
1052 C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
1053 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2
1054 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let
1055 H11 \def (H c d1 u H6 g x0 H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O
1056 x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
1057 (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2 (Bind Void) u2))))
1058 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2:
1059 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u)))
1060 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1061 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1062 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H12: (ex2 C
1063 (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2:
1064 C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x0 (CHead d2
1065 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
1066 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u)))
1067 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1068 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1069 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda
1070 (H13: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H14: (csuba g x
1071 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void)
1072 x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
1073 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1)
1074 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1075 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1)
1076 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop
1077 (Bind Void) n x0 (CHead x (Bind Abst) u) H13 x1) H14))))) H12)) (\lambda
1078 (H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2
1079 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1080 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead
1081 d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or
1082 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
1083 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1084 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
1085 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1086 (x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void)
1087 x3))).(\lambda (H14: (csuba g x2 d1)).(or_intror (ex2 C (\lambda (d2:
1088 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u)))
1089 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1090 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1091 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda
1092 (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
1093 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3
1094 (drop_drop (Bind Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12))
1095 H11)) c2 H9))))) H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abst)
1096 t))).(\lambda (H6: (drop (r (Bind Abst) n) O c (CHead d1 (Bind Abst)
1097 u))).(let H_x \def (csuba_gen_abst_rev g c c2 t H5) in (let H7 \def H_x in
1098 (or_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda
1099 (d2: C).(csuba g d2 c))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C
1100 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1101 c)))) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u)))
1102 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1103 T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1104 (_: T).(csuba g d2 d1))))) (\lambda (H8: (ex2 C (\lambda (d2: C).(eq C c2
1105 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba g d2 c)))).(ex2_ind C
1106 (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba
1107 g d2 c)) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst)
1108 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
1109 (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1110 C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq C c2
1111 (CHead x (Bind Abst) t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C (CHead x
1112 (Bind Abst) t) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0
1113 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
1114 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void)
1115 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H11 \def (H
1116 c d1 u H6 g x H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2
1117 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1118 C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1119 C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n)
1120 O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba
1121 g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
1122 x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1123 T).(csuba g d2 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x
1124 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
1125 (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u))) (\lambda (d2:
1126 C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind
1127 Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
1128 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t)
1129 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1130 d1))))) (\lambda (x0: C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abst)
1131 u))).(\lambda (H14: (csuba g x0 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop
1132 (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2:
1133 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
1134 O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1135 C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S
1136 n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2:
1137 C).(csuba g d2 d1)) x0 (drop_drop (Bind Abst) n x (CHead x0 (Bind Abst) u)
1138 H13 t) H14))))) H12)) (\lambda (H12: (ex2_2 C T (\lambda (d2: C).(\lambda
1139 (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1140 (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2:
1141 T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1142 T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind
1143 Abst) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
1144 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t)
1145 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1146 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead
1147 x0 (Bind Void) x1))).(\lambda (H14: (csuba g x0 d1)).(or_intror (ex2 C
1148 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst)
1149 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
1150 (u2: T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2))))
1151 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda
1152 (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2
1153 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1
1154 (drop_drop (Bind Abst) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12))
1155 H11)) c2 H9)))) H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1156 T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1157 T).(csuba g d2 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C
1158 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1159 c))) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u)))
1160 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1161 T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1162 (_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H9:
1163 (eq C c2 (CHead x0 (Bind Void) x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r
1164 C (CHead x0 (Bind Void) x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2:
1165 C).(drop (S n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
1166 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2
1167 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let
1168 H11 \def (H c d1 u H6 g x0 H10) in (or_ind (ex2 C (\lambda (d2: C).(drop n O
1169 x0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
1170 (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2 (Bind Void) u2))))
1171 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2:
1172 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u)))
1173 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1174 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1175 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H12: (ex2 C
1176 (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2:
1177 C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x0 (CHead d2
1178 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
1179 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u)))
1180 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1181 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1182 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda
1183 (H13: (drop n O x0 (CHead x (Bind Abst) u))).(\lambda (H14: (csuba g x
1184 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void)
1185 x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T
1186 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1)
1187 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1188 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1)
1189 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop
1190 (Bind Void) n x0 (CHead x (Bind Abst) u) H13 x1) H14))))) H12)) (\lambda
1191 (H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead d2
1192 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1193 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x0 (CHead
1194 d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or
1195 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
1196 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1197 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
1198 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1199 (x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void)
1200 x3))).(\lambda (H14: (csuba g x2 d1)).(or_intror (ex2 C (\lambda (d2:
1201 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u)))
1202 (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1203 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1204 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda
1205 (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
1206 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3
1207 (drop_drop (Bind Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12))
1208 H11)) c2 H9))))) H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Void)
1209 t))).(\lambda (H6: (drop (r (Bind Void) n) O c (CHead d1 (Bind Abst)
1210 u))).(let H_x \def (csuba_gen_void_rev g c c2 t H5) in (let H7 \def H_x in
1211 (ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Void) t))) (\lambda (d2:
1212 C).(csuba g d2 c)) (or (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2
1213 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1214 C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
1215 (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H8: (eq
1216 C c2 (CHead x (Bind Void) t))).(\lambda (H9: (csuba g x c)).(eq_ind_r C
1217 (CHead x (Bind Void) t) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S
1218 n) O c0 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
1219 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void)
1220 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H10 \def (H
1221 c d1 u H6 g x H9) in (or_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2
1222 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1223 C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1224 C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n)
1225 O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba
1226 g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
