1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1/csubc/fwd.ma".
19 include "basic_1/sc3/props.ma".
21 theorem csubc_drop_conf_O:
22 \forall (g: G).(\forall (c1: C).(\forall (e1: C).(\forall (h: nat).((drop h
23 O c1 e1) \to (\forall (c2: C).((csubc g c1 c2) \to (ex2 C (\lambda (e2:
24 C).(drop h O c2 e2)) (\lambda (e2: C).(csubc g e1 e2)))))))))
26 \lambda (g: G).(\lambda (c1: C).(let TMP_3 \def (\lambda (c: C).(\forall
27 (e1: C).(\forall (h: nat).((drop h O c e1) \to (\forall (c2: C).((csubc g c
28 c2) \to (let TMP_1 \def (\lambda (e2: C).(drop h O c2 e2)) in (let TMP_2 \def
29 (\lambda (e2: C).(csubc g e1 e2)) in (ex2 C TMP_1 TMP_2))))))))) in (let
30 TMP_26 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda (h: nat).(\lambda (H:
31 (drop h O (CSort n) e1)).(\lambda (c2: C).(\lambda (H0: (csubc g (CSort n)
32 c2)).(let TMP_4 \def (CSort n) in (let TMP_5 \def (eq C e1 TMP_4) in (let
33 TMP_6 \def (eq nat h O) in (let TMP_7 \def (eq nat O O) in (let TMP_8 \def
34 (\lambda (e2: C).(drop h O c2 e2)) in (let TMP_9 \def (\lambda (e2: C).(csubc
35 g e1 e2)) in (let TMP_10 \def (ex2 C TMP_8 TMP_9) in (let TMP_24 \def
36 (\lambda (H1: (eq C e1 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (_:
37 (eq nat O O)).(let TMP_13 \def (\lambda (n0: nat).(let TMP_11 \def (\lambda
38 (e2: C).(drop n0 O c2 e2)) in (let TMP_12 \def (\lambda (e2: C).(csubc g e1
39 e2)) in (ex2 C TMP_11 TMP_12)))) in (let TMP_14 \def (CSort n) in (let TMP_17
40 \def (\lambda (c: C).(let TMP_15 \def (\lambda (e2: C).(drop O O c2 e2)) in
41 (let TMP_16 \def (\lambda (e2: C).(csubc g c e2)) in (ex2 C TMP_15 TMP_16))))
42 in (let TMP_18 \def (\lambda (e2: C).(drop O O c2 e2)) in (let TMP_20 \def
43 (\lambda (e2: C).(let TMP_19 \def (CSort n) in (csubc g TMP_19 e2))) in (let
44 TMP_21 \def (drop_refl c2) in (let TMP_22 \def (ex_intro2 C TMP_18 TMP_20 c2
45 TMP_21 H0) in (let TMP_23 \def (eq_ind_r C TMP_14 TMP_17 TMP_22 e1 H1) in
46 (eq_ind_r nat O TMP_13 TMP_23 h H2)))))))))))) in (let TMP_25 \def
47 (drop_gen_sort n h O e1 H) in (and3_ind TMP_5 TMP_6 TMP_7 TMP_10 TMP_24
48 TMP_25)))))))))))))))) in (let TMP_196 \def (\lambda (c: C).(\lambda (H:
49 ((\forall (e1: C).(\forall (h: nat).((drop h O c e1) \to (\forall (c2:
50 C).((csubc g c c2) \to (ex2 C (\lambda (e2: C).(drop h O c2 e2)) (\lambda
51 (e2: C).(csubc g e1 e2)))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda
52 (e1: C).(\lambda (h: nat).(let TMP_29 \def (\lambda (n: nat).((drop n O
53 (CHead c k t) e1) \to (\forall (c2: C).((csubc g (CHead c k t) c2) \to (let
54 TMP_27 \def (\lambda (e2: C).(drop n O c2 e2)) in (let TMP_28 \def (\lambda
55 (e2: C).(csubc g e1 e2)) in (ex2 C TMP_27 TMP_28))))))) in (let TMP_41 \def
56 (\lambda (H0: (drop O O (CHead c k t) e1)).(\lambda (c2: C).(\lambda (H1:
57 (csubc g (CHead c k t) c2)).(let TMP_30 \def (CHead c k t) in (let TMP_33
58 \def (\lambda (c0: C).(let TMP_31 \def (\lambda (e2: C).(drop O O c2 e2)) in
59 (let TMP_32 \def (\lambda (e2: C).(csubc g c0 e2)) in (ex2 C TMP_31
60 TMP_32)))) in (let TMP_34 \def (\lambda (e2: C).(drop O O c2 e2)) in (let
61 TMP_36 \def (\lambda (e2: C).(let TMP_35 \def (CHead c k t) in (csubc g
62 TMP_35 e2))) in (let TMP_37 \def (drop_refl c2) in (let TMP_38 \def
63 (ex_intro2 C TMP_34 TMP_36 c2 TMP_37 H1) in (let TMP_39 \def (CHead c k t) in
64 (let TMP_40 \def (drop_gen_refl TMP_39 e1 H0) in (eq_ind C TMP_30 TMP_33
65 TMP_38 e1 TMP_40)))))))))))) in (let TMP_195 \def (\lambda (n: nat).(\lambda
66 (H0: (((drop n O (CHead c k t) e1) \to (\forall (c2: C).((csubc g (CHead c k
67 t) c2) \to (ex2 C (\lambda (e2: C).(drop n O c2 e2)) (\lambda (e2: C).(csubc
68 g e1 e2)))))))).(\lambda (H1: (drop (S n) O (CHead c k t) e1)).(\lambda (c2:
69 C).(\lambda (H2: (csubc g (CHead c k t) c2)).(let H_x \def (csubc_gen_head_l
70 g c c2 t k H2) in (let H3 \def H_x in (let TMP_43 \def (\lambda (c3: C).(let
71 TMP_42 \def (CHead c3 k t) in (eq C c2 TMP_42))) in (let TMP_44 \def (\lambda
72 (c3: C).(csubc g c c3)) in (let TMP_45 \def (ex2 C TMP_43 TMP_44) in (let
73 TMP_47 \def (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(let TMP_46 \def
74 (Bind Abst) in (eq K k TMP_46))))) in (let TMP_50 \def (\lambda (c3:
75 C).(\lambda (w: T).(\lambda (_: A).(let TMP_48 \def (Bind Abbr) in (let
76 TMP_49 \def (CHead c3 TMP_48 w) in (eq C c2 TMP_49)))))) in (let TMP_51 \def
77 (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) in (let
78 TMP_53 \def (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(let TMP_52 \def
79 (asucc g a) in (sc3 g TMP_52 c t))))) in (let TMP_54 \def (\lambda (c3:
80 C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_55 \def
81 (ex5_3 C T A TMP_47 TMP_50 TMP_51 TMP_53 TMP_54) in (let TMP_58 \def (\lambda
82 (b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_56 \def (Bind b) in (let
83 TMP_57 \def (CHead c3 TMP_56 v2) in (eq C c2 TMP_57)))))) in (let TMP_60 \def
84 (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_59 \def (Bind Void)
85 in (eq K k TMP_59))))) in (let TMP_62 \def (\lambda (b: B).(\lambda (_:
86 C).(\lambda (_: T).(let TMP_61 \def (eq B b Void) in (not TMP_61))))) in (let
87 TMP_63 \def (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g c
88 c3)))) in (let TMP_64 \def (ex4_3 B C T TMP_58 TMP_60 TMP_62 TMP_63) in (let
89 TMP_66 \def (\lambda (e2: C).(let TMP_65 \def (S n) in (drop TMP_65 O c2
90 e2))) in (let TMP_67 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_68
91 \def (ex2 C TMP_66 TMP_67) in (let TMP_99 \def (\lambda (H4: (ex2 C (\lambda
92 (c3: C).(eq C c2 (CHead c3 k t))) (\lambda (c3: C).(csubc g c c3)))).(let
93 TMP_70 \def (\lambda (c3: C).(let TMP_69 \def (CHead c3 k t) in (eq C c2
94 TMP_69))) in (let TMP_71 \def (\lambda (c3: C).(csubc g c c3)) in (let TMP_73
95 \def (\lambda (e2: C).(let TMP_72 \def (S n) in (drop TMP_72 O c2 e2))) in
96 (let TMP_74 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_75 \def (ex2 C
