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/Level-1/LambdaDelta/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))).((match x in C return (\lambda (c: C).((drop i O c1 c) \to ((clear
39 c (CHead d1 (Bind Abbr) u)) \to (\forall (c2: C).((csuba g c1 c2) \to (ex2 C
40 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
41 C).(csuba g d1 d2)))))))) with [(CSort n) \Rightarrow (\lambda (_: (drop i O
42 c1 (CSort n))).(\lambda (H4: (clear (CSort n) (CHead d1 (Bind Abbr)
43 u))).(clear_gen_sort (CHead d1 (Bind Abbr) u) n H4 (\forall (c2: C).((csuba g
44 c1 c2) \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u)))
45 (\lambda (d2: C).(csuba g d1 d2)))))))) | (CHead c k t) \Rightarrow (\lambda
46 (H3: (drop i O c1 (CHead c k t))).(\lambda (H4: (clear (CHead c k t) (CHead
47 d1 (Bind Abbr) u))).((match k in K return (\lambda (k0: K).((drop i O c1
48 (CHead c k0 t)) \to ((clear (CHead c k0 t) (CHead d1 (Bind Abbr) u)) \to
49 (\forall (c2: C).((csuba g c1 c2) \to (ex2 C (\lambda (d2: C).(getl i c2
50 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))))))) with
51 [(Bind b) \Rightarrow (\lambda (H5: (drop i O c1 (CHead c (Bind b)
52 t))).(\lambda (H6: (clear (CHead c (Bind b) t) (CHead d1 (Bind Abbr)
53 u))).(let H7 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
54 (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c0 _ _) \Rightarrow c0]))
55 (CHead d1 (Bind Abbr) u) (CHead c (Bind b) t) (clear_gen_bind b c (CHead d1
56 (Bind Abbr) u) t H6)) in ((let H8 \def (f_equal C B (\lambda (e: C).(match e
57 in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow Abbr | (CHead _ k0
58 _) \Rightarrow (match k0 in K return (\lambda (_: K).B) with [(Bind b0)
59 \Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead d1 (Bind Abbr) u)
60 (CHead c (Bind b) t) (clear_gen_bind b c (CHead d1 (Bind Abbr) u) t H6)) in
61 ((let H9 \def (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_:
62 C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) (CHead
63 d1 (Bind Abbr) u) (CHead c (Bind b) t) (clear_gen_bind b c (CHead d1 (Bind
64 Abbr) u) t H6)) in (\lambda (H10: (eq B Abbr b)).(\lambda (H11: (eq C d1
65 c)).(\lambda (c2: C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r
66 T t (\lambda (t0: T).(drop i O c1 (CHead c (Bind b) t0))) H5 u H9) in (let
67 H14 \def (eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead c (Bind b0) u)))
68 H13 Abbr H10) in (let H15 \def (eq_ind_r C c (\lambda (c0: C).(drop i O c1
69 (CHead c0 (Bind Abbr) u))) H14 d1 H11) in (let H16 \def (csuba_drop_abbr i c1
70 d1 u H15 g c2 H12) in (ex2_ind C (\lambda (d2: C).(drop i O c2 (CHead d2
71 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2:
72 C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)))
73 (\lambda (x0: C).(\lambda (H17: (drop i O c2 (CHead x0 (Bind Abbr)
74 u))).(\lambda (H18: (csuba g d1 x0)).(ex_intro2 C (\lambda (d2: C).(getl i c2
75 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x0 (getl_intro i
76 c2 (CHead x0 (Bind Abbr) u) (CHead x0 (Bind Abbr) u) H17 (clear_bind Abbr x0
77 u)) H18)))) H16)))))))))) H8)) H7)))) | (Flat f) \Rightarrow (\lambda (H5:
78 (drop i O c1 (CHead c (Flat f) t))).(\lambda (H6: (clear (CHead c (Flat f) t)
79 (CHead d1 (Bind Abbr) u))).(let H7 \def H5 in (unintro C c1 (\lambda (c0:
80 C).((drop i O c0 (CHead c (Flat f) t)) \to (\forall (c2: C).((csuba g c0 c2)
81 \to (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abbr) u))) (\lambda
82 (d2: C).(csuba g d1 d2))))))) (nat_ind (\lambda (n: nat).(\forall (x0:
83 C).((drop n O x0 (CHead c (Flat f) t)) \to (\forall (c2: C).((csuba g x0 c2)
84 \to (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abbr) u))) (\lambda
85 (d2: C).(csuba g d1 d2)))))))) (\lambda (x0: C).(\lambda (H8: (drop O O x0
86 (CHead c (Flat f) t))).(\lambda (c2: C).(\lambda (H9: (csuba g x0 c2)).(let
87 H10 \def (eq_ind C x0 (\lambda (c0: C).(csuba g c0 c2)) H9 (CHead c (Flat f)
88 t) (drop_gen_refl x0 (CHead c (Flat f) t) H8)) in (let H_y \def (clear_flat c
89 (CHead d1 (Bind Abbr) u) (clear_gen_flat f c (CHead d1 (Bind Abbr) u) t H6) f
90 t) in (let H11 \def (csuba_clear_conf g (CHead c (Flat f) t) c2 H10 (CHead d1
91 (Bind Abbr) u) H_y) in (ex2_ind C (\lambda (e2: C).(csuba g (CHead d1 (Bind