1227 x (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1228 T).(csuba g d2 d1))))) (\lambda (H11: (ex2 C (\lambda (d2: C).(drop n O x
1229 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
1230 (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abst) u))) (\lambda (d2:
1231 C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind
1232 Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
1233 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Void) t)
1234 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1235 d1))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0 (Bind Abst)
1236 u))).(\lambda (H13: (csuba g x0 d1)).(or_introl (ex2 C (\lambda (d2: C).(drop
1237 (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2:
1238 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
1239 O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1240 C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S
1241 n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2:
1242 C).(csuba g d2 d1)) x0 (drop_drop (Bind Void) n x (CHead x0 (Bind Abst) u)
1243 H12 t) H13))))) H11)) (\lambda (H11: (ex2_2 C T (\lambda (d2: C).(\lambda
1244 (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1245 (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2:
1246 T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1247 T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind
1248 Void) t) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2
1249 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Void) t)
1250 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1251 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H12: (drop n O x (CHead
1252 x0 (Bind Void) x1))).(\lambda (H13: (csuba g x0 d1)).(or_intror (ex2 C
1253 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abst)
1254 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
1255 (u2: T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2))))
1256 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda
1257 (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2
1258 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1
1259 (drop_drop (Bind Void) n x (CHead x0 (Bind Void) x1) H12 t) H13)))))) H11))
1260 H10)) c2 H8)))) H7))))) b H3 H4)))) (\lambda (f: F).(\lambda (H3: (csuba g c2
1261 (CHead c (Flat f) t))).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind
1262 Abst) u))).(let H_x \def (csuba_gen_flat_rev g c c2 t f H3) in (let H5 \def
1263 H_x in (ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2
1264 (Flat f) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c))) (or (ex2 C
1265 (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
1266 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
1267 O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
1268 d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (eq C c2 (CHead x0
1269 (Flat f) x1))).(\lambda (H7: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Flat f)
1270 x1) (\lambda (c0: C).(or (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2
1271 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2:
1272 C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda
1273 (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H8 \def (H0 d1 u H4 g x0
1274 H7) in (or_ind (ex2 C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst)
1275 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
1276 (u2: T).(drop (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1277 C).(\lambda (_: T).(csuba g d2 d1)))) (or (ex2 C (\lambda (d2: C).(drop (S n)
1278 O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g
1279 d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0
1280 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1281 T).(csuba g d2 d1))))) (\lambda (H9: (ex2 C (\lambda (d2: C).(drop (S n) O x0
1282 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C
1283 (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abst) u))) (\lambda (d2:
1284 C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat
1285 f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C
1286 T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f) x1)
1287 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1288 d1))))) (\lambda (x: C).(\lambda (H10: (drop (S n) O x0 (CHead x (Bind Abst)
1289 u))).(\lambda (H11: (csuba g x d1)).(or_introl (ex2 C (\lambda (d2: C).(drop
1290 (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2:
1291 C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n)
1292 O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1293 C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S
1294 n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2:
1295 C).(csuba g d2 d1)) x (drop_drop (Flat f) n x0 (CHead x (Bind Abst) u) H10
1296 x1) H11))))) H9)) (\lambda (H9: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1297 T).(drop (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1298 (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2:
1299 T).(drop (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1300 (_: T).(csuba g d2 d1))) (or (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0
1301 (Flat f) x1) (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
1302 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f)
1303 x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1304 d1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (H10: (drop (S n) O x0
1305 (CHead x2 (Bind Void) x3))).(\lambda (H11: (csuba g x2 d1)).(or_intror (ex2 C
1306 (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst)
1307 u))) (\lambda (d2: C).(csuba g d2 d1))) (ex2_2 C T (\lambda (d2: C).(\lambda
1308 (u2: T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2))))
1309 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda
1310 (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind
1311 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3
1312 (drop_drop (Flat f) n x0 (CHead x2 (Bind Void) x3) H10 x1) H11)))))) H9))
1313 H8)) c2 H6))))) H5)))))) k H2 (drop_gen_drop k c (CHead d1 (Bind Abst) u) t n
1314 H1)))))))))))) c1)))) i).
1316 Initial nodes: 11438
1319 theorem csuba_drop_abbr_rev:
1320 \forall (i: nat).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).((drop i
1321 O c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba
1322 g c2 c1) \to (or3 (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr)
1323 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1324 C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst)
1325 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1326 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1327 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1328 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop i O c2 (CHead d2 (Bind
1329 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))
1331 \lambda (i: nat).(nat_ind (\lambda (n: nat).(\forall (c1: C).(\forall (d1:
1332 C).(\forall (u1: T).((drop n O c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (g:
1333 G).(\forall (c2: C).((csuba g c2 c1) \to (or3 (ex2 C (\lambda (d2: C).(drop n
1334 O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C
1335 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O c2 (CHead d2
1336 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1337 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1338 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1339 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O c2 (CHead d2
1340 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1341 d1))))))))))))) (\lambda (c1: C).(\lambda (d1: C).(\lambda (u1: T).(\lambda
1342 (H: (drop O O c1 (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda (c2:
1343 C).(\lambda (H0: (csuba g c2 c1)).(let H1 \def (eq_ind C c1 (\lambda (c:
1344 C).(csuba g c2 c)) H0 (CHead d1 (Bind Abbr) u1) (drop_gen_refl c1 (CHead d1
1345 (Bind Abbr) u1) H)) in (let H_x \def (csuba_gen_abbr_rev g d1 c2 u1 H1) in
1346 (let H2 \def H_x in (or3_ind (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
1347 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1348 C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2)))))
1349 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
1350 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1351 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
1352 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void) u2))))
1353 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2:
1354 C).(drop O O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1355 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O
1356 O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1357 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1358 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1359 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1360 T).(drop O O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1361 T).(csuba g d2 d1))))) (\lambda (H3: (ex2 C (\lambda (d2: C).(eq C c2 (CHead
1362 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda
1363 (d2: C).(eq C c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1364 d1)) (or3 (ex2 C (\lambda (d2: C).(drop O O c2 (CHead d2 (Bind Abbr) u1)))
1365 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
1366 (u2: T).(\lambda (_: A).(drop O O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
1367 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1368 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1369 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1370 (\lambda (d2: C).(\lambda (u2: T).(drop O O c2 (CHead d2 (Bind Void) u2))))
1371 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda
1372 (H4: (eq C c2 (CHead x (Bind Abbr) u1))).(\lambda (H5: (csuba g x
1373 d1)).(eq_ind_r C (CHead x (Bind Abbr) u1) (\lambda (c: C).(or3 (ex2 C
1374 (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1375 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1376 (_: A).(drop O O c (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
1377 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1378 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1379 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1380 C).(\lambda (u2: T).(drop O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1381 C).(\lambda (_: T).(csuba g d2 d1)))))) (or3_intro0 (ex2 C (\lambda (d2:
1382 C).(drop O O (CHead x (Bind Abbr) u1) (CHead d2 (Bind Abbr) u1))) (\lambda
1383 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
1384 T).(\lambda (_: A).(drop O O (CHead x (Bind Abbr) u1) (CHead d2 (Bind Abst)
1385 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1386 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1387 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1388 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x (Bind Abbr)
1389 u1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1390 d1)))) (ex_intro2 C (\lambda (d2: C).(drop O O (CHead x (Bind Abbr) u1)
1391 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_refl
1392 (CHead x (Bind Abbr) u1)) H5)) c2 H4)))) H3)) (\lambda (H3: (ex4_3 C T A
1393 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind
1394 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
1395 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1396 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1397 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
1398 A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1399 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1400 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1401 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C (\lambda (d2:
1402 C).(drop O O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1403 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O
1404 O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1405 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1406 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1407 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1408 T).(drop O O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1409 T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2:
1410 A).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abst) x1))).(\lambda (H5: (csuba g
1411 x0 d1)).(\lambda (H6: (arity g x0 x1 (asucc g x2))).(\lambda (H7: (arity g d1
1412 u1 x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1) (\lambda (c: C).(or3 (ex2 C
1413 (\lambda (d2: C).(drop O O c (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1414 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1415 (_: A).(drop O O c (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
1416 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1417 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1418 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1419 C).(\lambda (u2: T).(drop O O c (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1420 C).(\lambda (_: T).(csuba g d2 d1)))))) (or3_intro1 (ex2 C (\lambda (d2:
1421 C).(drop O O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1))) (\lambda
1422 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
1423 T).(\lambda (_: A).(drop O O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst)
1424 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1425 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1426 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1427 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x0 (Bind Abst)
1428 x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1429 d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
1430 A).(drop O O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda
1431 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1432 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1433 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2
1434 (drop_refl (CHead x0 (Bind Abst) x1)) H5 H6 H7)) c2 H4)))))))) H3)) (\lambda
1435 (H3: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind
1436 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind
1437 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Bind Void) u2))))
1438 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C (\lambda (d2:
1439 C).(drop O O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1440 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O
1441 O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1442 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1443 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1444 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1445 T).(drop O O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1446 T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H4: (eq C
1447 c2 (CHead x0 (Bind Void) x1))).(\lambda (H5: (csuba g x0 d1)).(eq_ind_r C
1448 (CHead x0 (Bind Void) x1) (\lambda (c: C).(or3 (ex2 C (\lambda (d2: C).(drop
1449 O O c (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C
1450 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O c (CHead d2
1451 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1452 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1453 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1454 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop O O c (CHead d2
1455 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))
1456 (or3_intro2 (ex2 C (\lambda (d2: C).(drop O O (CHead x0 (Bind Void) x1)
1457 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
1458 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop O O (CHead x0 (Bind
1459 Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1460 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1461 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1462 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1463 C).(\lambda (u2: T).(drop O O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void)
1464 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex2_2_intro C T
1465 (\lambda (d2: C).(\lambda (u2: T).(drop O O (CHead x0 (Bind Void) x1) (CHead
1466 d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0
1467 x1 (drop_refl (CHead x0 (Bind Void) x1)) H5)) c2 H4))))) H3)) H2)))))))))))
1468 (\lambda (n: nat).(\lambda (H: ((\forall (c1: C).(\forall (d1: C).(\forall
1469 (u1: T).((drop n O c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall
1470 (c2: C).((csuba g c2 c1) \to (or3 (ex2 C (\lambda (d2: C).(drop n O c2 (CHead
1471 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1472 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O c2 (CHead d2 (Bind Abst)
1473 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1474 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1475 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1476 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O c2 (CHead d2 (Bind
1477 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1478 d1)))))))))))))).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (d1:
1479 C).(\forall (u1: T).((drop (S n) O c (CHead d1 (Bind Abbr) u1)) \to (\forall
1480 (g: G).(\forall (c2: C).((csuba g c2 c) \to (or3 (ex2 C (\lambda (d2:
1481 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1482 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1483 n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1484 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1485 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1486 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1487 C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
1488 (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))))))) (\lambda (n0:
1489 nat).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H0: (drop (S n) O (CSort n0)
1490 (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda (c2: C).(\lambda (_:
1491 (csuba g c2 (CSort n0))).(and3_ind (eq C (CHead d1 (Bind Abbr) u1) (CSort
1492 n0)) (eq nat (S n) O) (eq nat O O) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O
1493 c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T
1494 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead
1495 d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
1496 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1497 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1498 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1499 T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1500 (_: T).(csuba g d2 d1))))) (\lambda (_: (eq C (CHead d1 (Bind Abbr) u1)
1501 (CSort n0))).(\lambda (H3: (eq nat (S n) O)).(\lambda (_: (eq nat O O)).(let
1502 H5 \def (eq_ind nat (S n) (\lambda (ee: nat).(match ee in nat return (\lambda
1503 (_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True])) I O H3)
1504 in (False_ind (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind
1505 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1506 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
1507 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1508 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1509 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1510 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
1511 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) H5)))))
1512 (drop_gen_sort n0 (S n) O (CHead d1 (Bind Abbr) u1) H0))))))))) (\lambda (c:
1513 C).(\lambda (H0: ((\forall (d1: C).(\forall (u1: T).((drop (S n) O c (CHead
1514 d1 (Bind Abbr) u1)) \to (\forall (g: G).(\forall (c2: C).((csuba g c2 c) \to
1515 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1)))
1516 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
1517 (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2)))))
1518 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
1519 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1520 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
1521 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
1522 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))))))))))).(\lambda
1523 (k: K).(\lambda (t: T).(\lambda (d1: C).(\lambda (u1: T).(\lambda (H1: (drop
1524 (S n) O (CHead c k t) (CHead d1 (Bind Abbr) u1))).(\lambda (g: G).(\lambda
1525 (c2: C).(\lambda (H2: (csuba g c2 (CHead c k t))).(K_ind (\lambda (k0:
1526 K).((csuba g c2 (CHead c k0 t)) \to ((drop (r k0 n) O c (CHead d1 (Bind Abbr)
1527 u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr)
1528 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1529 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
1530 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1531 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1532 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1533 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
1534 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))))) (\lambda
1535 (b: B).(\lambda (H3: (csuba g c2 (CHead c (Bind b) t))).(\lambda (H4: (drop
1536 (r (Bind b) n) O c (CHead d1 (Bind Abbr) u1))).(B_ind (\lambda (b0:
1537 B).((csuba g c2 (CHead c (Bind b0) t)) \to ((drop (r (Bind b0) n) O c (CHead
1538 d1 (Bind Abbr) u1)) \to (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead
1539 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1540 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind
1541 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
1542 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1543 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1544 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2
1545 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1546 d1)))))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abbr) t))).(\lambda (H6:
1547 (drop (r (Bind Abbr) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def
1548 (csuba_gen_abbr_rev g c c2 t H5) in (let H7 \def H_x in (or3_ind (ex2 C
1549 (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda (d2: C).(csuba
1550 g d2 c))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq
1551 C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1552 (_: A).(csuba g d2 c)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1553 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1554 (a: A).(arity g c t a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C
1555 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1556 c)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr)
1557 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1558 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
1559 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1560 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1561 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1562 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
1563 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1564 (H8: (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abbr) t))) (\lambda
1565 (d2: C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2
1566 (Bind Abbr) t))) (\lambda (d2: C).(csuba g d2 c)) (or3 (ex2 C (\lambda (d2:
1567 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1568 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1569 n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1570 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1571 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1572 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1573 C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