97 TMP_73 TMP_74) in (let TMP_98 \def (\lambda (x: C).(\lambda (H5: (eq C c2
98 (CHead x k t))).(\lambda (H6: (csubc g c x)).(let TMP_76 \def (CHead x k t)
99 in (let TMP_80 \def (\lambda (c0: C).(let TMP_78 \def (\lambda (e2: C).(let
100 TMP_77 \def (S n) in (drop TMP_77 O c0 e2))) in (let TMP_79 \def (\lambda
101 (e2: C).(csubc g e1 e2)) in (ex2 C TMP_78 TMP_79)))) in (let TMP_81 \def (r k
102 n) in (let TMP_82 \def (drop_gen_drop k c e1 t n H1) in (let H_x0 \def (H e1
103 TMP_81 TMP_82 x H6) in (let H7 \def H_x0 in (let TMP_84 \def (\lambda (e2:
104 C).(let TMP_83 \def (r k n) in (drop TMP_83 O x e2))) in (let TMP_85 \def
105 (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_88 \def (\lambda (e2: C).(let
106 TMP_86 \def (S n) in (let TMP_87 \def (CHead x k t) in (drop TMP_86 O TMP_87
107 e2)))) in (let TMP_89 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_90
108 \def (ex2 C TMP_88 TMP_89) in (let TMP_96 \def (\lambda (x0: C).(\lambda (H8:
109 (drop (r k n) O x x0)).(\lambda (H9: (csubc g e1 x0)).(let TMP_93 \def
110 (\lambda (e2: C).(let TMP_91 \def (S n) in (let TMP_92 \def (CHead x k t) in
111 (drop TMP_91 O TMP_92 e2)))) in (let TMP_94 \def (\lambda (e2: C).(csubc g e1
112 e2)) in (let TMP_95 \def (drop_drop k n x x0 H8 t) in (ex_intro2 C TMP_93
113 TMP_94 x0 TMP_95 H9))))))) in (let TMP_97 \def (ex2_ind C TMP_84 TMP_85
114 TMP_90 TMP_96 H7) in (eq_ind_r C TMP_76 TMP_80 TMP_97 c2 H5)))))))))))))))))
115 in (ex2_ind C TMP_70 TMP_71 TMP_75 TMP_98 H4)))))))) in (let TMP_147 \def
116 (\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_:
117 A).(eq K k (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
118 A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
119 T).(\lambda (_: A).(csubc g c c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
120 (a: A).(sc3 g (asucc g a) c t)))) (\lambda (c3: C).(\lambda (w: T).(\lambda
121 (a: A).(sc3 g a c3 w)))))).(let TMP_101 \def (\lambda (_: C).(\lambda (_:
122 T).(\lambda (_: A).(let TMP_100 \def (Bind Abst) in (eq K k TMP_100))))) in
123 (let TMP_104 \def (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(let
124 TMP_102 \def (Bind Abbr) in (let TMP_103 \def (CHead c3 TMP_102 w) in (eq C
125 c2 TMP_103)))))) in (let TMP_105 \def (\lambda (c3: C).(\lambda (_:
126 T).(\lambda (_: A).(csubc g c c3)))) in (let TMP_107 \def (\lambda (_:
127 C).(\lambda (_: T).(\lambda (a: A).(let TMP_106 \def (asucc g a) in (sc3 g
128 TMP_106 c t))))) in (let TMP_108 \def (\lambda (c3: C).(\lambda (w:
129 T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_110 \def (\lambda (e2:
130 C).(let TMP_109 \def (S n) in (drop TMP_109 O c2 e2))) in (let TMP_111 \def
131 (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_112 \def (ex2 C TMP_110
132 TMP_111) in (let TMP_146 \def (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2:
133 A).(\lambda (H5: (eq K k (Bind Abst))).(\lambda (H6: (eq C c2 (CHead x0 (Bind
134 Abbr) x1))).(\lambda (H7: (csubc g c x0)).(\lambda (_: (sc3 g (asucc g x2) c
135 t)).(\lambda (_: (sc3 g x2 x0 x1)).(let TMP_113 \def (Bind Abbr) in (let
136 TMP_114 \def (CHead x0 TMP_113 x1) in (let TMP_118 \def (\lambda (c0: C).(let
137 TMP_116 \def (\lambda (e2: C).(let TMP_115 \def (S n) in (drop TMP_115 O c0
138 e2))) in (let TMP_117 \def (\lambda (e2: C).(csubc g e1 e2)) in (ex2 C
139 TMP_116 TMP_117)))) in (let TMP_120 \def (\lambda (k0: K).(let TMP_119 \def
140 (r k0 n) in (drop TMP_119 O c e1))) in (let TMP_121 \def (drop_gen_drop k c
141 e1 t n H1) in (let TMP_122 \def (Bind Abst) in (let H10 \def (eq_ind K k
142 TMP_120 TMP_121 TMP_122 H5) in (let TMP_125 \def (\lambda (k0: K).((drop n O
143 (CHead c k0 t) e1) \to (\forall (c3: C).((csubc g (CHead c k0 t) c3) \to (let
144 TMP_123 \def (\lambda (e2: C).(drop n O c3 e2)) in (let TMP_124 \def (\lambda
145 (e2: C).(csubc g e1 e2)) in (ex2 C TMP_123 TMP_124))))))) in (let TMP_126
146 \def (Bind Abst) in (let H11 \def (eq_ind K k TMP_125 H0 TMP_126 H5) in (let
147 TMP_127 \def (Bind Abst) in (let TMP_128 \def (r TMP_127 n) in (let H_x0 \def
148 (H e1 TMP_128 H10 x0 H7) in (let H12 \def H_x0 in (let TMP_129 \def (\lambda
149 (e2: C).(drop n O x0 e2)) in (let TMP_130 \def (\lambda (e2: C).(csubc g e1
150 e2)) in (let TMP_134 \def (\lambda (e2: C).(let TMP_131 \def (S n) in (let
151 TMP_132 \def (Bind Abbr) in (let TMP_133 \def (CHead x0 TMP_132 x1) in (drop
152 TMP_131 O TMP_133 e2))))) in (let TMP_135 \def (\lambda (e2: C).(csubc g e1
153 e2)) in (let TMP_136 \def (ex2 C TMP_134 TMP_135) in (let TMP_144 \def
154 (\lambda (x: C).(\lambda (H13: (drop n O x0 x)).(\lambda (H14: (csubc g e1
155 x)).(let TMP_140 \def (\lambda (e2: C).(let TMP_137 \def (S n) in (let
156 TMP_138 \def (Bind Abbr) in (let TMP_139 \def (CHead x0 TMP_138 x1) in (drop
157 TMP_137 O TMP_139 e2))))) in (let TMP_141 \def (\lambda (e2: C).(csubc g e1
158 e2)) in (let TMP_142 \def (Bind Abbr) in (let TMP_143 \def (drop_drop TMP_142
159 n x0 x H13 x1) in (ex_intro2 C TMP_140 TMP_141 x TMP_143 H14)))))))) in (let
160 TMP_145 \def (ex2_ind C TMP_129 TMP_130 TMP_136 TMP_144 H12) in (eq_ind_r C
161 TMP_114 TMP_118 TMP_145 c2 H6)))))))))))))))))))))))))))))) in (ex5_3_ind C T
162 A TMP_101 TMP_104 TMP_105 TMP_107 TMP_108 TMP_112 TMP_146 H4))))))))))) in
163 (let TMP_194 \def (\lambda (H4: (ex4_3 B C T (\lambda (b: B).(\lambda (c3:
164 C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_:
165 B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b:
166 B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
167 B).(\lambda (c3: C).(\lambda (_: T).(csubc g c c3)))))).(let TMP_150 \def
168 (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_148 \def (Bind b)
169 in (let TMP_149 \def (CHead c3 TMP_148 v2) in (eq C c2 TMP_149)))))) in (let
170 TMP_152 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_151
171 \def (Bind Void) in (eq K k TMP_151))))) in (let TMP_154 \def (\lambda (b:
172 B).(\lambda (_: C).(\lambda (_: T).(let TMP_153 \def (eq B b Void) in (not
173 TMP_153))))) in (let TMP_155 \def (\lambda (_: B).(\lambda (c3: C).(\lambda
174 (_: T).(csubc g c c3)))) in (let TMP_157 \def (\lambda (e2: C).(let TMP_156
175 \def (S n) in (drop TMP_156 O c2 e2))) in (let TMP_158 \def (\lambda (e2:
176 C).(csubc g e1 e2)) in (let TMP_159 \def (ex2 C TMP_157 TMP_158) in (let
177 TMP_193 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H5:
178 (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda (H6: (eq K k (Bind
179 Void))).(\lambda (_: (not (eq B x0 Void))).(\lambda (H8: (csubc g c x1)).(let
180 TMP_160 \def (Bind x0) in (let TMP_161 \def (CHead x1 TMP_160 x2) in (let
181 TMP_165 \def (\lambda (c0: C).(let TMP_163 \def (\lambda (e2: C).(let TMP_162
182 \def (S n) in (drop TMP_162 O c0 e2))) in (let TMP_164 \def (\lambda (e2:
183 C).(csubc g e1 e2)) in (ex2 C TMP_163 TMP_164)))) in (let TMP_167 \def
184 (\lambda (k0: K).(let TMP_166 \def (r k0 n) in (drop TMP_166 O c e1))) in
185 (let TMP_168 \def (drop_gen_drop k c e1 t n H1) in (let TMP_169 \def (Bind
186 Void) in (let H9 \def (eq_ind K k TMP_167 TMP_168 TMP_169 H6) in (let TMP_172
187 \def (\lambda (k0: K).((drop n O (CHead c k0 t) e1) \to (\forall (c3:
188 C).((csubc g (CHead c k0 t) c3) \to (let TMP_170 \def (\lambda (e2: C).(drop
189 n O c3 e2)) in (let TMP_171 \def (\lambda (e2: C).(csubc g e1 e2)) in (ex2 C
190 TMP_170 TMP_171))))))) in (let TMP_173 \def (Bind Void) in (let H10 \def
191 (eq_ind K k TMP_172 H0 TMP_173 H6) in (let TMP_174 \def (Bind Void) in (let
192 TMP_175 \def (r TMP_174 n) in (let H_x0 \def (H e1 TMP_175 H9 x1 H8) in (let
193 H11 \def H_x0 in (let TMP_176 \def (\lambda (e2: C).(drop n O x1 e2)) in (let
194 TMP_177 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_181 \def (\lambda
195 (e2: C).(let TMP_178 \def (S n) in (let TMP_179 \def (Bind x0) in (let
196 TMP_180 \def (CHead x1 TMP_179 x2) in (drop TMP_178 O TMP_180 e2))))) in (let
197 TMP_182 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_183 \def (ex2 C
198 TMP_181 TMP_182) in (let TMP_191 \def (\lambda (x: C).(\lambda (H12: (drop n
199 O x1 x)).(\lambda (H13: (csubc g e1 x)).(let TMP_187 \def (\lambda (e2:
200 C).(let TMP_184 \def (S n) in (let TMP_185 \def (Bind x0) in (let TMP_186
201 \def (CHead x1 TMP_185 x2) in (drop TMP_184 O TMP_186 e2))))) in (let TMP_188
202 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_189 \def (Bind x0) in (let
203 TMP_190 \def (drop_drop TMP_189 n x1 x H12 x2) in (ex_intro2 C TMP_187
204 TMP_188 x TMP_190 H13)))))))) in (let TMP_192 \def (ex2_ind C TMP_176 TMP_177
205 TMP_183 TMP_191 H11) in (eq_ind_r C TMP_161 TMP_165 TMP_192 c2
206 H5))))))))))))))))))))))))))))) in (ex4_3_ind B C T TMP_150 TMP_152 TMP_154
207 TMP_155 TMP_159 TMP_193 H4)))))))))) in (or3_ind TMP_45 TMP_55 TMP_64 TMP_68
208 TMP_99 TMP_147 TMP_194 H3)))))))))))))))))))))))))))) in (nat_ind TMP_29
209 TMP_41 TMP_195 h)))))))))) in (C_ind TMP_3 TMP_26 TMP_196 c1))))).
211 theorem drop_csubc_trans:
212 \forall (g: G).(\forall (c2: C).(\forall (e2: C).(\forall (d: nat).(\forall
213 (h: nat).((drop h d c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C
214 (\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c2 c1))))))))))
216 \lambda (g: G).(\lambda (c2: C).(let TMP_3 \def (\lambda (c: C).(\forall
217 (e2: C).(\forall (d: nat).(\forall (h: nat).((drop h d c e2) \to (\forall
218 (e1: C).((csubc g e2 e1) \to (let TMP_1 \def (\lambda (c1: C).(drop h d c1
219 e1)) in (let TMP_2 \def (\lambda (c1: C).(csubc g c c1)) in (ex2 C TMP_1
220 TMP_2)))))))))) in (let TMP_30 \def (\lambda (n: nat).(\lambda (e2:
221 C).(\lambda (d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n)
222 e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e2 e1)).(let TMP_4 \def (CSort
223 n) in (let TMP_5 \def (eq C e2 TMP_4) in (let TMP_6 \def (eq nat h O) in (let
224 TMP_7 \def (eq nat d O) in (let TMP_8 \def (\lambda (c1: C).(drop h d c1 e1))
225 in (let TMP_10 \def (\lambda (c1: C).(let TMP_9 \def (CSort n) in (csubc g
226 TMP_9 c1))) in (let TMP_11 \def (ex2 C TMP_8 TMP_10) in (let TMP_28 \def
227 (\lambda (H1: (eq C e2 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (H3:
228 (eq nat d O)).(let TMP_15 \def (\lambda (n0: nat).(let TMP_12 \def (\lambda
229 (c1: C).(drop n0 d c1 e1)) in (let TMP_14 \def (\lambda (c1: C).(let TMP_13
230 \def (CSort n) in (csubc g TMP_13 c1))) in (ex2 C TMP_12 TMP_14)))) in (let
231 TMP_19 \def (\lambda (n0: nat).(let TMP_16 \def (\lambda (c1: C).(drop O n0
232 c1 e1)) in (let TMP_18 \def (\lambda (c1: C).(let TMP_17 \def (CSort n) in
233 (csubc g TMP_17 c1))) in (ex2 C TMP_16 TMP_18)))) in (let TMP_20 \def
234 (\lambda (c: C).(csubc g c e1)) in (let TMP_21 \def (CSort n) in (let H4 \def
235 (eq_ind C e2 TMP_20 H0 TMP_21 H1) in (let TMP_22 \def (\lambda (c1: C).(drop
236 O O c1 e1)) in (let TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (CSort n)
237 in (csubc g TMP_23 c1))) in (let TMP_25 \def (drop_refl e1) in (let TMP_26
238 \def (ex_intro2 C TMP_22 TMP_24 e1 TMP_25 H4) in (let TMP_27 \def (eq_ind_r
239 nat O TMP_19 TMP_26 d H3) in (eq_ind_r nat O TMP_15 TMP_27 h H2))))))))))))))
240 in (let TMP_29 \def (drop_gen_sort n h d e2 H) in (and3_ind TMP_5 TMP_6 TMP_7
241 TMP_11 TMP_28 TMP_29))))))))))))))))) in (let TMP_354 \def (\lambda (c:
242 C).(\lambda (H: ((\forall (e2: C).(\forall (d: nat).(\forall (h: nat).((drop
243 h d c e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda (c1:
244 C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c c1))))))))))).(\lambda (k:
245 K).(\lambda (t: T).(\lambda (e2: C).(\lambda (d: nat).(let TMP_34 \def
246 (\lambda (n: nat).(\forall (h: nat).((drop h n (CHead c k t) e2) \to (\forall
247 (e1: C).((csubc g e2 e1) \to (let TMP_31 \def (\lambda (c1: C).(drop h n c1
248 e1)) in (let TMP_33 \def (\lambda (c1: C).(let TMP_32 \def (CHead c k t) in