92 Abbr) u) e2)) (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda (d2: C).(getl O
93 c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda
94 (x1: C).(\lambda (H12: (csuba g (CHead d1 (Bind Abbr) u) x1)).(\lambda (H13:
95 (clear c2 x1)).(let H14 \def (csuba_gen_abbr g d1 x1 u H12) in (ex2_ind C
96 (\lambda (d2: C).(eq C x1 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba
97 g d1 d2)) (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u)))
98 (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x2: C).(\lambda (H15: (eq C x1
99 (CHead x2 (Bind Abbr) u))).(\lambda (H16: (csuba g d1 x2)).(let H17 \def
100 (eq_ind C x1 (\lambda (c0: C).(clear c2 c0)) H13 (CHead x2 (Bind Abbr) u)
101 H15) in (ex_intro2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abbr) u)))
102 (\lambda (d2: C).(csuba g d1 d2)) x2 (getl_intro O c2 (CHead x2 (Bind Abbr)
103 u) c2 (drop_refl c2) H17) H16))))) H14))))) H11)))))))) (\lambda (n:
104 nat).(\lambda (H8: ((\forall (x0: C).((drop n O x0 (CHead c (Flat f) t)) \to
105 (\forall (c2: C).((csuba g x0 c2) \to (ex2 C (\lambda (d2: C).(getl n c2
106 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))))))))).(\lambda
107 (x0: C).(\lambda (H9: (drop (S n) O x0 (CHead c (Flat f) t))).(\lambda (c2:
108 C).(\lambda (H10: (csuba g x0 c2)).(let H11 \def (drop_clear x0 (CHead c
109 (Flat f) t) n H9) in (ex2_3_ind B C T (\lambda (b: B).(\lambda (e:
110 C).(\lambda (v: T).(clear x0 (CHead e (Bind b) v))))) (\lambda (_:
111 B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead c (Flat f) t))))) (ex2
112 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2:
113 C).(csuba g d1 d2))) (\lambda (x1: B).(\lambda (x2: C).(\lambda (x3:
114 T).(\lambda (H12: (clear x0 (CHead x2 (Bind x1) x3))).(\lambda (H13: (drop n
115 O x2 (CHead c (Flat f) t))).(let H14 \def (csuba_clear_conf g x0 c2 H10
116 (CHead x2 (Bind x1) x3) H12) in (ex2_ind C (\lambda (e2: C).(csuba g (CHead
117 x2 (Bind x1) x3) e2)) (\lambda (e2: C).(clear c2 e2)) (ex2 C (\lambda (d2:
118 C).(getl (S n) c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1
119 d2))) (\lambda (x4: C).(\lambda (H15: (csuba g (CHead x2 (Bind x1) x3)
120 x4)).(\lambda (H16: (clear c2 x4)).(let H17 \def (csuba_gen_bind g x1 x2 x4
121 x3 H15) in (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
122 T).(eq C x4 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
123 C).(\lambda (_: T).(csuba g x2 e2)))) (ex2 C (\lambda (d2: C).(getl (S n) c2
124 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda (x5:
125 B).(\lambda (x6: C).(\lambda (x7: T).(\lambda (H18: (eq C x4 (CHead x6 (Bind
126 x5) x7))).(\lambda (H19: (csuba g x2 x6)).(let H20 \def (eq_ind C x4 (\lambda
127 (c0: C).(clear c2 c0)) H16 (CHead x6 (Bind x5) x7) H18) in (let H21 \def (H8
128 x2 H13 x6 H19) in (ex2_ind C (\lambda (d2: C).(getl n x6 (CHead d2 (Bind
129 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) (ex2 C (\lambda (d2: C).(getl (S
130 n) c2 (CHead d2 (Bind Abbr) u))) (\lambda (d2: C).(csuba g d1 d2))) (\lambda
131 (x8: C).(\lambda (H22: (getl n x6 (CHead x8 (Bind Abbr) u))).(\lambda (H23:
132 (csuba g d1 x8)).(ex_intro2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
133 Abbr) u))) (\lambda (d2: C).(csuba g d1 d2)) x8 (getl_clear_bind x5 c2 x6 x7
134 H20 (CHead x8 (Bind Abbr) u) n H22) H23)))) H21)))))))) H17))))) H14)))))))
135 H11)))))))) i) H7))))]) H3 H4)))]) H1 H2)))) H0))))))).
137 theorem csuba_getl_abst:
138 \forall (g: G).(\forall (c1: C).(\forall (d1: C).(\forall (u1: T).(\forall
139 (i: nat).((getl i c1 (CHead d1 (Bind Abst) u1)) \to (\forall (c2: C).((csuba
140 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
141 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
142 C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
143 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
144 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
145 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
148 \lambda (g: G).(\lambda (c1: C).(\lambda (d1: C).(\lambda (u1: T).(\lambda
149 (i: nat).(\lambda (H: (getl i c1 (CHead d1 (Bind Abst) u1))).(let H0 \def
150 (getl_gen_all c1 (CHead d1 (Bind Abst) u1) i H) in (ex2_ind C (\lambda (e:
151 C).(drop i O c1 e)) (\lambda (e: C).(clear e (CHead d1 (Bind Abst) u1)))
152 (\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2
153 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
154 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind
155 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
156 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
157 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
158 a)))))))) (\lambda (x: C).(\lambda (H1: (drop i O c1 x)).(\lambda (H2: (clear
159 x (CHead d1 (Bind Abst) u1))).((match x in C return (\lambda (c: C).((drop i
160 O c1 c) \to ((clear c (CHead d1 (Bind Abst) u1)) \to (\forall (c2: C).((csuba
161 g c1 c2) \to (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
162 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
163 C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
164 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
165 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
166 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))))))))
167 with [(CSort n) \Rightarrow (\lambda (_: (drop i O c1 (CSort n))).(\lambda
168 (H4: (clear (CSort n) (CHead d1 (Bind Abst) u1))).(clear_gen_sort (CHead d1
169 (Bind Abst) u1) n H4 (\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C
170 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
171 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
172 (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
173 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
174 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
175 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))))))) | (CHead c k t)
176 \Rightarrow (\lambda (H3: (drop i O c1 (CHead c k t))).(\lambda (H4: (clear
177 (CHead c k t) (CHead d1 (Bind Abst) u1))).((match k in K return (\lambda (k0:
178 K).((drop i O c1 (CHead c k0 t)) \to ((clear (CHead c k0 t) (CHead d1 (Bind
179 Abst) u1)) \to (\forall (c2: C).((csuba g c1 c2) \to (or (ex2 C (\lambda (d2:
180 C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
181 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
182 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
183 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
184 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
185 A).(arity g d2 u2 a))))))))))) with [(Bind b) \Rightarrow (\lambda (H5: (drop
186 i O c1 (CHead c (Bind b) t))).(\lambda (H6: (clear (CHead c (Bind b) t)
187 (CHead d1 (Bind Abst) u1))).(let H7 \def (f_equal C C (\lambda (e: C).(match
188 e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c0 _
189 _) \Rightarrow c0])) (CHead d1 (Bind Abst) u1) (CHead c (Bind b) t)
190 (clear_gen_bind b c (CHead d1 (Bind Abst) u1) t H6)) in ((let H8 \def
191 (f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with
192 [(CSort _) \Rightarrow Abst | (CHead _ k0 _) \Rightarrow (match k0 in K
193 return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _)
194 \Rightarrow Abst])])) (CHead d1 (Bind Abst) u1) (CHead c (Bind b) t)
195 (clear_gen_bind b c (CHead d1 (Bind Abst) u1) t H6)) in ((let H9 \def
196 (f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with
197 [(CSort _) \Rightarrow u1 | (CHead _ _ t0) \Rightarrow t0])) (CHead d1 (Bind
198 Abst) u1) (CHead c (Bind b) t) (clear_gen_bind b c (CHead d1 (Bind Abst) u1)
199 t H6)) in (\lambda (H10: (eq B Abst b)).(\lambda (H11: (eq C d1 c)).(\lambda
200 (c2: C).(\lambda (H12: (csuba g c1 c2)).(let H13 \def (eq_ind_r T t (\lambda
201 (t0: T).(drop i O c1 (CHead c (Bind b) t0))) H5 u1 H9) in (let H14 \def
202 (eq_ind_r B b (\lambda (b0: B).(drop i O c1 (CHead c (Bind b0) u1))) H13 Abst
203 H10) in (let H15 \def (eq_ind_r C c (\lambda (c0: C).(drop i O c1 (CHead c0
204 (Bind Abst) u1))) H14 d1 H11) in (let H16 \def (csuba_drop_abst i c1 d1 u1
205 H15 g c2 H12) in (or_ind (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind
206 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
207 C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr)
208 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
209 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
210 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
211 a))))) (or (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1)))