1574 (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq
1575 C c2 (CHead x (Bind Abbr) t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C
1576 (CHead x (Bind Abbr) t) (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop
1577 (S n) O c0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
1578 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
1579 c0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1580 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1581 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1582 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1583 T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1584 (_: T).(csuba g d2 d1)))))) (let H11 \def (H c d1 u1 H6 g x H10) in (or3_ind
1585 (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1586 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1587 (_: A).(drop n O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
1588 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1589 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1590 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1591 C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1592 C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S
1593 n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1594 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1595 (_: A).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u2)))))
1596 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
1597 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1598 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
1599 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abbr) t)
1600 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1601 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind
1602 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2:
1603 C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))
1604 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2
1605 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1606 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr)
1607 t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1608 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1609 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1610 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1611 T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2))))
1612 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
1613 C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abbr) u1))).(\lambda (H14:
1614 (csuba g x0 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x
1615 (Bind Abbr) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
1616 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
1617 (CHead x (Bind Abbr) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1618 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1619 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1620 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1621 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abbr) t)
1622 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1623 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t)
1624 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop
1625 (Bind Abbr) n x (CHead x0 (Bind Abbr) u1) H13 t) H14))))) H12)) (\lambda
1626 (H12: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n
1627 O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1628 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1629 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1630 (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
1631 T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1632 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1633 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1634 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C
1635 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr)
1636 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1637 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr) t)
1638 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
1639 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1640 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1641 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1642 T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2))))
1643 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
1644 C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H13: (drop n O x (CHead x0
1645 (Bind Abst) x1))).(\lambda (H14: (csuba g x0 d1)).(\lambda (H15: (arity g x0
1646 x1 (asucc g x2))).(\lambda (H16: (arity g d1 u1 x2)).(or3_intro1 (ex2 C
1647 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr)
1648 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1649 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr) t)
1650 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
1651 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1652 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1653 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1654 T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2))))
1655 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A
1656 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x
1657 (Bind Abbr) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1658 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1659 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1660 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2 (drop_drop (Bind Abbr) n
1661 x (CHead x0 (Bind Abst) x1) H13 t) H14 H15 H16))))))))) H12)) (\lambda (H12:
1662 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind
1663 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind
1664 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void)
1665 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C
1666 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr)
1667 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1668 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr) t)
1669 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
1670 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1671 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1672 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1673 T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2))))
1674 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
1675 C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead x0 (Bind Void)
1676 x1))).(\lambda (H14: (csuba g x0 d1)).(or3_intro2 (ex2 C (\lambda (d2:
1677 C).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Abbr) u1))) (\lambda
1678 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
1679 T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind
1680 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
1681 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1682 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1683 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x
1684 (Bind Abbr) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1685 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
1686 T).(drop (S n) O (CHead x (Bind Abbr) t) (CHead d2 (Bind Void) u2))))
1687 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_drop (Bind
1688 Abbr) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12)) H11)) c2 H9))))
1689 H8)) (\lambda (H8: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1690 (_: A).(eq C c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1691 T).(\lambda (_: A).(csuba g d2 c)))) (\lambda (d2: C).(\lambda (u2:
1692 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1693 (_: T).(\lambda (a: A).(arity g c t a)))))).(ex4_3_ind C T A (\lambda (d2:
1694 C).(\lambda (u2: T).(\lambda (_: A).(eq C c2 (CHead d2 (Bind Abst) u2)))))
1695 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 c)))) (\lambda
1696 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1697 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g c t a)))) (or3 (ex2
1698 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1699 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1700 (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1701 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1702 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1703 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1704 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
1705 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
1706 C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H9: (eq C c2 (CHead x0 (Bind
1707 Abst) x1))).(\lambda (H10: (csuba g x0 c)).(\lambda (_: (arity g x0 x1 (asucc
1708 g x2))).(\lambda (_: (arity g c t x2)).(eq_ind_r C (CHead x0 (Bind Abst) x1)
1709 (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2
1710 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1711 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (CHead d2 (Bind
1712 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
1713 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1714 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1715 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0
1716 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1717 d1)))))) (let H13 \def (H c d1 u1 H6 g x0 H10) in (or3_ind (ex2 C (\lambda
1718 (d2: C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1719 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n
1720 O x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1721 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1722 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1723 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1724 T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1725 T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0
1726 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1727 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1728 n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1729 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1730 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1731 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1732 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1)
1733 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1734 d1))))) (\lambda (H14: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind
1735 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2:
1736 C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))
1737 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead
1738 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1739 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Abst)
1740 x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1741 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1742 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1743 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1744 T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2))))
1745 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda
1746 (H15: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H16: (csuba g x
1747 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst)
1748 x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T
1749 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
1750 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1751 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1752 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1753 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1754 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1755 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C