249 (csubc g TMP_32 c1))) in (ex2 C TMP_31 TMP_33)))))))) in (let TMP_67 \def
250 (\lambda (h: nat).(let TMP_38 \def (\lambda (n: nat).((drop n O (CHead c k t)
251 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (let TMP_35 \def (\lambda (c1:
252 C).(drop n O c1 e1)) in (let TMP_37 \def (\lambda (c1: C).(let TMP_36 \def
253 (CHead c k t) in (csubc g TMP_36 c1))) in (ex2 C TMP_35 TMP_37))))))) in (let
254 TMP_47 \def (\lambda (H0: (drop O O (CHead c k t) e2)).(\lambda (e1:
255 C).(\lambda (H1: (csubc g e2 e1)).(let TMP_39 \def (\lambda (c0: C).(csubc g
256 c0 e1)) in (let TMP_40 \def (CHead c k t) in (let TMP_41 \def (CHead c k t)
257 in (let TMP_42 \def (drop_gen_refl TMP_41 e2 H0) in (let H2 \def (eq_ind_r C
258 e2 TMP_39 H1 TMP_40 TMP_42) in (let TMP_43 \def (\lambda (c1: C).(drop O O c1
259 e1)) in (let TMP_45 \def (\lambda (c1: C).(let TMP_44 \def (CHead c k t) in
260 (csubc g TMP_44 c1))) in (let TMP_46 \def (drop_refl e1) in (ex_intro2 C
261 TMP_43 TMP_45 e1 TMP_46 H2)))))))))))) in (let TMP_66 \def (\lambda (n:
262 nat).(\lambda (_: (((drop n O (CHead c k t) e2) \to (\forall (e1: C).((csubc
263 g e2 e1) \to (ex2 C (\lambda (c1: C).(drop n O c1 e1)) (\lambda (c1:
264 C).(csubc g (CHead c k t) c1)))))))).(\lambda (H1: (drop (S n) O (CHead c k
265 t) e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e2 e1)).(let TMP_48 \def (r k
266 n) in (let TMP_49 \def (drop_gen_drop k c e2 t n H1) in (let H_x \def (H e2 O
267 TMP_48 TMP_49 e1 H2) in (let H3 \def H_x in (let TMP_51 \def (\lambda (c1:
268 C).(let TMP_50 \def (r k n) in (drop TMP_50 O c1 e1))) in (let TMP_52 \def
269 (\lambda (c1: C).(csubc g c c1)) in (let TMP_54 \def (\lambda (c1: C).(let
270 TMP_53 \def (S n) in (drop TMP_53 O c1 e1))) in (let TMP_56 \def (\lambda
271 (c1: C).(let TMP_55 \def (CHead c k t) in (csubc g TMP_55 c1))) in (let
272 TMP_57 \def (ex2 C TMP_54 TMP_56) in (let TMP_65 \def (\lambda (x:
273 C).(\lambda (H4: (drop (r k n) O x e1)).(\lambda (H5: (csubc g c x)).(let
274 TMP_59 \def (\lambda (c1: C).(let TMP_58 \def (S n) in (drop TMP_58 O c1
275 e1))) in (let TMP_61 \def (\lambda (c1: C).(let TMP_60 \def (CHead c k t) in
276 (csubc g TMP_60 c1))) in (let TMP_62 \def (CHead x k t) in (let TMP_63 \def
277 (drop_drop k n x e1 H4 t) in (let TMP_64 \def (csubc_head g c x H5 k t) in
278 (ex_intro2 C TMP_59 TMP_61 TMP_62 TMP_63 TMP_64))))))))) in (ex2_ind C TMP_51
279 TMP_52 TMP_57 TMP_65 H3)))))))))))))))) in (nat_ind TMP_38 TMP_47 TMP_66
280 h))))) in (let TMP_353 \def (\lambda (n: nat).(\lambda (H0: ((\forall (h:
281 nat).((drop h n (CHead c k t) e2) \to (\forall (e1: C).((csubc g e2 e1) \to
282 (ex2 C (\lambda (c1: C).(drop h n c1 e1)) (\lambda (c1: C).(csubc g (CHead c
283 k t) c1))))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c k t)
284 e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e2 e1)).(let TMP_69 \def
285 (\lambda (e: C).(\lambda (v: T).(let TMP_68 \def (CHead e k v) in (eq C e2
286 TMP_68)))) in (let TMP_72 \def (\lambda (_: C).(\lambda (v: T).(let TMP_70
287 \def (r k n) in (let TMP_71 \def (lift h TMP_70 v) in (eq T t TMP_71))))) in
288 (let TMP_74 \def (\lambda (e: C).(\lambda (_: T).(let TMP_73 \def (r k n) in
289 (drop h TMP_73 c e)))) in (let TMP_76 \def (\lambda (c1: C).(let TMP_75 \def
290 (S n) in (drop h TMP_75 c1 e1))) in (let TMP_78 \def (\lambda (c1: C).(let
291 TMP_77 \def (CHead c k t) in (csubc g TMP_77 c1))) in (let TMP_79 \def (ex2 C
292 TMP_76 TMP_78) in (let TMP_351 \def (\lambda (x0: C).(\lambda (x1:
293 T).(\lambda (H3: (eq C e2 (CHead x0 k x1))).(\lambda (H4: (eq T t (lift h (r
294 k n) x1))).(\lambda (H5: (drop h (r k n) c x0)).(let TMP_80 \def (\lambda
295 (c0: C).(csubc g c0 e1)) in (let TMP_81 \def (CHead x0 k x1) in (let H6 \def
296 (eq_ind C e2 TMP_80 H2 TMP_81 H3) in (let TMP_85 \def (\lambda (c0:
297 C).(\forall (h0: nat).((drop h0 n (CHead c k t) c0) \to (\forall (e3:
298 C).((csubc g c0 e3) \to (let TMP_82 \def (\lambda (c1: C).(drop h0 n c1 e3))
299 in (let TMP_84 \def (\lambda (c1: C).(let TMP_83 \def (CHead c k t) in (csubc
300 g TMP_83 c1))) in (ex2 C TMP_82 TMP_84)))))))) in (let TMP_86 \def (CHead x0
301 k x1) in (let H7 \def (eq_ind C e2 TMP_85 H0 TMP_86 H3) in (let TMP_90 \def
302 (\lambda (t0: T).(\forall (h0: nat).((drop h0 n (CHead c k t0) (CHead x0 k
303 x1)) \to (\forall (e3: C).((csubc g (CHead x0 k x1) e3) \to (let TMP_87 \def
304 (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_89 \def (\lambda (c1: C).(let
305 TMP_88 \def (CHead c k t0) in (csubc g TMP_88 c1))) in (ex2 C TMP_87
306 TMP_89)))))))) in (let TMP_91 \def (r k n) in (let TMP_92 \def (lift h TMP_91
307 x1) in (let H8 \def (eq_ind T t TMP_90 H7 TMP_92 H4) in (let TMP_93 \def (r k
308 n) in (let TMP_94 \def (lift h TMP_93 x1) in (let TMP_99 \def (\lambda (t0:
309 T).(let TMP_96 \def (\lambda (c1: C).(let TMP_95 \def (S n) in (drop h TMP_95
310 c1 e1))) in (let TMP_98 \def (\lambda (c1: C).(let TMP_97 \def (CHead c k t0)
311 in (csubc g TMP_97 c1))) in (ex2 C TMP_96 TMP_98)))) in (let H_x \def
312 (csubc_gen_head_l g x0 e1 x1 k H6) in (let H9 \def H_x in (let TMP_101 \def
313 (\lambda (c3: C).(let TMP_100 \def (CHead c3 k x1) in (eq C e1 TMP_100))) in
314 (let TMP_102 \def (\lambda (c3: C).(csubc g x0 c3)) in (let TMP_103 \def (ex2
315 C TMP_101 TMP_102) in (let TMP_105 \def (\lambda (_: C).(\lambda (_:
316 T).(\lambda (_: A).(let TMP_104 \def (Bind Abst) in (eq K k TMP_104))))) in
317 (let TMP_108 \def (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(let
318 TMP_106 \def (Bind Abbr) in (let TMP_107 \def (CHead c3 TMP_106 w) in (eq C
319 e1 TMP_107)))))) in (let TMP_109 \def (\lambda (c3: C).(\lambda (_:
320 T).(\lambda (_: A).(csubc g x0 c3)))) in (let TMP_111 \def (\lambda (_:
321 C).(\lambda (_: T).(\lambda (a: A).(let TMP_110 \def (asucc g a) in (sc3 g
322 TMP_110 x0 x1))))) in (let TMP_112 \def (\lambda (c3: C).(\lambda (w:
323 T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_113 \def (ex5_3 C T A