212 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
213 (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
214 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
215 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
216 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda
217 (H17: (ex2 C (\lambda (d2: C).(drop i O c2 (CHead d2 (Bind Abst) u1)))
218 (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2: C).(drop i O c2
219 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C
220 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
221 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
222 (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
223 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
224 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
225 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x0: C).(\lambda
226 (H18: (drop i O c2 (CHead x0 (Bind Abst) u1))).(\lambda (H19: (csuba g d1
227 x0)).(or_introl (ex2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst)
228 u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
229 C).(\lambda (u2: T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2)))))
230 (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda
231 (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a)))))
232 (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))
233 (ex_intro2 C (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda
234 (d2: C).(csuba g d1 d2)) x0 (getl_intro i c2 (CHead x0 (Bind Abst) u1) (CHead
235 x0 (Bind Abst) u1) H18 (clear_bind Abst x0 u1)) H19))))) H17)) (\lambda (H17:
236 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(drop i O c2
237 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
238 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
239 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
240 A).(arity g d2 u2 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2:
241 T).(\lambda (_: A).(drop i O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
242 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
243 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
244 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) (or (ex2 C
245 (\lambda (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
246 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
247 (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
248 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
249 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
250 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x0: C).(\lambda (x1:
251 T).(\lambda (x2: A).(\lambda (H18: (drop i O c2 (CHead x0 (Bind Abbr)
252 x1))).(\lambda (H19: (csuba g d1 x0)).(\lambda (H20: (arity g d1 u1 (asucc g
253 x2))).(\lambda (H21: (arity g x0 x1 x2)).(or_intror (ex2 C (\lambda (d2:
254 C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
255 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i c2
256 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
257 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
258 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
259 A).(arity g d2 u2 a))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2:
260 T).(\lambda (_: A).(getl i c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
261 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
262 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
263 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x0 x1 x2
264 (getl_intro i c2 (CHead x0 (Bind Abbr) x1) (CHead x0 (Bind Abbr) x1) H18
265 (clear_bind Abbr x0 x1)) H19 H20 H21))))))))) H17)) H16)))))))))) H8)) H7))))
266 | (Flat f) \Rightarrow (\lambda (H5: (drop i O c1 (CHead c (Flat f)
267 t))).(\lambda (H6: (clear (CHead c (Flat f) t) (CHead d1 (Bind Abst)
268 u1))).(let H7 \def H5 in (unintro C c1 (\lambda (c0: C).((drop i O c0 (CHead
269 c (Flat f) t)) \to (\forall (c2: C).((csuba g c0 c2) \to (or (ex2 C (\lambda
270 (d2: C).(getl i c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
271 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl i
272 c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
273 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
274 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