1756 (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1757 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind Abst) n x0
1758 (CHead x (Bind Abbr) u1) H15 x1) H16))))) H14)) (\lambda (H14: (ex4_3 C T A
1759 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (CHead d2
1760 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1761 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1762 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1763 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
1764 A).(drop n O x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1765 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1766 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1767 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C (\lambda (d2:
1768 C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1)))
1769 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
1770 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2
1771 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1772 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1773 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1774 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
1775 x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1776 T).(csuba g d2 d1))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5:
1777 A).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Abst) x4))).(\lambda (H16:
1778 (csuba g x3 d1)).(\lambda (H17: (arity g x3 x4 (asucc g x5))).(\lambda (H18:
1779 (arity g d1 u1 x5)).(or3_intro1 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead
1780 x0 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1781 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1782 n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1783 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1784 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1785 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1786 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1)
1787 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1788 d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
1789 A).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abst) u2)))))
1790 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
1791 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1792 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x3 x4 x5
1793 (drop_drop (Bind Abst) n x0 (CHead x3 (Bind Abst) x4) H15 x1) H16 H17
1794 H18))))))))) H14)) (\lambda (H14: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1795 T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1796 T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop
1797 n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
1798 d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Abst) x1)
1799 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
1800 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
1801 (Bind Abst) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1802 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1803 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1804 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1805 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind
1806 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1807 (x3: C).(\lambda (x4: T).(\lambda (H15: (drop n O x0 (CHead x3 (Bind Void)
1808 x4))).(\lambda (H16: (csuba g x3 d1)).(or3_intro2 (ex2 C (\lambda (d2:
1809 C).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Abbr) u1)))
1810 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
1811 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2
1812 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1813 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1814 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1815 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
1816 x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1817 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
1818 T).(drop (S n) O (CHead x0 (Bind Abst) x1) (CHead d2 (Bind Void) u2))))
1819 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x3 x4 (drop_drop (Bind
1820 Abst) n x0 (CHead x3 (Bind Void) x4) H15 x1) H16)))))) H14)) H13)) c2
1821 H9)))))))) H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1822 T).(eq C c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1823 T).(csuba g d2 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C
1824 c2 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1825 c))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr)
1826 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
1827 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst)
1828 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
1829 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
1830 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
1831 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind
1832 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1833 (x0: C).(\lambda (x1: T).(\lambda (H9: (eq C c2 (CHead x0 (Bind Void)
1834 x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Bind Void) x1)
1835 (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2
1836 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1837 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (CHead d2 (Bind
1838 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
1839 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1840 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1841 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0
1842 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1843 d1)))))) (let H11 \def (H c d1 u1 H6 g x0 H10) in (or3_ind (ex2 C (\lambda
1844 (d2: C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1845 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n
1846 O x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1847 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1848 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1849 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1850 T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1851 T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0
1852 (Bind Void) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1853 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1854 n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1855 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1856 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1857 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1858 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1)
1859 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1860 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind
1861 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2:
1862 C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))
1863 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead
1864 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
1865 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void)
1866 x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1867 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1868 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1869 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1870 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1871 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda
1872 (H13: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H14: (csuba g x
1873 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void)
1874 x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T
1875 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
1876 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1877 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1878 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1879 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1880 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
1881 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C
1882 (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
1883 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind Void) n x0
1884 (CHead x (Bind Abbr) u1) H13 x1) H14))))) H12)) (\lambda (H12: (ex4_3 C T A
1885 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (CHead d2
1886 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1887 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1888 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1889 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
1890 A).(drop n O x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1891 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1892 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1893 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C (\lambda (d2:
1894 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abbr) u1)))
1895 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
1896 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
1897 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1898 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1899 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1900 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
1901 x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1902 T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4:
1903 A).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Abst) x3))).(\lambda (H14:
1904 (csuba g x2 d1)).(\lambda (H15: (arity g x2 x3 (asucc g x4))).(\lambda (H16:
1905 (arity g d1 u1 x4)).(or3_intro1 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead
1906 x0 (Bind Void) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1907 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1908 n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
1909 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1910 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1911 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1912 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1)
1913 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1914 d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
1915 A).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u2)))))
1916 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
1917 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1918 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x2 x3 x4
1919 (drop_drop (Bind Void) n x0 (CHead x2 (Bind Abst) x3) H13 x1) H14 H15
1920 H16))))))))) H12)) (\lambda (H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1921 T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1922 T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop
1923 n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
1924 d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1)
1925 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
1926 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
1927 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1928 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1929 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1930 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1931 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
1932 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
1933 (x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void)
1934 x3))).(\lambda (H14: (csuba g x2 d1)).(or3_intro2 (ex2 C (\lambda (d2:
1935 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abbr) u1)))
1936 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
1937 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
1938 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
