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 set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/csuba/getl".
19 include "csuba/drop.ma".
21 include "csuba/clear.ma".
23 include "getl/clear.ma".
25 theorem csuba_getl_abbr:
26 \forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).(\forall
27 (i: nat).((getl i c1 (CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csuba g
28 c1 c2) \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u)))
29 (\lambda (d2: C).(csuba g d1 d2))))))))))
31 \lambda (g: G).(\lambda (c1: C).(\lambda (d1: C).(\lambda (u: T).(\lambda
32 (i: nat).(\lambda (H: (getl i c1 (CHead d1 (Bind Abbr) u))).(let H0 \def
33 (getl_gen_all c1 (CHead d1 (Bind Abbr) u) i H) in (ex2_ind C (\lambda (e:
34 C).(drop i O c1 e)) (\lambda (e: C).(clear e (CHead d1 (Bind Abbr) u)))
35 (\forall (c2: C).((csuba g c1 c2) \to (ex2 C (\lambda (d2: C).(getl i c2
36 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))) (\lambda (x:
37 C).(\lambda (H1: (drop i O c1 x)).(\lambda (H2: (clear x (CHead d1 (Bind
38 Abbr) u))).(C_ind (\lambda (c: C).((drop i O c1 c) \to ((clear c (CHead d1
39 (Bind Abbr) u)) \to (\forall (c2: C).((csuba g c1 c2) \to (ex2 C (\lambda
40 (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
41 d2)))))))) (\lambda (n: nat).(\lambda (_: (drop i O c1 (CSort n))).(\lambda
42 (H4: (clear (CSort n) (CHead d1 (Bind Abbr) u))).(clear_gen_sort (CHead d1
43 (Bind Abbr) u) n H4 (\forall (c2: C).((csuba g c1 c2) \to (ex2 C (\lambda
44 (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
45 d2))))))))) (\lambda (x0: C).(\lambda (_: (((drop i O c1 x0) \to ((clear x0
46 (CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csuba g c1 c2) \to (ex2 C
47 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
48 C).(csuba g d1 d2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (H3:
49 (drop i O c1 (CHead x0 k t))).(\lambda (H4: (clear (CHead x0 k t) (CHead d1
50 (Bind Abbr) u))).(K_ind (\lambda (k0: K).((drop i O c1 (CHead x0 k0 t)) \to
51 ((clear (CHead x0 k0 t) (CHead d1 (Bind Abbr) u)) \to (\forall (c2:
52 C).((csuba g c1 c2) \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
53 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))))) (\lambda (b: B).(\lambda
54 (H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear (CHead x0
55 (Bind b) t) (CHead d1 (Bind Abbr) u))).(let H7 \def (f_equal C C (\lambda (e:
56 C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 |
57 (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t)
58 (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H8 \def
59 (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
60 [(CSort _) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 in K
61 return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
62 \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u) (CHead x0 (Bind b) t)
63 (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u) t H6)) in ((let H9 \def
64 (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
65 [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
66 Abbr) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u)
67 t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda
68 (c2: C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda
69 (t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def
70 (eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abbr
71 H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c
72 (Bind Abbr) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abbr i c1 d1 u H15
73 g c2 H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr)
74 u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl i c2
75 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x1:
76 C).(\lambda (H17: (drop i O c2 (CHead x1 (Bind Abbr) u))).(\lambda (H18:
77 (csuba g d1 x1)).(ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
78 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x1 (getl_intro i c2 (CHead x1
79 (Bind Abbr) u) (CHead x1 (Bind Abbr) u) H17 (clear_bind Abbr x1 u)) H18))))
80 H16)))))))))) H8)) H7))))) (\lambda (f: F).(\lambda (H5: (drop i O c1 (CHead
81 x0 (Flat f) t))).(\lambda (H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind
82 Abbr) u))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop i O c
83 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c c2) \to (ex2 C
84 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
85 C).(csuba g d1 d2))))))) (nat_ind (\lambda (n: nat).(\forall (x1: C).((drop n
86 O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g x1 c2) \to (ex2 C
87 (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
88 C).(csuba g d1 d2)))))))) (\lambda (x1: C).(\lambda (H8: (drop O O x1 (CHead
89 x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H9: (csuba g x1 c2)).(let H10
90 \def (eq_ind C x1 (\lambda (c: C).(csuba g c c2)) H9 (CHead x0 (Flat f) t)
91 (drop_gen_refl x1 (CHead x0 (Flat f) t) H8)) in (let H_y \def (clear_flat x0
92 (CHead d1 (Bind Abbr) u) (clear_gen_flat f x0 (CHead d1 (Bind Abbr) u) t H6)
93 f t) in (let H11 \def (csuba_clear_conf g (CHead x0 (Flat f) t) c2 H10 (CHead
94 d1 (Bind Abbr) u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba g (CHead d1
95 (Bind Abbr) u) e2)) (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda (d2:
96 C).(getl O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))
97 (\lambda (x2: C).(\lambda (H12: (csuba g (CHead d1 (Bind Abbr) u)
98 x2)).(\lambda (H13: (clear c2 x2)).(let H_x \def (csuba_gen_abbr g d1 x2 u
99 H12) in (let H14 \def H_x in (ex2_ind C (\lambda (d2: C).(eq C x2 (CHead d2
100 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2:
101 C).(getl O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))
102 (\lambda (x3: C).(\lambda (H15: (eq C x2 (CHead x3 (Bind Abbr) u))).(\lambda
103 (H16: (csuba g d1 x3)).(let H17 \def (eq_ind C x2 (\lambda (c: C).(clear c2
104 c)) H13 (CHead x3 (Bind Abbr) u) H15) in (ex_intro2 C (\lambda (d2: C).(getl
105 O c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x3
106 (getl_intro O c2 (CHead x3 (Bind Abbr) u) c2 (drop_refl c2) H17) H16)))))
107 H14)))))) H11)))))))) (\lambda (n: nat).(\lambda (H8: ((\forall (x1:
108 C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g x1 c2)
109 \to (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u))) (\lambda
110 (d2: C).(csuba g d1 d2))))))))).(\lambda (x1: C).(\lambda (H9: (drop (S n) O
111 x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H10: (csuba g x1
112 c2)).(let H11 \def (drop_clear x1 (CHead x0 (Flat f) t) n H9) in (ex2_3_ind B
113 C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear x1 (CHead e (Bind
114 b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead
115 x0 (Flat f) t))))) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
116 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x2: B).(\lambda (x3:
117 C).(\lambda (x4: T).(\lambda (H12: (clear x1 (CHead x3 (Bind x2)
118 x4))).(\lambda (H13: (drop n O x3 (CHead x0 (Flat f) t))).(let H14 \def
119 (csuba_clear_conf g x1 c2 H10 (CHead x3 (Bind x2) x4) H12) in (ex2_ind C
120 (\lambda (e2: C).(csuba g (CHead x3 (Bind x2) x4) e2)) (\lambda (e2:
121 C).(clear c2 e2)) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
122 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x5: C).(\lambda (H15:
123 (csuba g (CHead x3 (Bind x2) x4) x5)).(\lambda (H16: (clear c2 x5)).(let H_x
124 \def (csuba_gen_bind g x2 x3 x5 x4 H15) in (let H17 \def H_x in (ex2_3_ind B
125 C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C x5 (CHead e2
126 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_: T).(csuba g
127 x3 e2)))) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr) u)))
128 (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x6: B).(\lambda (x7: C).(\lambda
129 (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind x6) x8))).(\lambda (H19:
130 (csuba g x3 x7)).(let H20 \def (eq_ind C x5 (\lambda (c: C).(clear c2 c)) H16
131 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 H13 x7 H19) in (ex2_ind
132 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
133 C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
134 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x9: C).(\lambda (H22:
135 (getl n x7 (CHead x9 (Bind Abbr) u))).(\lambda (H23: (csuba g d1
136 x9)).(ex_intro2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr) u)))
137 (\lambda (d2: C).(csuba g d1 d2)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead
138 x9 (Bind Abbr) u) n H22) H23)))) H21)))))))) H17)))))) H14))))))) H11))))))))
139 i) H7))))) k H3 H4))))))) x H1 H2)))) H0))))))).
141 theorem csuba_getl_abst:
142 \forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
143 (i: nat).((getl i c1 (CHead d1 (Bind Abst) u1)) \to (\forall (c2: C).((csuba
144 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
145 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
146 C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
147 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
148 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
149 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
152 \lambda (g: G).(\lambda (c1: C).(\lambda (d1: C).(\lambda (u1: T).(\lambda
153 (i: nat).(\lambda (H: (getl i c1 (CHead d1 (Bind Abst) u1))).(let H0 \def
154 (getl_gen_all c1 (CHead d1 (Bind Abst) u1) i H) in (ex2_ind C (\lambda (e:
155 C).(drop i O c1 e)) (\lambda (e: C).(clear e (CHead d1 (Bind Abst) u1)))
156 (\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2
157 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
158 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
159 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
160 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
161 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
162 a)))))))) (\lambda (x: C).(\lambda (H1: (drop i O c1 x)).(\lambda (H2: (clear
163 x (CHead d1 (Bind Abst) u1))).(C_ind (\lambda (c: C).((drop i O c1 c) \to
164 ((clear c (CHead d1 (Bind Abst) u1)) \to (\forall (c2: C).((csuba g c1 c2)
165 \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
166 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
167 (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
168 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
169 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
170 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))))))) (\lambda
171 (n: nat).(\lambda (_: (drop i O c1 (CSort n))).(\lambda (H4: (clear (CSort n)
172 (CHead d1 (Bind Abst) u1))).(clear_gen_sort (CHead d1 (Bind Abst) u1) n H4
173 (\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2
174 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
175 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
176 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
177 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
178 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
179 a)))))))))))) (\lambda (x0: C).(\lambda (_: (((drop i O c1 x0) \to ((clear x0
180 (CHead d1 (Bind Abst) u1)) \to (\forall (c2: C).((csuba g c1 c2) \to (or (ex2
181 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
182 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
183 (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
184 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
185 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
186 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))))))).(\lambda (k: K).(\lambda
187 (t: T).(\lambda (H3: (drop i O c1 (CHead x0 k t))).(\lambda (H4: (clear
188 (CHead x0 k t) (CHead d1 (Bind Abst) u1))).(K_ind (\lambda (k0: K).((drop i O
189 c1 (CHead x0 k0 t)) \to ((clear (CHead x0 k0 t) (CHead d1 (Bind Abst) u1))
190 \to (\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i
191 c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
192 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2
193 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
194 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
195 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
196 u2 a))))))))))) (\lambda (b: B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b)
197 t))).(\lambda (H6: (clear (CHead x0 (Bind b) t) (CHead d1 (Bind Abst)
198 u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
199 (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c]))
200 (CHead d1 (Bind Abst) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead
201 d1 (Bind Abst) u1) t H6)) in ((let H8 \def (f_equal C B (\lambda (e:
202 C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abst |
203 (CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with
204 [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abst])])) (CHead d1 (Bind
205 Abst) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst)
206 u1) t H6)) in ((let H9 \def (f_equal C T (\lambda (e: C).(match e in C return
207 (\lambda (_: C).T) with [(CSort _) \Rightarrow u1 | (CHead _ _ t0)
208 \Rightarrow t0])) (CHead d1 (Bind Abst) u1) (CHead x0 (Bind b) t)
209 (clear_gen_bind b x0 (CHead d1 (Bind Abst) u1) t H6)) in (\lambda (H10: (eq B
210 Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
211 g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
212 (Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r B b (\lambda (b0:
213 B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abst H10) in (let H15 \def
214 (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind Abst) u1))) H14 d1
215 H11) in (let H16 \def (csuba_drop_abst i c1 d1 u1 H15 g c2 H12) in (or_ind
216 (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1))) (\lambda
217 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
218 T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
219 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
220 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
221 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or (ex2 C
222 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
223 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
224 (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
225 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
226 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
227 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H17: (ex2 C (\lambda
228 (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
229 d2)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1)))
230 (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(getl i c2
231 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
232 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
233 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
234 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
235 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
236 a)))))) (\lambda (x1: C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abst)
237 u1))).(\lambda (H19: (csuba g d1 x1)).(or_introl (ex2 C (\lambda (d2:
238 C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
239 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
240 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
241 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
242 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
243 A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2
244 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) x1 (getl_intro i c2
245 (CHead x1 (Bind Abst) u1) (CHead x1 (Bind Abst) u1) H18 (clear_bind Abst x1
246 u1)) H19))))) H17)) (\lambda (H17: (ex4_3 C T A (\lambda (d2: C).(\lambda
247 (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
248 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
249 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