275 (a: A).(arity g d2 u2 a)))))))))) (nat_ind (\lambda (n: nat).(\forall (x0:
276 C).((drop n O x0 (CHead c (Flat f) t)) \to (\forall (c2: C).((csuba g x0 c2)
277 \to (or (ex2 C (\lambda (d2: C).(getl n c2 (CHead d2 (Bind Abst) u1)))
278 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
279 (u2: T).(\lambda (_: A).(getl n c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
280 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
281 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
282 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))))))))) (\lambda
283 (x0: C).(\lambda (H8: (drop O O x0 (CHead c (Flat f) t))).(\lambda (c2:
284 C).(\lambda (H9: (csuba g x0 c2)).(let H10 \def (eq_ind C x0 (\lambda (c0:
285 C).(csuba g c0 c2)) H9 (CHead c (Flat f) t) (drop_gen_refl x0 (CHead c (Flat
286 f) t) H8)) in (let H_y \def (clear_flat c (CHead d1 (Bind Abst) u1)
287 (clear_gen_flat f c (CHead d1 (Bind Abst) u1) t H6) f t) in (let H11 \def
288 (csuba_clear_conf g (CHead c (Flat f) t) c2 H10 (CHead d1 (Bind Abst) u1)
289 H_y) in (ex2_ind C (\lambda (e2: C).(csuba g (CHead d1 (Bind Abst) u1) e2))
290 (\lambda (e2: C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead
291 d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
292 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abbr)
293 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
294 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
295 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
296 a)))))) (\lambda (x1: C).(\lambda (H12: (csuba g (CHead d1 (Bind Abst) u1)
297 x1)).(\lambda (H13: (clear c2 x1)).(let H14 \def (csuba_gen_abst g d1 x1 u1
298 H12) in (or_ind (ex2 C (\lambda (d2: C).(eq C x1 (CHead d2 (Bind Abst) u1)))
299 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
300 (u2: T).(\lambda (_: A).(eq C x1 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
301 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
302 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
303 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (or (ex2 C
304 (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
305 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
306 (_: A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
307 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
308 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
309 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (H15: (ex2 C (\lambda
310 (d2: C).(eq C x1 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
311 d2)))).(ex2_ind C (\lambda (d2: C).(eq C x1 (CHead d2 (Bind Abst) u1)))
312 (\lambda (d2: C).(csuba g d1 d2)) (or (ex2 C (\lambda (d2: C).(getl O c2
313 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
314 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind
315 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
316 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
317 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
318 a)))))) (\lambda (x2: C).(\lambda (H16: (eq C x1 (CHead x2 (Bind Abst)
319 u1))).(\lambda (H17: (csuba g d1 x2)).(let H18 \def (eq_ind C x1 (\lambda
320 (c0: C).(clear c2 c0)) H13 (CHead x2 (Bind Abst) u1) H16) in (or_introl (ex2
321 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2:
322 C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda
323 (_: A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
324 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
325 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
326 (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex_intro2 C (\lambda (d2:
327 C).(getl O c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))
328 x2 (getl_intro O c2 (CHead x2 (Bind Abst) u1) c2 (drop_refl c2) H18)
329 H17)))))) H15)) (\lambda (H15: (ex4_3 C T A (\lambda (d2: C).(\lambda (u2:
330 T).(\lambda (_: A).(eq C x1 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2:
331 C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
332 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
333 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))).(ex4_3_ind C
334 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(eq C x1 (CHead d2
335 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