1939 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
1940 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
1941 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
1942 x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
1943 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
1944 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
1945 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Bind
1946 Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12)) H11)) c2 H9)))))
1947 H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Abst) t))).(\lambda
1948 (H6: (drop (r (Bind Abst) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def
1949 (csuba_gen_abst_rev g c c2 t H5) in (let H7 \def H_x in (or_ind (ex2 C
1950 (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2: C).(csuba
1951 g d2 c))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2
1952 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c)))) (or3
1953 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda
1954 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
1955 T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
1956 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
1957 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
1958 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
1959 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
1960 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H8:
1961 (ex2 C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind Abst) t))) (\lambda (d2:
1962 C).(csuba g d2 c)))).(ex2_ind C (\lambda (d2: C).(eq C c2 (CHead d2 (Bind
1963 Abst) t))) (\lambda (d2: C).(csuba g d2 c)) (or3 (ex2 C (\lambda (d2:
1964 C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
1965 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
1966 n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
1967 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1968 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1969 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1970 C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
1971 (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda (H9: (eq
1972 C c2 (CHead x (Bind Abst) t))).(\lambda (H10: (csuba g x c)).(eq_ind_r C
1973 (CHead x (Bind Abst) t) (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop
1974 (S n) O c0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
1975 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
1976 c0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
1977 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
1978 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
1979 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
1980 T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
1981 (_: T).(csuba g d2 d1)))))) (let H11 \def (H c d1 u1 H6 g x H10) in (or3_ind
1982 (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1983 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1984 (_: A).(drop n O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
1985 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
1986 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
1987 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
1988 C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void) u2)))) (\lambda (d2:
1989 C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S
1990 n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
1991 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
1992 (_: A).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u2)))))
1993 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
1994 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
1995 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
1996 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t)
1997 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
1998 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind
1999 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2:
2000 C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))
2001 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2
2002 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
2003 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst)
2004 t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
2005 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2006 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2007 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2008 T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2))))
2009 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
2010 C).(\lambda (H13: (drop n O x (CHead x0 (Bind Abbr) u1))).(\lambda (H14:
2011 (csuba g x0 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x
2012 (Bind Abst) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
2013 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
2014 (CHead x (Bind Abst) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
2015 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2016 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2017 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
2018 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x (Bind Abst) t)
2019 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2020 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t)
2021 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x0 (drop_drop
2022 (Bind Abst) n x (CHead x0 (Bind Abbr) u1) H13 t) H14))))) H12)) (\lambda
2023 (H12: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n
2024 O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
2025 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2026 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2027 (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
2028 T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
2029 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2030 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2031 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C
2032 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr)
2033 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2034 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t)
2035 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2036 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2037 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2038 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2039 T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2))))
2040 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
2041 C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H13: (drop n O x (CHead x0
2042 (Bind Abst) x1))).(\lambda (H14: (csuba g x0 d1)).(\lambda (H15: (arity g x0
2043 x1 (asucc g x2))).(\lambda (H16: (arity g d1 u1 x2)).(or3_intro1 (ex2 C
2044 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr)
2045 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2046 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t)
2047 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2048 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2049 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2050 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2051 T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2))))
2052 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A
2053 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x
2054 (Bind Abst) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
2055 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2056 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2057 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2 (drop_drop (Bind Abst) n
2058 x (CHead x0 (Bind Abst) x1) H13 t) H14 H15 H16))))))))) H12)) (\lambda (H12:
2059 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind
2060 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind
2061 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void)
2062 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C
2063 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr)
2064 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2065 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t)
2066 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2067 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2068 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2069 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2070 T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2))))
2071 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
2072 C).(\lambda (x1: T).(\lambda (H13: (drop n O x (CHead x0 (Bind Void)
2073 x1))).(\lambda (H14: (csuba g x0 d1)).(or3_intro2 (ex2 C (\lambda (d2:
2074 C).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Abbr) u1))) (\lambda
2075 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2076 T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind
2077 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
2078 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2079 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2080 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x
2081 (Bind Abst) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2082 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
2083 T).(drop (S n) O (CHead x (Bind Abst) t) (CHead d2 (Bind Void) u2))))
2084 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_drop (Bind
2085 Abst) n x (CHead x0 (Bind Void) x1) H13 t) H14)))))) H12)) H11)) c2 H9))))
2086 H8)) (\lambda (H8: (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2
2087 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2088 c))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2
2089 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c))) (or3
2090 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda
2091 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2092 T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
2093 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2094 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2095 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
2096 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
2097 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
2098 C).(\lambda (x1: T).(\lambda (H9: (eq C c2 (CHead x0 (Bind Void)
2099 x1))).(\lambda (H10: (csuba g x0 c)).(eq_ind_r C (CHead x0 (Bind Void) x1)
2100 (\lambda (c0: C).(or3 (ex2 C (\lambda (d2: C).(drop (S n) O c0 (CHead d2
2101 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
2102 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O c0 (CHead d2 (Bind
2103 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
2104 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2105 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2106 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c0
2107 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2108 d1)))))) (let H11 \def (H c d1 u1 H6 g x0 H10) in (or3_ind (ex2 C (\lambda
2109 (d2: C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
2110 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n
2111 O x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
2112 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2113 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2114 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2115 T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2116 T).(csuba g d2 d1)))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0
2117 (Bind Void) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
2118 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
2119 n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