324 TMP_105 TMP_108 TMP_109 TMP_111 TMP_112) in (let TMP_116 \def (\lambda (b:
325 B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_114 \def (Bind b) in (let
326 TMP_115 \def (CHead c3 TMP_114 v2) in (eq C e1 TMP_115)))))) in (let TMP_118
327 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_117 \def (Bind
328 Void) in (eq K k TMP_117))))) in (let TMP_120 \def (\lambda (b: B).(\lambda
329 (_: C).(\lambda (_: T).(let TMP_119 \def (eq B b Void) in (not TMP_119)))))
330 in (let TMP_121 \def (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc
331 g x0 c3)))) in (let TMP_122 \def (ex4_3 B C T TMP_116 TMP_118 TMP_120
332 TMP_121) in (let TMP_124 \def (\lambda (c1: C).(let TMP_123 \def (S n) in
333 (drop h TMP_123 c1 e1))) in (let TMP_128 \def (\lambda (c1: C).(let TMP_125
334 \def (r k n) in (let TMP_126 \def (lift h TMP_125 x1) in (let TMP_127 \def
335 (CHead c k TMP_126) in (csubc g TMP_127 c1))))) in (let TMP_129 \def (ex2 C
336 TMP_124 TMP_128) in (let TMP_177 \def (\lambda (H10: (ex2 C (\lambda (c3:
337 C).(eq C e1 (CHead c3 k x1))) (\lambda (c3: C).(csubc g x0 c3)))).(let
338 TMP_131 \def (\lambda (c3: C).(let TMP_130 \def (CHead c3 k x1) in (eq C e1
339 TMP_130))) in (let TMP_132 \def (\lambda (c3: C).(csubc g x0 c3)) in (let
340 TMP_134 \def (\lambda (c1: C).(let TMP_133 \def (S n) in (drop h TMP_133 c1
341 e1))) in (let TMP_138 \def (\lambda (c1: C).(let TMP_135 \def (r k n) in (let
342 TMP_136 \def (lift h TMP_135 x1) in (let TMP_137 \def (CHead c k TMP_136) in
343 (csubc g TMP_137 c1))))) in (let TMP_139 \def (ex2 C TMP_134 TMP_138) in (let
344 TMP_176 \def (\lambda (x: C).(\lambda (H11: (eq C e1 (CHead x k
345 x1))).(\lambda (H12: (csubc g x0 x)).(let TMP_140 \def (CHead x k x1) in (let
346 TMP_147 \def (\lambda (c0: C).(let TMP_142 \def (\lambda (c1: C).(let TMP_141
347 \def (S n) in (drop h TMP_141 c1 c0))) in (let TMP_146 \def (\lambda (c1:
348 C).(let TMP_143 \def (r k n) in (let TMP_144 \def (lift h TMP_143 x1) in (let
349 TMP_145 \def (CHead c k TMP_144) in (csubc g TMP_145 c1))))) in (ex2 C
350 TMP_142 TMP_146)))) in (let TMP_148 \def (r k n) in (let H_x0 \def (H x0
351 TMP_148 h H5 x H12) in (let H13 \def H_x0 in (let TMP_150 \def (\lambda (c1:
352 C).(let TMP_149 \def (r k n) in (drop h TMP_149 c1 x))) in (let TMP_151 \def
353 (\lambda (c1: C).(csubc g c c1)) in (let TMP_154 \def (\lambda (c1: C).(let
354 TMP_152 \def (S n) in (let TMP_153 \def (CHead x k x1) in (drop h TMP_152 c1
355 TMP_153)))) in (let TMP_158 \def (\lambda (c1: C).(let TMP_155 \def (r k n)
356 in (let TMP_156 \def (lift h TMP_155 x1) in (let TMP_157 \def (CHead c k
357 TMP_156) in (csubc g TMP_157 c1))))) in (let TMP_159 \def (ex2 C TMP_154
358 TMP_158) in (let TMP_174 \def (\lambda (x2: C).(\lambda (H14: (drop h (r k n)
359 x2 x)).(\lambda (H15: (csubc g c x2)).(let TMP_162 \def (\lambda (c1: C).(let
360 TMP_160 \def (S n) in (let TMP_161 \def (CHead x k x1) in (drop h TMP_160 c1
361 TMP_161)))) in (let TMP_166 \def (\lambda (c1: C).(let TMP_163 \def (r k n)
362 in (let TMP_164 \def (lift h TMP_163 x1) in (let TMP_165 \def (CHead c k
363 TMP_164) in (csubc g TMP_165 c1))))) in (let TMP_167 \def (r k n) in (let
364 TMP_168 \def (lift h TMP_167 x1) in (let TMP_169 \def (CHead x2 k TMP_168) in
365 (let TMP_170 \def (drop_skip k h n x2 x H14 x1) in (let TMP_171 \def (r k n)
366 in (let TMP_172 \def (lift h TMP_171 x1) in (let TMP_173 \def (csubc_head g c
367 x2 H15 k TMP_172) in (ex_intro2 C TMP_162 TMP_166 TMP_169 TMP_170
368 TMP_173))))))))))))) in (let TMP_175 \def (ex2_ind C TMP_150 TMP_151 TMP_159
369 TMP_174 H13) in (eq_ind_r C TMP_140 TMP_147 TMP_175 e1 H11)))))))))))))))) in
370 (ex2_ind C TMP_131 TMP_132 TMP_139 TMP_176 H10)))))))) in (let TMP_266 \def
371 (\lambda (H10: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_:
372 A).(eq K k (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
373 A).(eq C e1 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
374 T).(\lambda (_: A).(csubc g x0 c3)))) (\lambda (_: C).(\lambda (_:
375 T).(\lambda (a: A).(sc3 g (asucc g a) x0 x1)))) (\lambda (c3: C).(\lambda (w:
376 T).(\lambda (a: A).(sc3 g a c3 w)))))).(let TMP_179 \def (\lambda (_:
377 C).(\lambda (_: T).(\lambda (_: A).(let TMP_178 \def (Bind Abst) in (eq K k
378 TMP_178))))) in (let TMP_182 \def (\lambda (c3: C).(\lambda (w: T).(\lambda
379 (_: A).(let TMP_180 \def (Bind Abbr) in (let TMP_181 \def (CHead c3 TMP_180
380 w) in (eq C e1 TMP_181)))))) in (let TMP_183 \def (\lambda (c3: C).(\lambda
381 (_: T).(\lambda (_: A).(csubc g x0 c3)))) in (let TMP_185 \def (\lambda (_:
382 C).(\lambda (_: T).(\lambda (a: A).(let TMP_184 \def (asucc g a) in (sc3 g
383 TMP_184 x0 x1))))) in (let TMP_186 \def (\lambda (c3: C).(\lambda (w:
384 T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_188 \def (\lambda (c1:
385 C).(let TMP_187 \def (S n) in (drop h TMP_187 c1 e1))) in (let TMP_192 \def
386 (\lambda (c1: C).(let TMP_189 \def (r k n) in (let TMP_190 \def (lift h
387 TMP_189 x1) in (let TMP_191 \def (CHead c k TMP_190) in (csubc g TMP_191
388 c1))))) in (let TMP_193 \def (ex2 C TMP_188 TMP_192) in (let TMP_265 \def
389 (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H11: (eq K k
390 (Bind Abst))).(\lambda (H12: (eq C e1 (CHead x2 (Bind Abbr) x3))).(\lambda
391 (H13: (csubc g x0 x2)).(\lambda (H14: (sc3 g (asucc g x4) x0 x1)).(\lambda
392 (H15: (sc3 g x4 x2 x3)).(let TMP_194 \def (Bind Abbr) in (let TMP_195 \def
393 (CHead x2 TMP_194 x3) in (let TMP_202 \def (\lambda (c0: C).(let TMP_197 \def
394 (\lambda (c1: C).(let TMP_196 \def (S n) in (drop h TMP_196 c1 c0))) in (let
395 TMP_201 \def (\lambda (c1: C).(let TMP_198 \def (r k n) in (let TMP_199 \def
396 (lift h TMP_198 x1) in (let TMP_200 \def (CHead c k TMP_199) in (csubc g
397 TMP_200 c1))))) in (ex2 C TMP_197 TMP_201)))) in (let TMP_208 \def (\lambda
398 (k0: K).(\forall (h0: nat).((drop h0 n (CHead c k0 (lift h (r k0 n) x1))