250 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C
251 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2
252 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
253 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
254 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
255 u2 a)))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
256 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
257 (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
258 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
259 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
260 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x1:
261 C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1
262 (Bind Abbr) x2))).(\lambda (H19: (csuba g d1 x1)).(\lambda (H20: (arity g d1
263 u1 (asucc g x3))).(\lambda (H21: (arity g x1 x2 x3)).(or_intror (ex2 C
264 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
265 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
266 (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
267 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
268 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
269 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda
270 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr)
271 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
272 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
273 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))
274 x1 x2 x3 (getl_intro i c2 (CHead x1 (Bind Abbr) x2) (CHead x1 (Bind Abbr) x2)
275 H18 (clear_bind Abbr x1 x2)) H19 H20 H21))))))))) H17)) H16)))))))))) H8))
276 H7))))) (\lambda (f: F).(\lambda (H5: (drop i O c1 (CHead x0 (Flat f)
277 t))).(\lambda (H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abst)
278 u1))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop i O c (CHead x0
279 (Flat f) t)) \to (\forall (c2: C).((csuba g c c2) \to (or (ex2 C (\lambda
280 (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
281 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i
282 c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
283 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
284 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
285 (a: A).(arity g d2 u2 a)))))))))) (nat_ind (\lambda (n: nat).(\forall (x1:
286 C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g x1 c2)
287 \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u1)))
288 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
289 (u2: T).(\lambda (_: A).(getl n c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
290 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
291 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
292 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))))))) (\lambda
293 (x1: C).(\lambda (H8: (drop O O x1 (CHead x0 (Flat f) t))).(\lambda (c2:
294 C).(\lambda (H9: (csuba g x1 c2)).(let H10 \def (eq_ind C x1 (\lambda (c:
295 C).(csuba g c c2)) H9 (CHead x0 (Flat f) t) (drop_gen_refl x1 (CHead x0 (Flat
296 f) t) H8)) in (let H_y \def (clear_flat x0 (CHead d1 (Bind Abst) u1)
297 (clear_gen_flat f x0 (CHead d1 (Bind Abst) u1) t H6) f t) in (let H11 \def
298 (csuba_clear_conf g (CHead x0 (Flat f) t) c2 H10 (CHead d1 (Bind Abst) u1)
299 H_y) in (ex2_ind C (\lambda (e2: C).(csuba g (CHead d1 (Bind Abst) u1) e2))
300 (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead
301 d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
302 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abbr)
303 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
304 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
305 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
306 a)))))) (\lambda (x2: C).(\lambda (H12: (csuba g (CHead d1 (Bind Abst) u1)
307 x2)).(\lambda (H13: (clear c2 x2)).(let H_x \def (csuba_gen_abst g d1 x2 u1
308 H12) in (let H14 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C x2 (CHead
309 d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
310 (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C x2 (CHead d2 (Bind Abbr)
311 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
312 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
313 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
314 a))))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1)))
315 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
316 (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
317 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
318 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
319 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
320 (H15: (ex2 C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind Abst) u1))) (\lambda
321 (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(eq C x2 (CHead d2
322 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2:
323 C).(getl O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
324 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2
325 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
326 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
327 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
328 A).(arity g d2 u2 a)))))) (\lambda (x3: C).(\lambda (H16: (eq C x2 (CHead x3
329 (Bind Abst) u1))).(\lambda (H17: (csuba g d1 x3)).(let H18 \def (eq_ind C x2
330 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 (Bind Abst) u1) H16) in
331 (or_introl (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1)))
332 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
333 (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
334 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
335 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
336 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C
337 (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
338 C).(csuba g d1 d2)) x3 (getl_intro O c2 (CHead x3 (Bind Abst) u1) c2
339 (drop_refl c2) H18) H17)))))) H15)) (\lambda (H15: (ex4_3 C T A (\lambda (d2:
340 C).(\lambda (u2: T).(\lambda (_: A).(eq C x2 (CHead d2 (Bind Abbr) u2)))))
341 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
342 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
343 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
344 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
345 A).(eq C x2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
346 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
347 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
348 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C (\lambda (d2:
349 C).(getl O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
350 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2
351 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
352 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
353 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
354 A).(arity g d2 u2 a)))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5:
355 A).(\lambda (H16: (eq C x2 (CHead x3 (Bind Abbr) x4))).(\lambda (H17: (csuba
356 g d1 x3)).(\lambda (H18: (arity g d1 u1 (asucc g x5))).(\lambda (H19: (arity
357 g x3 x4 x5)).(let H20 \def (eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13
358 (CHead x3 (Bind Abbr) x4) H16) in (or_intror (ex2 C (\lambda (d2: C).(getl O
359 c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
360 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2
361 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
362 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
363 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
364 u2 a))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
365 A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
366 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
367 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