2120 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2121 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2122 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
2123 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1)
2124 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2125 d1))))) (\lambda (H12: (ex2 C (\lambda (d2: C).(drop n O x0 (CHead d2 (Bind
2126 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2:
2127 C).(drop n O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))
2128 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead
2129 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
2130 (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void)
2131 x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
2132 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2133 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2134 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2135 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
2136 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x: C).(\lambda
2137 (H13: (drop n O x0 (CHead x (Bind Abbr) u1))).(\lambda (H14: (csuba g x
2138 d1)).(or3_intro0 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void)
2139 x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T
2140 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
2141 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
2142 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2143 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2144 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
2145 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
2146 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex_intro2 C
2147 (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
2148 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop (Bind Void) n x0
2149 (CHead x (Bind Abbr) u1) H13 x1) H14))))) H12)) (\lambda (H12: (ex4_3 C T A
2150 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop n O x0 (CHead d2
2151 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
2152 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2153 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2154 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2155 A).(drop n O x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
2156 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2157 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2158 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C (\lambda (d2:
2159 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abbr) u1)))
2160 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
2161 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
2162 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
2163 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2164 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2165 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
2166 x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2167 T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4:
2168 A).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Abst) x3))).(\lambda (H14:
2169 (csuba g x2 d1)).(\lambda (H15: (arity g x2 x3 (asucc g x4))).(\lambda (H16:
2170 (arity g d1 u1 x4)).(or3_intro1 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead
2171 x0 (Bind Void) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
2172 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S
2173 n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
2174 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2175 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2176 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
2177 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1)
2178 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2179 d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2180 A).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abst) u2)))))
2181 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
2182 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
2183 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x2 x3 x4
2184 (drop_drop (Bind Void) n x0 (CHead x2 (Bind Abst) x3) H13 x1) H14 H15
2185 H16))))))))) H12)) (\lambda (H12: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2186 T).(drop n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2187 T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(drop
2188 n O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g
2189 d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Bind Void) x1)
2190 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
2191 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0
2192 (Bind Void) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
2193 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2194 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2195 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
2196 C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind
2197 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda
2198 (x2: C).(\lambda (x3: T).(\lambda (H13: (drop n O x0 (CHead x2 (Bind Void)
2199 x3))).(\lambda (H14: (csuba g x2 d1)).(or3_intro2 (ex2 C (\lambda (d2:
2200 C).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Abbr) u1)))
2201 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
2202 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2
2203 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
2204 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2205 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2206 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
2207 x0 (Bind Void) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2208 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
2209 T).(drop (S n) O (CHead x0 (Bind Void) x1) (CHead d2 (Bind Void) u2))))
2210 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Bind
2211 Void) n x0 (CHead x2 (Bind Void) x3) H13 x1) H14)))))) H12)) H11)) c2 H9)))))
2212 H8)) H7))))) (\lambda (H5: (csuba g c2 (CHead c (Bind Void) t))).(\lambda
2213 (H6: (drop (r (Bind Void) n) O c (CHead d1 (Bind Abbr) u1))).(let H_x \def
2214 (csuba_gen_void_rev g c c2 t H5) in (let H7 \def H_x in (ex2_ind C (\lambda
2215 (d2: C).(eq C c2 (CHead d2 (Bind Void) t))) (\lambda (d2: C).(csuba g d2 c))
2216 (or3 (ex2 C (\lambda (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1)))
2217 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
2218 (u2: T).(\lambda (_: A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2)))))
2219 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
2220 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
2221 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
2222 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void)
2223 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x:
2224 C).(\lambda (H8: (eq C c2 (CHead x (Bind Void) t))).(\lambda (H9: (csuba g x
2225 c)).(eq_ind_r C (CHead x (Bind Void) t) (\lambda (c0: C).(or3 (ex2 C (\lambda
2226 (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
2227 g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2228 A).(drop (S n) O c0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
2229 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2230 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2231 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
2232 C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda
2233 (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H10 \def (H c d1 u1 H6 g x
2234 H9) in (or3_ind (ex2 C (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr)
2235 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2236 C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abst) u2)))))
2237 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
2238 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
2239 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2
2240 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void)
2241 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C
2242 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr)
2243 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2244 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t)
2245 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2246 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2247 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2248 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2249 T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2))))
2250 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H11: (ex2 C
2251 (\lambda (d2: C).(drop n O x (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
2252 C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop n O x (CHead d2 (Bind
2253 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2:
2254 C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr) u1))) (\lambda
2255 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2256 T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind
2257 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
2258 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2259 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2260 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x
2261 (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2262 T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (H12: (drop n O x (CHead x0
2263 (Bind Abbr) u1))).(\lambda (H13: (csuba g x0 d1)).(or3_intro0 (ex2 C (\lambda
2264 (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr) u1)))
2265 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
2266 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind
2267 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
2268 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2269 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2270 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x
2271 (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2272 T).(csuba g d2 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x
2273 (Bind Void) t) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))
2274 x0 (drop_drop (Bind Void) n x (CHead x0 (Bind Abbr) u1) H12 t) H13))))) H11))
2275 (\lambda (H11: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2276 A).(drop n O x (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
2277 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2278 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2279 (_: T).(\lambda (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2:
2280 C).(\lambda (u2: T).(\lambda (_: A).(drop n O x (CHead d2 (Bind Abst) u2)))))
2281 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
2282 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
2283 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3
2284 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind
2285 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2286 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t)
2287 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2288 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2289 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2290 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2291 T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2))))
2292 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
2293 C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H12: (drop n O x (CHead x0
2294 (Bind Abst) x1))).(\lambda (H13: (csuba g x0 d1)).(\lambda (H14: (arity g x0
2295 x1 (asucc g x2))).(\lambda (H15: (arity g d1 u1 x2)).(or3_intro1 (ex2 C