399 (CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g (CHead x0 k0 x1) e3) \to
400 (let TMP_203 \def (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_207 \def
401 (\lambda (c1: C).(let TMP_204 \def (r k0 n) in (let TMP_205 \def (lift h
402 TMP_204 x1) in (let TMP_206 \def (CHead c k0 TMP_205) in (csubc g TMP_206
403 c1))))) in (ex2 C TMP_203 TMP_207)))))))) in (let TMP_209 \def (Bind Abst) in
404 (let H16 \def (eq_ind K k TMP_208 H8 TMP_209 H11) in (let TMP_211 \def
405 (\lambda (k0: K).(let TMP_210 \def (r k0 n) in (drop h TMP_210 c x0))) in
406 (let TMP_212 \def (Bind Abst) in (let H17 \def (eq_ind K k TMP_211 H5 TMP_212
407 H11) in (let TMP_213 \def (Bind Abst) in (let TMP_222 \def (\lambda (k0:
408 K).(let TMP_217 \def (\lambda (c1: C).(let TMP_214 \def (S n) in (let TMP_215
409 \def (Bind Abbr) in (let TMP_216 \def (CHead x2 TMP_215 x3) in (drop h
410 TMP_214 c1 TMP_216))))) in (let TMP_221 \def (\lambda (c1: C).(let TMP_218
411 \def (r k0 n) in (let TMP_219 \def (lift h TMP_218 x1) in (let TMP_220 \def
412 (CHead c k0 TMP_219) in (csubc g TMP_220 c1))))) in (ex2 C TMP_217
413 TMP_221)))) in (let TMP_223 \def (Bind Abst) in (let TMP_224 \def (r TMP_223
414 n) in (let H_x0 \def (H x0 TMP_224 h H17 x2 H13) in (let H18 \def H_x0 in
415 (let TMP_225 \def (\lambda (c1: C).(drop h n c1 x2)) in (let TMP_226 \def
416 (\lambda (c1: C).(csubc g c c1)) in (let TMP_230 \def (\lambda (c1: C).(let
417 TMP_227 \def (S n) in (let TMP_228 \def (Bind Abbr) in (let TMP_229 \def
418 (CHead x2 TMP_228 x3) in (drop h TMP_227 c1 TMP_229))))) in (let TMP_236 \def
419 (\lambda (c1: C).(let TMP_231 \def (Bind Abst) in (let TMP_232 \def (Bind
420 Abst) in (let TMP_233 \def (r TMP_232 n) in (let TMP_234 \def (lift h TMP_233
421 x1) in (let TMP_235 \def (CHead c TMP_231 TMP_234) in (csubc g TMP_235
422 c1))))))) in (let TMP_237 \def (ex2 C TMP_230 TMP_236) in (let TMP_262 \def
423 (\lambda (x: C).(\lambda (H19: (drop h n x x2)).(\lambda (H20: (csubc g c
424 x)).(let TMP_241 \def (\lambda (c1: C).(let TMP_238 \def (S n) in (let
425 TMP_239 \def (Bind Abbr) in (let TMP_240 \def (CHead x2 TMP_239 x3) in (drop
426 h TMP_238 c1 TMP_240))))) in (let TMP_247 \def (\lambda (c1: C).(let TMP_242
427 \def (Bind Abst) in (let TMP_243 \def (Bind Abst) in (let TMP_244 \def (r
428 TMP_243 n) in (let TMP_245 \def (lift h TMP_244 x1) in (let TMP_246 \def
429 (CHead c TMP_242 TMP_245) in (csubc g TMP_246 c1))))))) in (let TMP_248 \def
430 (Bind Abbr) in (let TMP_249 \def (lift h n x3) in (let TMP_250 \def (CHead x
431 TMP_248 TMP_249) in (let TMP_251 \def (drop_skip_bind h n x x2 H19 Abbr x3)
432 in (let TMP_252 \def (Bind Abst) in (let TMP_253 \def (r TMP_252 n) in (let
433 TMP_254 \def (lift h TMP_253 x1) in (let TMP_255 \def (asucc g x4) in (let
434 TMP_256 \def (Bind Abst) in (let TMP_257 \def (r TMP_256 n) in (let TMP_258
435 \def (sc3_lift g TMP_255 x0 x1 H14 c h TMP_257 H17) in (let TMP_259 \def
436 (lift h n x3) in (let TMP_260 \def (sc3_lift g x4 x2 x3 H15 x h n H19) in
437 (let TMP_261 \def (csubc_abst g c x H20 TMP_254 x4 TMP_258 TMP_259 TMP_260)
438 in (ex_intro2 C TMP_241 TMP_247 TMP_250 TMP_251 TMP_261))))))))))))))))))))
439 in (let TMP_263 \def (ex2_ind C TMP_225 TMP_226 TMP_237 TMP_262 H18) in (let
440 TMP_264 \def (eq_ind_r K TMP_213 TMP_222 TMP_263 k H11) in (eq_ind_r C
441 TMP_195 TMP_202 TMP_264 e1 H12)))))))))))))))))))))))))))))))) in (ex5_3_ind
442 C T A TMP_179 TMP_182 TMP_183 TMP_185 TMP_186 TMP_193 TMP_265 H10)))))))))))
443 in (let TMP_349 \def (\lambda (H10: (ex4_3 B C T (\lambda (b: B).(\lambda
444 (c3: C).(\lambda (v2: T).(eq C e1 (CHead c3 (Bind b) v2))))) (\lambda (_:
445 B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b:
446 B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
447 B).(\lambda (c3: C).(\lambda (_: T).(csubc g x0 c3)))))).(let TMP_269 \def
448 (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_267 \def (Bind b)
449 in (let TMP_268 \def (CHead c3 TMP_267 v2) in (eq C e1 TMP_268)))))) in (let
450 TMP_271 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_270
451 \def (Bind Void) in (eq K k TMP_270))))) in (let TMP_273 \def (\lambda (b:
452 B).(\lambda (_: C).(\lambda (_: T).(let TMP_272 \def (eq B b Void) in (not
453 TMP_272))))) in (let TMP_274 \def (\lambda (_: B).(\lambda (c3: C).(\lambda
454 (_: T).(csubc g x0 c3)))) in (let TMP_276 \def (\lambda (c1: C).(let TMP_275
455 \def (S n) in (drop h TMP_275 c1 e1))) in (let TMP_280 \def (\lambda (c1:
456 C).(let TMP_277 \def (r k n) in (let TMP_278 \def (lift h TMP_277 x1) in (let
457 TMP_279 \def (CHead c k TMP_278) in (csubc g TMP_279 c1))))) in (let TMP_281
458 \def (ex2 C TMP_276 TMP_280) in (let TMP_348 \def (\lambda (x2: B).(\lambda
459 (x3: C).(\lambda (x4: T).(\lambda (H11: (eq C e1 (CHead x3 (Bind x2)
460 x4))).(\lambda (H12: (eq K k (Bind Void))).(\lambda (H13: (not (eq B x2
461 Void))).(\lambda (H14: (csubc g x0 x3)).(let TMP_282 \def (Bind x2) in (let
462 TMP_283 \def (CHead x3 TMP_282 x4) in (let TMP_290 \def (\lambda (c0: C).(let
463 TMP_285 \def (\lambda (c1: C).(let TMP_284 \def (S n) in (drop h TMP_284 c1
464 c0))) in (let TMP_289 \def (\lambda (c1: C).(let TMP_286 \def (r k n) in (let
465 TMP_287 \def (lift h TMP_286 x1) in (let TMP_288 \def (CHead c k TMP_287) in
466 (csubc g TMP_288 c1))))) in (ex2 C TMP_285 TMP_289)))) in (let TMP_296 \def
467 (\lambda (k0: K).(\forall (h0: nat).((drop h0 n (CHead c k0 (lift h (r k0 n)
468 x1)) (CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g (CHead x0 k0 x1) e3)
469 \to (let TMP_291 \def (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_295
470 \def (\lambda (c1: C).(let TMP_292 \def (r k0 n) in (let TMP_293 \def (lift h
471 TMP_292 x1) in (let TMP_294 \def (CHead c k0 TMP_293) in (csubc g TMP_294
472 c1))))) in (ex2 C TMP_291 TMP_295)))))))) in (let TMP_297 \def (Bind Void) in
473 (let H15 \def (eq_ind K k TMP_296 H8 TMP_297 H12) in (let TMP_299 \def