336 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
337 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
338 u2 a)))) (or (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1)))
339 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
340 (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
341 (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))))) (\lambda
343 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x2:
344 C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H16: (eq C x1 (CHead x2 (Bind
345 Abbr) x3))).(\lambda (H17: (csuba g d1 x2)).(\lambda (H18: (arity g d1 u1
346 (asucc g x4))).(\lambda (H19: (arity g x2 x3 x4)).(let H20 \def (eq_ind C x1
347 (\lambda (c0: C).(clear c2 c0)) H13 (CHead x2 (Bind Abbr) x3) H16) in
348 (or_intror (ex2 C (\lambda (d2: C).(getl O c2 (CHead d2 (Bind Abst) u1)))
349 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
350 (u2: T).(\lambda (_: A).(getl O c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
351 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
352 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
353 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a))))) (ex4_3_intro C
354 T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl O c2 (CHead d2
355 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
356 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
357 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
358 u2 a)))) x2 x3 x4 (getl_intro O c2 (CHead x2 (Bind Abbr) x3) c2 (drop_refl
359 c2) H20) H17 H18 H19)))))))))) H15)) H14))))) H11)))))))) (\lambda (n:
360 nat).(\lambda (H8: ((\forall (x0: C).((drop n O x0 (CHead c (Flat f) t)) \to
361 (\forall (c2: C).((csuba g x0 c2) \to (or (ex2 C (\lambda (d2: C).(getl n c2
362 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A
363 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl n c2 (CHead d2 (Bind
364 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
365 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
366 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
367 a)))))))))))).(\lambda (x0: C).(\lambda (H9: (drop (S n) O x0 (CHead c (Flat
368 f) t))).(\lambda (c2: C).(\lambda (H10: (csuba g x0 c2)).(let H11 \def
369 (drop_clear x0 (CHead c (Flat f) t) n H9) in (ex2_3_ind B C T (\lambda (b:
370 B).(\lambda (e: C).(\lambda (v: T).(clear x0 (CHead e (Bind b) v)))))
371 (\lambda (_: B).(\lambda (e: C).(\lambda (_: T).(drop n O e (CHead c (Flat f)
372 t))))) (or (ex2 C (\lambda (d2: C).(getl (S 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 (S 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 a)))))) (\lambda (x1:
378 B).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H12: (clear x0 (CHead x2 (Bind
379 x1) x3))).(\lambda (H13: (drop n O x2 (CHead c (Flat f) t))).(let H14 \def
380 (csuba_clear_conf g x0 c2 H10 (CHead x2 (Bind x1) x3) H12) in (ex2_ind C
381 (\lambda (e2: C).(csuba g (CHead x2 (Bind x1) x3) e2)) (\lambda (e2:
382 C).(clear c2 e2)) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind
383 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2:
384 C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
385 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
386 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
387 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
388 a)))))) (\lambda (x4: C).(\lambda (H15: (csuba g (CHead x2 (Bind x1) x3)
389 x4)).(\lambda (H16: (clear c2 x4)).(let H17 \def (csuba_gen_bind g x1 x2 x4
390 x3 H15) in (ex2_3_ind B C T (\lambda (b2: B).(\lambda (e2: C).(\lambda (v2:
391 T).(eq C x4 (CHead e2 (Bind b2) v2))))) (\lambda (_: B).(\lambda (e2:
392 C).(\lambda (_: T).(csuba g x2 e2)))) (or (ex2 C (\lambda (d2: C).(getl (S n)
393 c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T
394 A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2
395 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g
396 d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1
397 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2
398 u2 a)))))) (\lambda (x5: B).(\lambda (x6: C).(\lambda (x7: T).(\lambda (H18:
399 (eq C x4 (CHead x6 (Bind x5) x7))).(\lambda (H19: (csuba g x2 x6)).(let H20