2296 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr)
2297 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2298 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t)
2299 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2300 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2301 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2302 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2303 T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2))))
2304 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (ex4_3_intro C T A
2305 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x
2306 (Bind Void) t) (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
2307 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2308 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2309 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x0 x1 x2 (drop_drop (Bind Void) n
2310 x (CHead x0 (Bind Abst) x1) H12 t) H13 H14 H15))))))))) H11)) (\lambda (H11:
2311 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind
2312 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))).(ex2_2_ind
2313 C T (\lambda (d2: C).(\lambda (u2: T).(drop n O x (CHead d2 (Bind Void)
2314 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) (or3 (ex2 C
2315 (\lambda (d2: C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr)
2316 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2317 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t)
2318 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2319 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2320 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2321 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2322 T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2))))
2323 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0:
2324 C).(\lambda (x1: T).(\lambda (H12: (drop n O x (CHead x0 (Bind Void)
2325 x1))).(\lambda (H13: (csuba g x0 d1)).(or3_intro2 (ex2 C (\lambda (d2:
2326 C).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Abbr) u1))) (\lambda
2327 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2328 T).(\lambda (_: A).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind
2329 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
2330 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2331 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2332 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x
2333 (Bind Void) t) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2334 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
2335 T).(drop (S n) O (CHead x (Bind Void) t) (CHead d2 (Bind Void) u2))))
2336 (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1))) x0 x1 (drop_drop (Bind
2337 Void) n x (CHead x0 (Bind Void) x1) H12 t) H13)))))) H11)) H10)) c2 H8))))
2338 H7))))) b H3 H4)))) (\lambda (f: F).(\lambda (H3: (csuba g c2 (CHead c (Flat
2339 f) t))).(\lambda (H4: (drop (r (Flat f) n) O c (CHead d1 (Bind Abbr)
2340 u1))).(let H_x \def (csuba_gen_flat_rev g c c2 t f H3) in (let H5 \def H_x in
2341 (ex2_2_ind C T (\lambda (d2: C).(\lambda (u2: T).(eq C c2 (CHead d2 (Flat f)
2342 u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 c))) (or3 (ex2 C (\lambda
2343 (d2: C).(drop (S n) O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
2344 g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2345 A).(drop (S n) O c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
2346 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2347 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2348 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
2349 C).(\lambda (u2: T).(drop (S n) O c2 (CHead d2 (Bind Void) u2)))) (\lambda
2350 (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x0: C).(\lambda (x1:
2351 T).(\lambda (H6: (eq C c2 (CHead x0 (Flat f) x1))).(\lambda (H7: (csuba g x0
2352 c)).(eq_ind_r C (CHead x0 (Flat f) x1) (\lambda (c0: C).(or3 (ex2 C (\lambda
2353 (d2: C).(drop (S n) O c0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
2354 g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2355 A).(drop (S n) O c0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
2356 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
2357 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
2358 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2:
2359 C).(\lambda (u2: T).(drop (S n) O c0 (CHead d2 (Bind Void) u2)))) (\lambda
2360 (d2: C).(\lambda (_: T).(csuba g d2 d1)))))) (let H8 \def (H0 d1 u1 H4 g x0
2361 H7) in (or3_ind (ex2 C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind
2362 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2363 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O x0 (CHead d2 (Bind Abst)
2364 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
2365 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
2366 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
2367 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O x0 (CHead d2 (Bind
2368 Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))) (or3 (ex2 C
2369 (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr)
2370 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2371 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1)
2372 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2373 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2374 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2375 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2376 T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda
2377 (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (H9: (ex2 C (\lambda
2378 (d2: C).(drop (S n) O x0 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba
2379 g d2 d1)))).(ex2_ind C (\lambda (d2: C).(drop (S n) O x0 (CHead d2 (Bind
2380 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or3 (ex2 C (\lambda (d2:
2381 C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u1))) (\lambda
2382 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2383 T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst)
2384 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
2385 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
2386 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
2387 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f)
2388 x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2389 d1))))) (\lambda (x: C).(\lambda (H10: (drop (S n) O x0 (CHead x (Bind Abbr)
2390 u1))).(\lambda (H11: (csuba g x d1)).(or3_intro0 (ex2 C (\lambda (d2:
2391 C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u1))) (\lambda
2392 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2393 T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst)
2394 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
2395 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
2396 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
2397 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f)
2398 x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2399 d1)))) (ex_intro2 C (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1)
2400 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x (drop_drop
2401 (Flat f) n x0 (CHead x (Bind Abbr) u1) H10 x1) H11))))) H9)) (\lambda (H9:
2402 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
2403 x0 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
2404 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2405 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2406 (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
2407 T).(\lambda (_: A).(drop (S n) O x0 (CHead d2 (Bind Abst) u2))))) (\lambda
2408 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2409 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2410 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or3 (ex2 C
2411 (\lambda (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr)
2412 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
2413 C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1)
2414 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
2415 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
2416 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
2417 (a: A).(arity g d1 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2418 T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda
2419 (d2: C).(\lambda (_: T).(csuba g d2 d1))))) (\lambda (x2: C).(\lambda (x3:
2420 T).(\lambda (x4: A).(\lambda (H10: (drop (S n) O x0 (CHead x2 (Bind Abst)
2421 x3))).(\lambda (H11: (csuba g x2 d1)).(\lambda (H12: (arity g x2 x3 (asucc g
2422 x4))).(\lambda (H13: (arity g d1 u1 x4)).(or3_intro1 (ex2 C (\lambda (d2:
2423 C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u1))) (\lambda
2424 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
2425 T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst)
2426 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
2427 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
2428 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
2429 (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f)
2430 x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2
2431 d1)))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
2432 A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u2)))))
2433 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
2434 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
2435 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x2 x3 x4
2436 (drop_drop (Flat f) n x0 (CHead x2 (Bind Abst) x3) H10 x1) H11 H12
2437 H13))))))))) H9)) (\lambda (H9: (ex2_2 C T (\lambda (d2: C).(\lambda (u2:
2438 T).(drop (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
2439 (_: T).(csuba g d2 d1))))).(ex2_2_ind C T (\lambda (d2: C).(\lambda (u2:
2440 T).(drop (S n) O x0 (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda
2441 (_: T).(csuba g d2 d1))) (or3 (ex2 C (\lambda (d2: C).(drop (S n) O (CHead x0
2442 (Flat f) x1) (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
2443 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop (S n) O
2444 (CHead x0 (Flat f) x1) (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
2445 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
2446 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
2447 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex2_2 C T
2448 (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead
2449 d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_: T).(csuba g d2 d1)))))
2450 (\lambda (x2: C).(\lambda (x3: T).(\lambda (H10: (drop (S n) O x0 (CHead x2
2451 (Bind Void) x3))).(\lambda (H11: (csuba g x2 d1)).(or3_intro2 (ex2 C (\lambda
2452 (d2: C).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Abbr) u1)))
2453 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
2454 (u2: T).(\lambda (_: A).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind
2455 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
2456 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
2457 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
2458 u1 a))))) (ex2_2 C T (\lambda (d2: C).(\lambda (u2: T).(drop (S n) O (CHead
2459 x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda (d2: C).(\lambda (_:
2460 T).(csuba g d2 d1)))) (ex2_2_intro C T (\lambda (d2: C).(\lambda (u2:
2461 T).(drop (S n) O (CHead x0 (Flat f) x1) (CHead d2 (Bind Void) u2)))) (\lambda
2462 (d2: C).(\lambda (_: T).(csuba g d2 d1))) x2 x3 (drop_drop (Flat f) n x0
2463 (CHead x2 (Bind Void) x3) H10 x1) H11)))))) H9)) H8)) c2 H6))))) H5)))))) k
2464 H2 (drop_gen_drop k c (CHead d1 (Bind Abbr) u1) t n H1)))))))))))) c1)))) i).
2466 Initial nodes: 23852
projects / helm.git / blob