474 (\lambda (k0: K).(let TMP_298 \def (r k0 n) in (drop h TMP_298 c x0))) in
475 (let TMP_300 \def (Bind Void) in (let H16 \def (eq_ind K k TMP_299 H5 TMP_300
476 H12) in (let TMP_301 \def (Bind Void) in (let TMP_310 \def (\lambda (k0:
477 K).(let TMP_305 \def (\lambda (c1: C).(let TMP_302 \def (S n) in (let TMP_303
478 \def (Bind x2) in (let TMP_304 \def (CHead x3 TMP_303 x4) in (drop h TMP_302
479 c1 TMP_304))))) in (let TMP_309 \def (\lambda (c1: C).(let TMP_306 \def (r k0
480 n) in (let TMP_307 \def (lift h TMP_306 x1) in (let TMP_308 \def (CHead c k0
481 TMP_307) in (csubc g TMP_308 c1))))) in (ex2 C TMP_305 TMP_309)))) in (let
482 TMP_311 \def (Bind Void) in (let TMP_312 \def (r TMP_311 n) in (let H_x0 \def
483 (H x0 TMP_312 h H16 x3 H14) in (let H17 \def H_x0 in (let TMP_313 \def
484 (\lambda (c1: C).(drop h n c1 x3)) in (let TMP_314 \def (\lambda (c1:
485 C).(csubc g c c1)) in (let TMP_318 \def (\lambda (c1: C).(let TMP_315 \def (S
486 n) in (let TMP_316 \def (Bind x2) in (let TMP_317 \def (CHead x3 TMP_316 x4)
487 in (drop h TMP_315 c1 TMP_317))))) in (let TMP_324 \def (\lambda (c1: C).(let
488 TMP_319 \def (Bind Void) in (let TMP_320 \def (Bind Void) in (let TMP_321
489 \def (r TMP_320 n) in (let TMP_322 \def (lift h TMP_321 x1) in (let TMP_323
490 \def (CHead c TMP_319 TMP_322) in (csubc g TMP_323 c1))))))) in (let TMP_325
491 \def (ex2 C TMP_318 TMP_324) in (let TMP_345 \def (\lambda (x: C).(\lambda
492 (H18: (drop h n x x3)).(\lambda (H19: (csubc g c x)).(let TMP_329 \def
493 (\lambda (c1: C).(let TMP_326 \def (S n) in (let TMP_327 \def (Bind x2) in
494 (let TMP_328 \def (CHead x3 TMP_327 x4) in (drop h TMP_326 c1 TMP_328))))) in
495 (let TMP_335 \def (\lambda (c1: C).(let TMP_330 \def (Bind Void) in (let
496 TMP_331 \def (Bind Void) in (let TMP_332 \def (r TMP_331 n) in (let TMP_333
497 \def (lift h TMP_332 x1) in (let TMP_334 \def (CHead c TMP_330 TMP_333) in
498 (csubc g TMP_334 c1))))))) in (let TMP_336 \def (Bind x2) in (let TMP_337
499 \def (lift h n x4) in (let TMP_338 \def (CHead x TMP_336 TMP_337) in (let
500 TMP_339 \def (drop_skip_bind h n x x3 H18 x2 x4) in (let TMP_340 \def (Bind
501 Void) in (let TMP_341 \def (r TMP_340 n) in (let TMP_342 \def (lift h TMP_341
502 x1) in (let TMP_343 \def (lift h n x4) in (let TMP_344 \def (csubc_void g c x
503 H19 x2 H13 TMP_342 TMP_343) in (ex_intro2 C TMP_329 TMP_335 TMP_338 TMP_339
504 TMP_344))))))))))))))) in (let TMP_346 \def (ex2_ind C TMP_313 TMP_314
505 TMP_325 TMP_345 H17) in (let TMP_347 \def (eq_ind_r K TMP_301 TMP_310 TMP_346
506 k H12) in (eq_ind_r C TMP_283 TMP_290 TMP_347 e1
507 H11))))))))))))))))))))))))))))))) in (ex4_3_ind B C T TMP_269 TMP_271
508 TMP_273 TMP_274 TMP_281 TMP_348 H10)))))))))) in (let TMP_350 \def (or3_ind
509 TMP_103 TMP_113 TMP_122 TMP_129 TMP_177 TMP_266 TMP_349 H9) in (eq_ind_r T
510 TMP_94 TMP_99 TMP_350 t H4)))))))))))))))))))))))))))))))))))))))))) in (let
511 TMP_352 \def (drop_gen_skip_l c e2 t h n k H1) in (ex3_2_ind C T TMP_69
512 TMP_72 TMP_74 TMP_79 TMP_351 TMP_352))))))))))))))) in (nat_ind TMP_34 TMP_67
513 TMP_353 d)))))))))) in (C_ind TMP_3 TMP_30 TMP_354 c2))))).
515 theorem csubc_drop_conf_rev:
516 \forall (g: G).(\forall (c2: C).(\forall (e2: C).(\forall (d: nat).(\forall
517 (h: nat).((drop h d c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C
518 (\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c1 c2))))))))))
520 \lambda (g: G).(\lambda (c2: C).(let TMP_3 \def (\lambda (c: C).(\forall
521 (e2: C).(\forall (d: nat).(\forall (h: nat).((drop h d c e2) \to (\forall
522 (e1: C).((csubc g e1 e2) \to (let TMP_1 \def (\lambda (c1: C).(drop h d c1
523 e1)) in (let TMP_2 \def (\lambda (c1: C).(csubc g c1 c)) in (ex2 C TMP_1
524 TMP_2)))))))))) in (let TMP_30 \def (\lambda (n: nat).(\lambda (e2:
525 C).(\lambda (d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n)
526 e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e1 e2)).(let TMP_4 \def (CSort
527 n) in (let TMP_5 \def (eq C e2 TMP_4) in (let TMP_6 \def (eq nat h O) in (let
528 TMP_7 \def (eq nat d O) in (let TMP_8 \def (\lambda (c1: C).(drop h d c1 e1))
529 in (let TMP_10 \def (\lambda (c1: C).(let TMP_9 \def (CSort n) in (csubc g c1
530 TMP_9))) in (let TMP_11 \def (ex2 C TMP_8 TMP_10) in (let TMP_28 \def
531 (\lambda (H1: (eq C e2 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (H3:
532 (eq nat d O)).(let TMP_15 \def (\lambda (n0: nat).(let TMP_12 \def (\lambda
533 (c1: C).(drop n0 d c1 e1)) in (let TMP_14 \def (\lambda (c1: C).(let TMP_13
534 \def (CSort n) in (csubc g c1 TMP_13))) in (ex2 C TMP_12 TMP_14)))) in (let
535 TMP_19 \def (\lambda (n0: nat).(let TMP_16 \def (\lambda (c1: C).(drop O n0
536 c1 e1)) in (let TMP_18 \def (\lambda (c1: C).(let TMP_17 \def (CSort n) in
537 (csubc g c1 TMP_17))) in (ex2 C TMP_16 TMP_18)))) in (let TMP_20 \def
538 (\lambda (c: C).(csubc g e1 c)) in (let TMP_21 \def (CSort n) in (let H4 \def
539 (eq_ind C e2 TMP_20 H0 TMP_21 H1) in (let TMP_22 \def (\lambda (c1: C).(drop
540 O O c1 e1)) in (let TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (CSort n)
541 in (csubc g c1 TMP_23))) in (let TMP_25 \def (drop_refl e1) in (let TMP_26
542 \def (ex_intro2 C TMP_22 TMP_24 e1 TMP_25 H4) in (let TMP_27 \def (eq_ind_r
543 nat O TMP_19 TMP_26 d H3) in (eq_ind_r nat O TMP_15 TMP_27 h H2))))))))))))))
544 in (let TMP_29 \def (drop_gen_sort n h d e2 H) in (and3_ind TMP_5 TMP_6 TMP_7
545 TMP_11 TMP_28 TMP_29))))))))))))))))) in (let TMP_354 \def (\lambda (c:
546 C).(\lambda (H: ((\forall (e2: C).(\forall (d: nat).(\forall (h: nat).((drop
547 h d c e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda (c1:
548 C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c1 c))))))))))).(\lambda (k:
549 K).(\lambda (t: T).(\lambda (e2: C).(\lambda (d: nat).(let TMP_34 \def
550 (\lambda (n: nat).(\forall (h: nat).((drop h n (CHead c k t) e2) \to (\forall