368 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x3 x4 x5 (getl_intro O c2 (CHead
369 x3 (Bind Abbr) x4) c2 (drop_refl c2) H20) H17 H18 H19)))))))))) H15))
370 H14)))))) H11)))))))) (\lambda (n: nat).(\lambda (H8: ((\forall (x1:
371 C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g x1 c2)
372 \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u1)))
373 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
374 (u2: T).(\lambda (_: A).(getl n c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
375 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
376 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
377 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
378 a)))))))))))).(\lambda (x1: C).(\lambda (H9: (drop (S n) O x1 (CHead x0 (Flat
379 f) t))).(\lambda (c2: C).(\lambda (H10: (csuba g x1 c2)).(let H11 \def
380 (drop_clear x1 (CHead x0 (Flat f) t) n H9) in (ex2_3_ind B C T (\lambda (b:
381 B).(\lambda (e: C).(\lambda (v: T).(clear x1 (CHead e (Bind b) v)))))
382 (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead x0 (Flat
383 f) t))))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
384 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
385 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
386 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
387 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
388 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
389 a)))))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H12:
390 (clear x1 (CHead x3 (Bind x2) x4))).(\lambda (H13: (drop n O x3 (CHead x0
391 (Flat f) t))).(let H14 \def (csuba_clear_conf g x1 c2 H10 (CHead x3 (Bind x2)
392 x4) H12) in (ex2_ind C (\lambda (e2: C).(csuba g (CHead x3 (Bind x2) x4) e2))
393 (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2
394 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
395 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2
396 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
397 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
398 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
399 u2 a)))))) (\lambda (x5: C).(\lambda (H15: (csuba g (CHead x3 (Bind x2) x4)
400 x5)).(\lambda (H16: (clear c2 x5)).(let H_x \def (csuba_gen_bind g x2 x3 x5
401 x4 H15) in (let H17 \def H_x in (ex2_3_ind B C T (\lambda (b2: B).(\lambda
402 (e2: C).(\lambda (v2: T).(eq C x5 (CHead e2 (Bind b2) v2))))) (\lambda (_:
403 B).(\lambda (e2: C).(\lambda (_: T).(csuba g x3 e2)))) (or (ex2 C (\lambda
404 (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g
405 d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl
406 (S n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
407 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
408 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
409 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x6: B).(\lambda (x7:
410 C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind x6)
411 x8))).(\lambda (H19: (csuba g x3 x7)).(let H20 \def (eq_ind C x5 (\lambda (c:
412 C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 H13
413 x7 H19) in (or_ind (ex2 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst)
414 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
415 C).(\lambda (u2: T).(\lambda (_: A).(getl n x7 (CHead d2 (Bind Abbr) u2)))))
416 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
417 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
418 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or
419 (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u1))) (\lambda
420 (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
421 T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
422 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
423 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
424 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
425 (H22: (ex2 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u1))) (\lambda
426 (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(getl n x7 (CHead d2
427 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2:
428 C).(getl (S n) c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
429 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S
430 n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
431 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
432 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
433 (a: A).(arity g d2 u2 a)))))) (\lambda (x9: C).(\lambda (H23: (getl n x7
434 (CHead x9 (Bind Abst) u1))).(\lambda (H24: (csuba g d1 x9)).(or_introl (ex2 C
435 (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
436 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
437 (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda
438 (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
439 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
440 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2:
441 C).(getl (S n) c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
442 d2)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abst) u1) n H23)
443 H24))))) H22)) (\lambda (H22: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
444 T).(\lambda (_: A).(getl n x7 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
445 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
446 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
447 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C
448 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl n x7 (CHead d2
449 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
450 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
451 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
452 u2 a)))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
453 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
454 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
455 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
456 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
457 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
458 a)))))) (\lambda (x9: C).(\lambda (x10: T).(\lambda (x11: A).(\lambda (H23:
459 (getl n x7 (CHead x9 (Bind Abbr) x10))).(\lambda (H24: (csuba g d1
460 x9)).(\lambda (H25: (arity g d1 u1 (asucc g x11))).(\lambda (H26: (arity g x9
461 x10 x11)).(or_intror (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
462 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
463 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
464 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
465 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
466 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
467 a))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
468 A).(getl (S n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
469 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
470 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
471 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x9 x10 x11 (getl_clear_bind x6
472 c2 x7 x8 H20 (CHead x9 (Bind Abbr) x10) n H23) H24 H25 H26))))))))) H22))
473 H21)))))))) H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4))))))) x H1
476 theorem csuba_getl_abst_rev:
477 \forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u: T).(\forall
478 (i: nat).((getl i c1 (CHead d1 (Bind Abst) u)) \to (\forall (c2: C).((csuba g
479 c2 c1) \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u)))
480 (\lambda (d2: C).(csuba g d2 d1))))))))))
482 \lambda (g: G).(\lambda (c1: C).(\lambda (d1: C).(\lambda (u: T).(\lambda
483 (i: nat).(\lambda (H: (getl i c1 (CHead d1 (Bind Abst) u))).(let H0 \def
484 (getl_gen_all c1 (CHead d1 (Bind Abst) u) i H) in (ex2_ind C (\lambda (e:
485 C).(drop i O c1 e)) (\lambda (e: C).(clear e (CHead d1 (Bind Abst) u)))
486 (\forall (c2: C).((csuba g c2 c1) \to (ex2 C (\lambda (d2: C).(getl i c2
487 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))))) (\lambda (x:
488 C).(\lambda (H1: (drop i O c1 x)).(\lambda (H2: (clear x (CHead d1 (Bind
489 Abst) u))).(C_ind (\lambda (c: C).((drop i O c1 c) \to ((clear c (CHead d1
490 (Bind Abst) u)) \to (\forall (c2: C).((csuba g c2 c1) \to (ex2 C (\lambda
491 (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
492 d1)))))))) (\lambda (n: nat).(\lambda (_: (drop i O c1 (CSort n))).(\lambda
493 (H4: (clear (CSort n) (CHead d1 (Bind Abst) u))).(clear_gen_sort (CHead d1
494 (Bind Abst) u) n H4 (\forall (c2: C).((csuba g c2 c1) \to (ex2 C (\lambda
495 (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
496 d1))))))))) (\lambda (x0: C).(\lambda (_: (((drop i O c1 x0) \to ((clear x0
497 (CHead d1 (Bind Abst) u)) \to (\forall (c2: C).((csuba g c2 c1) \to (ex2 C
498 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
499 C).(csuba g d2 d1))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (H3:
500 (drop i O c1 (CHead x0 k t))).(\lambda (H4: (clear (CHead x0 k t) (CHead d1
501 (Bind Abst) u))).(K_ind (\lambda (k0: K).((drop i O c1 (CHead x0 k0 t)) \to
502 ((clear (CHead x0 k0 t) (CHead d1 (Bind Abst) u)) \to (\forall (c2:
503 C).((csuba g c2 c1) \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
504 Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))))))) (\lambda (b: B).(\lambda
505 (H5: (drop i O c1 (CHead x0 (Bind b) t))).(\lambda (H6: (clear (CHead x0
506 (Bind b) t) (CHead d1 (Bind Abst) u))).(let H7 \def (f_equal C C (\lambda (e:
507 C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 |
508 (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
509 (clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in ((let H8 \def
510 (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
511 [(CSort _) \Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0 in K
512 return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
513 \Rightarrow Abst])])) (CHead d1 (Bind Abst) u) (CHead x0 (Bind b) t)
514 (clear_gen_bind b x0 (CHead d1 (Bind Abst) u) t H6)) in ((let H9 \def
515 (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
516 [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
517 Abst) u) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abst) u)
518 t H6)) in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 x0)).(\lambda
519 (c2: C).(\lambda (H12: (csuba g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda
520 (t0: T).(drop i O c1 (CHead x0 (Bind b) t0))) H5 u H9) in (let H14 \def
521 (eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead x0 (Bind b0) u))) H13 Abst
522 H10) in (let H15 \def (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c
523 (Bind Abst) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abst_rev i c1 d1 u
524 H15 g c2 H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind
525 Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (ex2 C (\lambda (d2: C).(getl i
526 c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda
527 (x1: C).(\lambda (H17: (drop i O c2 (CHead x1 (Bind Abst) u))).(\lambda (H18:
528 (csuba g x1 d1)).(ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind
529 Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x1 (getl_intro i c2 (CHead x1
530 (Bind Abst) u) (CHead x1 (Bind Abst) u) H17 (clear_bind Abst x1 u)) H18))))
531 H16)))))))))) H8)) H7))))) (\lambda (f: F).(\lambda (H5: (drop i O c1 (CHead
532 x0 (Flat f) t))).(\lambda (H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind
533 Abst) u))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop i O c
534 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 c) \to (ex2 C
535 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
536 C).(csuba g d2 d1))))))) (nat_ind (\lambda (n: nat).(\forall (x1: C).((drop n
537 O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 x1) \to (ex2 C
538 (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u))) (\lambda (d2:
539 C).(csuba g d2 d1)))))))) (\lambda (x1: C).(\lambda (H8: (drop O O x1 (CHead
540 x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H9: (csuba g c2 x1)).(let H10
541 \def (eq_ind C x1 (\lambda (c: C).(csuba g c2 c)) H9 (CHead x0 (Flat f) t)
542 (drop_gen_refl x1 (CHead x0 (Flat f) t) H8)) in (let H_y \def (clear_flat x0
543 (CHead d1 (Bind Abst) u) (clear_gen_flat f x0 (CHead d1 (Bind Abst) u) t H6)
544 f t) in (let H11 \def (csuba_clear_trans g (CHead x0 (Flat f) t) c2 H10
545 (CHead d1 (Bind Abst) u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba g e2
546 (CHead d1 (Bind Abst) u))) (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda
547 (d2: C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2
548 d1))) (\lambda (x2: C).(\lambda (H12: (csuba g x2 (CHead d1 (Bind Abst)
549 u))).(\lambda (H13: (clear c2 x2)).(let H_x \def (csuba_gen_abst_rev g d1 x2
550 u H12) in (let H14 \def H_x in (ex2_ind C (\lambda (d2: C).(eq C x2 (CHead d2
551 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) (ex2 C (\lambda (d2:
552 C).(getl O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)))
553 (\lambda (x3: C).(\lambda (H15: (eq C x2 (CHead x3 (Bind Abst) u))).(\lambda
554 (H16: (csuba g x3 d1)).(let H17 \def (eq_ind C x2 (\lambda (c: C).(clear c2
555 c)) H13 (CHead x3 (Bind Abst) u) H15) in (ex_intro2 C (\lambda (d2: C).(getl
556 O c2 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1)) x3
557 (getl_intro O c2 (CHead x3 (Bind Abst) u) c2 (drop_refl c2) H17) H16)))))
558 H14)))))) H11)))))))) (\lambda (n: nat).(\lambda (H8: ((\forall (x1:
559 C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 x1)
560 \to (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u))) (\lambda
561 (d2: C).(csuba g d2 d1))))))))).(\lambda (x1: C).(\lambda (H9: (drop (S n) O
562 x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H10: (csuba g c2
563 x1)).(let H11 \def (drop_clear x1 (CHead x0 (Flat f) t) n H9) in (ex2_3_ind B
564 C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear x1 (CHead e (Bind
565 b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead
566 x0 (Flat f) t))))) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
567 Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x2: B).(\lambda (x3:
568 C).(\lambda (x4: T).(\lambda (H12: (clear x1 (CHead x3 (Bind x2)
569 x4))).(\lambda (H13: (drop n O x3 (CHead x0 (Flat f) t))).(let H14 \def
570 (csuba_clear_trans g x1 c2 H10 (CHead x3 (Bind x2) x4) H12) in (ex2_ind C
571 (\lambda (e2: C).(csuba g e2 (CHead x3 (Bind x2) x4))) (\lambda (e2:
572 C).(clear c2 e2)) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
573 Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x5: C).(\lambda (H15:
574 (csuba g x5 (CHead x3 (Bind x2) x4))).(\lambda (H16: (clear c2 x5)).(let H_x
575 \def (csuba_gen_bind_rev g x2 x3 x5 x4 H15) in (let H17 \def H_x in
576 (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2: T).(eq C x5
577 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2: C).(\lambda (_:
578 T).(csuba g e2 x3)))) (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
579 Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x6: B).(\lambda (x7:
580 C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind x6)
581 x8))).(\lambda (H19: (csuba g x7 x3)).(let H20 \def (eq_ind C x5 (\lambda (c:
582 C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 H13
583 x7 H19) in (ex2_ind C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abst) u)))
584 (\lambda (d2: C).(csuba g d2 d1)) (ex2 C (\lambda (d2: C).(getl (S n) c2
585 (CHead d2 (Bind Abst) u))) (\lambda (d2: C).(csuba g d2 d1))) (\lambda (x9:
586 C).(\lambda (H22: (getl n x7 (CHead x9 (Bind Abst) u))).(\lambda (H23: (csuba
587 g x9 d1)).(ex_intro2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
588 u))) (\lambda (d2: C).(csuba g d2 d1)) x9 (getl_clear_bind x6 c2 x7 x8 H20
589 (CHead x9 (Bind Abst) u) n H22) H23)))) H21)))))))) H17)))))) H14)))))))