400 \def (eq_ind C x4 (\lambda (c0: C).(clear c2 c0)) H16 (CHead x6 (Bind x5) x7)
401 H18) in (let H21 \def (H8 x2 H13 x6 H19) in (or_ind (ex2 C (\lambda (d2:
402 C).(getl n x6 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))
403 (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl n x6
404 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_:
405 A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity
406 g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a:
407 A).(arity g d2 u2 a))))) (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2
408 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
409 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
410 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
411 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
412 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
413 a)))))) (\lambda (H22: (ex2 C (\lambda (d2: C).(getl n x6 (CHead d2 (Bind
414 Abst) u1))) (\lambda (d2: C).(csuba g d1 d2)))).(ex2_ind C (\lambda (d2:
415 C).(getl n x6 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))
416 (or (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst) u1)))
417 (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda
418 (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda
419 (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_:
420 C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda
421 (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2 a)))))) (\lambda (x8:
422 C).(\lambda (H23: (getl n x6 (CHead x8 (Bind Abst) u1))).(\lambda (H24:
423 (csuba g d1 x8)).(or_introl (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2
424 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
425 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
426 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
427 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
428 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
429 a))))) (ex_intro2 C (\lambda (d2: C).(getl (S n) c2 (CHead d2 (Bind Abst)
430 u1))) (\lambda (d2: C).(csuba g d1 d2)) x8 (getl_clear_bind x5 c2 x6 x7 H20
431 (CHead x8 (Bind Abst) u1) n H23) H24))))) H22)) (\lambda (H22: (ex4_3 C T A
432 (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl n x6 (CHead d2 (Bind
433 Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1
434 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc
435 g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
436 a)))))).(ex4_3_ind C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
437 A).(getl n x6 (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)))) (or (ex2 C (\lambda (d2:
441 C).(getl (S n) c2 (CHead d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1
442 d2))) (ex4_3 C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S
443 n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda
444 (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a:
445 A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda
446 (a: A).(arity g d2 u2 a)))))) (\lambda (x8: C).(\lambda (x9: T).(\lambda
447 (x10: A).(\lambda (H23: (getl n x6 (CHead x8 (Bind Abbr) x9))).(\lambda (H24:
448 (csuba g d1 x8)).(\lambda (H25: (arity g d1 u1 (asucc g x10))).(\lambda (H26:
449 (arity g x8 x9 x10)).(or_intror (ex2 C (\lambda (d2: C).(getl (S n) c2 (CHead
450 d2 (Bind Abst) u1))) (\lambda (d2: C).(csuba g d1 d2))) (ex4_3 C T A (\lambda
451 (d2: C).(\lambda (u2: T).(\lambda (_: A).(getl (S n) c2 (CHead d2 (Bind Abbr)
452 u2))))) (\lambda (d2: C).(\lambda (_: T).(\lambda (_: A).(csuba g d1 d2))))
453 (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(arity g d1 u1 (asucc g
454 a))))) (\lambda (d2: C).(\lambda (u2: T).(\lambda (a: A).(arity g d2 u2
455 a))))) (ex4_3_intro C T A (\lambda (d2: C).(\lambda (u2: T).(\lambda (_:
456 A).(getl (S n) c2 (CHead d2 (Bind Abbr) u2))))) (\lambda (d2: C).(\lambda (_:
457 T).(\lambda (_: A).(csuba g d1 d2)))) (\lambda (_: C).(\lambda (_:
458 T).(\lambda (a: A).(arity g d1 u1 (asucc g a))))) (\lambda (d2: C).(\lambda
459 (u2: T).(\lambda (a: A).(arity g d2 u2 a)))) x8 x9 x10 (getl_clear_bind x5 c2
460 x6 x7 H20 (CHead x8 (Bind Abbr) x9) n H23) H24 H25 H26))))))))) H22))
461 H21)))))))) H17))))) H14))))))) H11)))))))) i) H7))))]) H3 H4)))]) H1 H2))))
projects / helm.git / blob