590 H11)))))))) i) H7))))) k H3 H4))))))) x H1 H2)))) H0))))))).
592 theorem csuba_getl_abbr_rev:
593 \forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
594 (i: nat).((getl i c1 (CHead d1 (Bind Abbr) u1)) \to (\forall (c2: C).((csuba
595 g c2 c1) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr)
596 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
597 C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2)))))
598 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
599 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
600 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))))))))))
602 \lambda (g: G).(\lambda (c1: C).(\lambda (d1: C).(\lambda (u1: T).(\lambda
603 (i: nat).(\lambda (H: (getl i c1 (CHead d1 (Bind Abbr) u1))).(let H0 \def
604 (getl_gen_all c1 (CHead d1 (Bind Abbr) u1) i H) in (ex2_ind C (\lambda (e:
605 C).(drop i O c1 e)) (\lambda (e: C).(clear e (CHead d1 (Bind Abbr) u1)))
606 (\forall (c2: C).((csuba g c2 c1) \to (or (ex2 C (\lambda (d2: C).(getl i c2
607 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
608 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
609 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
610 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
611 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
612 u1 a)))))))) (\lambda (x: C).(\lambda (H1: (drop i O c1 x)).(\lambda (H2:
613 (clear x (CHead d1 (Bind Abbr) u1))).(C_ind (\lambda (c: C).((drop i O c1 c)
614 \to ((clear c (CHead d1 (Bind Abbr) u1)) \to (\forall (c2: C).((csuba g c2
615 c1) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1)))
616 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
617 (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda
618 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
619 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
620 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))))))))) (\lambda
621 (n: nat).(\lambda (_: (drop i O c1 (CSort n))).(\lambda (H4: (clear (CSort n)
622 (CHead d1 (Bind Abbr) u1))).(clear_gen_sort (CHead d1 (Bind Abbr) u1) n H4
623 (\forall (c2: C).((csuba g c2 c1) \to (or (ex2 C (\lambda (d2: C).(getl i c2
624 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
625 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
626 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
627 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
628 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
629 u1 a)))))))))))) (\lambda (x0: C).(\lambda (_: (((drop i O c1 x0) \to ((clear
630 x0 (CHead d1 (Bind Abbr) u1)) \to (\forall (c2: C).((csuba g c2 c1) \to (or
631 (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
632 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
633 (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
634 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
635 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
636 (_: T).(\lambda (a: A).(arity g d1 u1 a)))))))))))).(\lambda (k: K).(\lambda
637 (t: T).(\lambda (H3: (drop i O c1 (CHead x0 k t))).(\lambda (H4: (clear
638 (CHead x0 k t) (CHead d1 (Bind Abbr) u1))).(K_ind (\lambda (k0: K).((drop i O
639 c1 (CHead x0 k0 t)) \to ((clear (CHead x0 k0 t) (CHead d1 (Bind Abbr) u1))
640 \to (\forall (c2: C).((csuba g c2 c1) \to (or (ex2 C (\lambda (d2: C).(getl i
641 c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T
642 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2
643 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
644 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
645 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
646 u1 a))))))))))) (\lambda (b: B).(\lambda (H5: (drop i O c1 (CHead x0 (Bind b)
647 t))).(\lambda (H6: (clear (CHead x0 (Bind b) t) (CHead d1 (Bind Abbr)
648 u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
649 (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c]))
650 (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead
651 d1 (Bind Abbr) u1) t H6)) in ((let H8 \def (f_equal C B (\lambda (e:
652 C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abbr |
653 (CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with
654 [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind
655 Abbr) u1) (CHead x0 (Bind b) t) (clear_gen_bind b x0 (CHead d1 (Bind Abbr)
656 u1) t H6)) in ((let H9 \def (f_equal C T (\lambda (e: C).(match e in C return
657 (\lambda (_: C).T) with [(CSort _) \Rightarrow u1 | (CHead _ _ t0)
658 \Rightarrow t0])) (CHead d1 (Bind Abbr) u1) (CHead x0 (Bind b) t)
659 (clear_gen_bind b x0 (CHead d1 (Bind Abbr) u1) t H6)) in (\lambda (H10: (eq B
660 Abbr b)).(\lambda (H11: (eq C d1 x0)).(\lambda (c2: C).(\lambda (H12: (csuba
661 g c2 c1)).(let H13 \def (eq_ind_r T t (\lambda (t0: T).(drop i O c1 (CHead x0
662 (Bind b) t0))) H5 u1 H9) in (let H14 \def (eq_ind_r B b (\lambda (b0:
663 B).(drop i O c1 (CHead x0 (Bind b0) u1))) H13 Abbr H10) in (let H15 \def
664 (eq_ind_r C x0 (\lambda (c: C).(drop i O c1 (CHead c (Bind Abbr) u1))) H14 d1
665 H11) in (let H16 \def (csuba_drop_abbr_rev i c1 d1 u1 H15 g c2 H12) in
666 (or_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1)))
667 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
668 (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
669 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
670 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
671 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (or (ex2 C
672 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
673 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
674 (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
675 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
676 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
677 (_: T).(\lambda (a: A).(arity g d1 u1 a)))))) (\lambda (H17: (ex2 C (\lambda
678 (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
679 d1)))).(ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abbr) u1)))
680 (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2: C).(getl i c2
681 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
682 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
683 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
684 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
685 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
686 u1 a)))))) (\lambda (x1: C).(\lambda (H18: (drop i O c2 (CHead x1 (Bind Abbr)
687 u1))).(\lambda (H19: (csuba g x1 d1)).(or_introl (ex2 C (\lambda (d2:
688 C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
689 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
690 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
691 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
692 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
693 (a: A).(arity g d1 u1 a))))) (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead
694 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) x1 (getl_intro i c2
695 (CHead x1 (Bind Abbr) u1) (CHead x1 (Bind Abbr) u1) H18 (clear_bind Abbr x1
696 u1)) H19))))) H17)) (\lambda (H17: (ex4_3 C T A (\lambda (d2: C).(\lambda
697 (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
698 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
699 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
700 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T
701 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2
702 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
703 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
704 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
705 u1 a)))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1)))
706 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
707 (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda
708 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
709 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
710 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))) (\lambda (x1:
711 C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H18: (drop i O c2 (CHead x1
712 (Bind Abst) x2))).(\lambda (H19: (csuba g x1 d1)).(\lambda (H20: (arity g x1
713 x2 (asucc g x3))).(\lambda (H21: (arity g d1 u1 x3)).(or_intror (ex2 C
714 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
715 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
716 (_: A).(getl i c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
717 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
718 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
719 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex4_3_intro C T A (\lambda (d2:
720 C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abst) u2)))))
721 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
722 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
723 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))) x1 x2 x3
724 (getl_intro i c2 (CHead x1 (Bind Abst) x2) (CHead x1 (Bind Abst) x2) H18
725 (clear_bind Abst x1 x2)) H19 H20 H21))))))))) H17)) H16)))))))))) H8))
726 H7))))) (\lambda (f: F).(\lambda (H5: (drop i O c1 (CHead x0 (Flat f)
727 t))).(\lambda (H6: (clear (CHead x0 (Flat f) t) (CHead d1 (Bind Abbr)
728 u1))).(let H7 \def H5 in (unintro C c1 (\lambda (c: C).((drop i O c (CHead x0
729 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 c) \to (or (ex2 C (\lambda
730 (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
731 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i
732 c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
733 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
734 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
735 (a: A).(arity g d1 u1 a)))))))))) (nat_ind (\lambda (n: nat).(\forall (x1:
736 C).((drop n O x1 (CHead x0 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 x1)
737 \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u1)))
738 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
739 (u2: T).(\lambda (_: A).(getl n c2 (CHead d2 (Bind Abst) u2))))) (\lambda
740 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
741 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
742 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))))))))) (\lambda
743 (x1: C).(\lambda (H8: (drop O O x1 (CHead x0 (Flat f) t))).(\lambda (c2:
744 C).(\lambda (H9: (csuba g c2 x1)).(let H10 \def (eq_ind C x1 (\lambda (c:
745 C).(csuba g c2 c)) H9 (CHead x0 (Flat f) t) (drop_gen_refl x1 (CHead x0 (Flat
746 f) t) H8)) in (let H_y \def (clear_flat x0 (CHead d1 (Bind Abbr) u1)
747 (clear_gen_flat f x0 (CHead d1 (Bind Abbr) u1) t H6) f t) in (let H11 \def
748 (csuba_clear_trans g (CHead x0 (Flat f) t) c2 H10 (CHead d1 (Bind Abbr) u1)
749 H_y) in (ex2_ind C (\lambda (e2: C).(csuba g e2 (CHead d1 (Bind Abbr) u1)))
750 (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead
751 d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda
752 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abst)
753 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
754 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
755 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))))
756 (\lambda (x2: C).(\lambda (H12: (csuba g x2 (CHead d1 (Bind Abbr)
757 u1))).(\lambda (H13: (clear c2 x2)).(let H_x \def (csuba_gen_abbr_rev g d1 x2
758 u1 H12) in (let H14 \def H_x in (or_ind (ex2 C (\lambda (d2: C).(eq C x2
759 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
760 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C x2 (CHead d2 (Bind
761 Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2
762 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
763 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
764 u1 a))))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u1)))
765 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
766 (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
767 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
768 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
769 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))) (\lambda (H15:
770 (ex2 C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
771 C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(eq C x2 (CHead d2 (Bind
772 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
773 C).(getl O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)))
774 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2
775 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
776 A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
777 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
778 (a: A).(arity g d1 u1 a)))))) (\lambda (x3: C).(\lambda (H16: (eq C x2 (CHead
779 x3 (Bind Abbr) u1))).(\lambda (H17: (csuba g x3 d1)).(let H18 \def (eq_ind C
780 x2 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 (Bind Abbr) u1) H16) in
781 (or_introl (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u1)))
782 (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda
783 (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abst) u2))))) (\lambda
784 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
785 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
786 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex_intro2 C
787 (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
788 C).(csuba g d2 d1)) x3 (getl_intro O c2 (CHead x3 (Bind Abbr) u1) c2
789 (drop_refl c2) H18) H17)))))) H15)) (\lambda (H15: (ex4_3 C T A (\lambda (d2:
790 C).(\lambda (u2: T).(\lambda (_: A).(eq C x2 (CHead d2 (Bind Abst) u2)))))
791 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
792 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
793 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
794 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
795 A).(eq C x2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
796 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
797 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
798 (_: T).(\lambda (a: A).(arity g d1 u1 a)))) (or (ex2 C (\lambda (d2: C).(getl
799 O c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C
800 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2
801 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
802 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
803 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
804 u1 a)))))) (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: A).(\lambda (H16:
805 (eq C x2 (CHead x3 (Bind Abst) x4))).(\lambda (H17: (csuba g x3 d1)).(\lambda
806 (H18: (arity g x3 x4 (asucc g x5))).(\lambda (H19: (arity g d1 u1 x5)).(let
807 H20 \def (eq_ind C x2 (\lambda (c: C).(clear c2 c)) H13 (CHead x3 (Bind Abst)
808 x4) H16) in (or_intror (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind
809 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
810 C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abst) u2)))))
811 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
812 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
813 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
814 (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O
815 c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
816 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
817 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
818 (a: A).(arity g d1 u1 a)))) x3 x4 x5 (getl_intro O c2 (CHead x3 (Bind Abst)
819 x4) c2 (drop_refl c2) H20) H17 H18 H19)))))))))) H15)) H14)))))) H11))))))))
820 (\lambda (n: nat).(\lambda (H8: ((\forall (x1: C).((drop n O x1 (CHead x0
821 (Flat f) t)) \to (\forall (c2: C).((csuba g c2 x1) \to (or (ex2 C (\lambda
822 (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
823 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl n
824 c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
825 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
826 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
827 (a: A).(arity g d1 u1 a)))))))))))).(\lambda (x1: C).(\lambda (H9: (drop (S
828 n) O x1 (CHead x0 (Flat f) t))).(\lambda (c2: C).(\lambda (H10: (csuba g c2
829 x1)).(let H11 \def (drop_clear x1 (CHead x0 (Flat f) t) n H9) in (ex2_3_ind B
830 C T (\lambda (b: B).(\lambda (e: C).(\lambda (v: T).(clear x1 (CHead e (Bind
831 b) v))))) (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead
832 x0 (Flat f) t))))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
833 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
834 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abst)
835 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
836 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
837 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))))
838 (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H12: (clear x1
839 (CHead x3 (Bind x2) x4))).(\lambda (H13: (drop n O x3 (CHead x0 (Flat f)
840 t))).(let H14 \def (csuba_clear_trans g x1 c2 H10 (CHead x3 (Bind x2) x4)
841 H12) in (ex2_ind C (\lambda (e2: C).(csuba g e2 (CHead x3 (Bind x2) x4)))
842 (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2
843 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A
844 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2
845 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
846 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
847 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
848 u1 a)))))) (\lambda (x5: C).(\lambda (H15: (csuba g x5 (CHead x3 (Bind x2)
849 x4))).(\lambda (H16: (clear c2 x5)).(let H_x \def (csuba_gen_bind_rev g x2 x3
850 x5 x4 H15) in (let H17 \def H_x in (ex2_3_ind B C T (\lambda (b2: B).(\lambda
851 (e2: C).(\lambda (v2: T).(eq C x5 (CHead e2 (Bind b2) v2))))) (\lambda (_:
852 B).(\lambda (e2: C).(\lambda (_: T).(csuba g e2 x3)))) (or (ex2 C (\lambda
853 (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g
854 d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl
855 (S n) c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_:
856 T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
857 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
858 (_: T).(\lambda (a: A).(arity g d1 u1 a)))))) (\lambda (x6: B).(\lambda (x7:
859 C).(\lambda (x8: T).(\lambda (H18: (eq C x5 (CHead x7 (Bind x6)
860 x8))).(\lambda (H19: (csuba g x7 x3)).(let H20 \def (eq_ind C x5 (\lambda (c:
861 C).(clear c2 c)) H16 (CHead x7 (Bind x6) x8) H18) in (let H21 \def (H8 x3 H13
862 x7 H19) in (or_ind (ex2 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abbr)
863 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
864 C).(\lambda (u2: T).(\lambda (_: A).(getl n x7 (CHead d2 (Bind Abst) u2)))))
865 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda
866 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a)))))
867 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (or
868 (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr) u1))) (\lambda
869 (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
870 T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
871 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
872 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
873 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))) (\lambda (H22:
874 (ex2 C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
875 C).(csuba g d2 d1)))).(ex2_ind C (\lambda (d2: C).(getl n x7 (CHead d2 (Bind
876 Abbr) u1))) (\lambda (d2: C).(csuba g d2 d1)) (or (ex2 C (\lambda (d2:
877 C).(getl (S n) c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
878 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S
879 n) c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
880 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
881 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
882 (a: A).(arity g d1 u1 a)))))) (\lambda (x9: C).(\lambda (H23: (getl n x7
883 (CHead x9 (Bind Abbr) u1))).(\lambda (H24: (csuba g x9 d1)).(or_introl (ex2 C
884 (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2:
885 C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
886 (_: A).(getl (S n) c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda
887 (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2:
888 T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda
889 (_: T).(\lambda (a: A).(arity g d1 u1 a))))) (ex_intro2 C (\lambda (d2:
890 C).(getl (S n) c2 (CHead d2 (Bind Abbr) u1))) (\lambda (d2: C).(csuba g d2
891 d1)) x9 (getl_clear_bind x6 c2 x7 x8 H20 (CHead x9 (Bind Abbr) u1) n H23)
892 H24))))) H22)) (\lambda (H22: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
893 T).(\lambda (_: A).(getl n x7 (CHead d2 (Bind Abst) u2))))) (\lambda (d2:
894 C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1)))) (\lambda (d2:
895 C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g a))))) (\lambda
896 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))).(ex4_3_ind C T
897 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl n x7 (CHead d2
898 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
899 d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
900 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1
901 u1 a)))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr)
902 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
903 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abst)
904 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
905 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
906 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a))))))
907 (\lambda (x9: C).(\lambda (x10: T).(\lambda (x11: A).(\lambda (H23: (getl n
908 x7 (CHead x9 (Bind Abst) x10))).(\lambda (H24: (csuba g x9 d1)).(\lambda
909 (H25: (arity g x9 x10 (asucc g x11))).(\lambda (H26: (arity g d1 u1
910 x11)).(or_intror (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr)
911 u1))) (\lambda (d2: C).(csuba g d2 d1))) (ex4_3 C T A (\lambda (d2:
912 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abst)
913 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d2 d1))))
914 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 (asucc g
915 a))))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 a)))))
916 (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S
917 n) c2 (CHead d2 (Bind Abst) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
918 (_: A).(csuba g d2 d1)))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
919 A).(arity g d2 u2 (asucc g a))))) (\lambda (_: C).(\lambda (_: T).(\lambda
920 (a: A).(arity g d1 u1 a)))) x9 x10 x11 (getl_clear_bind x6 c2 x7 x8 H20
921 (CHead x9 (Bind Abst) x10) n H23) H24 H25 H26))))))))) H22)) H21))))))))
922 H17)))))) H14))))))) H11)))))))) i) H7))))) k H3 H4))))))) x H1 H2))))
projects / helm.git / blob