551 (e1: C).((csubc g e1 e2) \to (let TMP_31 \def (\lambda (c1: C).(drop h n c1
552 e1)) in (let TMP_33 \def (\lambda (c1: C).(let TMP_32 \def (CHead c k t) in
553 (csubc g c1 TMP_32))) in (ex2 C TMP_31 TMP_33)))))))) in (let TMP_67 \def
554 (\lambda (h: nat).(let TMP_38 \def (\lambda (n: nat).((drop n O (CHead c k t)
555 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (let TMP_35 \def (\lambda (c1:
556 C).(drop n O c1 e1)) in (let TMP_37 \def (\lambda (c1: C).(let TMP_36 \def
557 (CHead c k t) in (csubc g c1 TMP_36))) in (ex2 C TMP_35 TMP_37))))))) in (let
558 TMP_47 \def (\lambda (H0: (drop O O (CHead c k t) e2)).(\lambda (e1:
559 C).(\lambda (H1: (csubc g e1 e2)).(let TMP_39 \def (\lambda (c0: C).(csubc g
560 e1 c0)) in (let TMP_40 \def (CHead c k t) in (let TMP_41 \def (CHead c k t)
561 in (let TMP_42 \def (drop_gen_refl TMP_41 e2 H0) in (let H2 \def (eq_ind_r C
562 e2 TMP_39 H1 TMP_40 TMP_42) in (let TMP_43 \def (\lambda (c1: C).(drop O O c1
563 e1)) in (let TMP_45 \def (\lambda (c1: C).(let TMP_44 \def (CHead c k t) in
564 (csubc g c1 TMP_44))) in (let TMP_46 \def (drop_refl e1) in (ex_intro2 C
565 TMP_43 TMP_45 e1 TMP_46 H2)))))))))))) in (let TMP_66 \def (\lambda (n:
566 nat).(\lambda (_: (((drop n O (CHead c k t) e2) \to (\forall (e1: C).((csubc
567 g e1 e2) \to (ex2 C (\lambda (c1: C).(drop n O c1 e1)) (\lambda (c1:
568 C).(csubc g c1 (CHead c k t))))))))).(\lambda (H1: (drop (S n) O (CHead c k
569 t) e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e1 e2)).(let TMP_48 \def (r k
570 n) in (let TMP_49 \def (drop_gen_drop k c e2 t n H1) in (let H_x \def (H e2 O
571 TMP_48 TMP_49 e1 H2) in (let H3 \def H_x in (let TMP_51 \def (\lambda (c1:
572 C).(let TMP_50 \def (r k n) in (drop TMP_50 O c1 e1))) in (let TMP_52 \def
573 (\lambda (c1: C).(csubc g c1 c)) in (let TMP_54 \def (\lambda (c1: C).(let
574 TMP_53 \def (S n) in (drop TMP_53 O c1 e1))) in (let TMP_56 \def (\lambda
575 (c1: C).(let TMP_55 \def (CHead c k t) in (csubc g c1 TMP_55))) in (let
576 TMP_57 \def (ex2 C TMP_54 TMP_56) in (let TMP_65 \def (\lambda (x:
577 C).(\lambda (H4: (drop (r k n) O x e1)).(\lambda (H5: (csubc g x c)).(let
578 TMP_59 \def (\lambda (c1: C).(let TMP_58 \def (S n) in (drop TMP_58 O c1
579 e1))) in (let TMP_61 \def (\lambda (c1: C).(let TMP_60 \def (CHead c k t) in
580 (csubc g c1 TMP_60))) in (let TMP_62 \def (CHead x k t) in (let TMP_63 \def
581 (drop_drop k n x e1 H4 t) in (let TMP_64 \def (csubc_head g x c H5 k t) in
582 (ex_intro2 C TMP_59 TMP_61 TMP_62 TMP_63 TMP_64))))))))) in (ex2_ind C TMP_51
583 TMP_52 TMP_57 TMP_65 H3)))))))))))))))) in (nat_ind TMP_38 TMP_47 TMP_66
584 h))))) in (let TMP_353 \def (\lambda (n: nat).(\lambda (H0: ((\forall (h:
585 nat).((drop h n (CHead c k t) e2) \to (\forall (e1: C).((csubc g e1 e2) \to
586 (ex2 C (\lambda (c1: C).(drop h n c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead
587 c k t)))))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c k t)
588 e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e1 e2)).(let TMP_69 \def
589 (\lambda (e: C).(\lambda (v: T).(let TMP_68 \def (CHead e k v) in (eq C e2
590 TMP_68)))) in (let TMP_72 \def (\lambda (_: C).(\lambda (v: T).(let TMP_70
591 \def (r k n) in (let TMP_71 \def (lift h TMP_70 v) in (eq T t TMP_71))))) in
592 (let TMP_74 \def (\lambda (e: C).(\lambda (_: T).(let TMP_73 \def (r k n) in
593 (drop h TMP_73 c e)))) in (let TMP_76 \def (\lambda (c1: C).(let TMP_75 \def
594 (S n) in (drop h TMP_75 c1 e1))) in (let TMP_78 \def (\lambda (c1: C).(let
595 TMP_77 \def (CHead c k t) in (csubc g c1 TMP_77))) in (let TMP_79 \def (ex2 C
596 TMP_76 TMP_78) in (let TMP_351 \def (\lambda (x0: C).(\lambda (x1:
597 T).(\lambda (H3: (eq C e2 (CHead x0 k x1))).(\lambda (H4: (eq T t (lift h (r
598 k n) x1))).(\lambda (H5: (drop h (r k n) c x0)).(let TMP_80 \def (\lambda
599 (c0: C).(csubc g e1 c0)) in (let TMP_81 \def (CHead x0 k x1) in (let H6 \def
600 (eq_ind C e2 TMP_80 H2 TMP_81 H3) in (let TMP_85 \def (\lambda (c0:
601 C).(\forall (h0: nat).((drop h0 n (CHead c k t) c0) \to (\forall (e3:
602 C).((csubc g e3 c0) \to (let TMP_82 \def (\lambda (c1: C).(drop h0 n c1 e3))
603 in (let TMP_84 \def (\lambda (c1: C).(let TMP_83 \def (CHead c k t) in (csubc
604 g c1 TMP_83))) in (ex2 C TMP_82 TMP_84)))))))) in (let TMP_86 \def (CHead x0
605 k x1) in (let H7 \def (eq_ind C e2 TMP_85 H0 TMP_86 H3) in (let TMP_90 \def
606 (\lambda (t0: T).(\forall (h0: nat).((drop h0 n (CHead c k t0) (CHead x0 k
607 x1)) \to (\forall (e3: C).((csubc g e3 (CHead x0 k x1)) \to (let TMP_87 \def
608 (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_89 \def (\lambda (c1: C).(let
609 TMP_88 \def (CHead c k t0) in (csubc g c1 TMP_88))) in (ex2 C TMP_87
610 TMP_89)))))))) in (let TMP_91 \def (r k n) in (let TMP_92 \def (lift h TMP_91
611 x1) in (let H8 \def (eq_ind T t TMP_90 H7 TMP_92 H4) in (let TMP_93 \def (r k
612 n) in (let TMP_94 \def (lift h TMP_93 x1) in (let TMP_99 \def (\lambda (t0:
613 T).(let TMP_96 \def (\lambda (c1: C).(let TMP_95 \def (S n) in (drop h TMP_95
614 c1 e1))) in (let TMP_98 \def (\lambda (c1: C).(let TMP_97 \def (CHead c k t0)
615 in (csubc g c1 TMP_97))) in (ex2 C TMP_96 TMP_98)))) in (let H_x \def
616 (csubc_gen_head_r g x0 e1 x1 k H6) in (let H9 \def H_x in (let TMP_101 \def
617 (\lambda (c1: C).(let TMP_100 \def (CHead c1 k x1) in (eq C e1 TMP_100))) in
618 (let TMP_102 \def (\lambda (c1: C).(csubc g c1 x0)) in (let TMP_103 \def (ex2
619 C TMP_101 TMP_102) in (let TMP_105 \def (\lambda (_: C).(\lambda (_:
620 T).(\lambda (_: A).(let TMP_104 \def (Bind Abbr) in (eq K k TMP_104))))) in
621 (let TMP_108 \def (\lambda (c1: C).(\lambda (v: T).(\lambda (_: A).(let
622 TMP_106 \def (Bind Abst) in (let TMP_107 \def (CHead c1 TMP_106 v) in (eq C
623 e1 TMP_107)))))) in (let TMP_109 \def (\lambda (c1: C).(\lambda (_:
624 T).(\lambda (_: A).(csubc g c1 x0)))) in (let TMP_111 \def (\lambda (c1:
625 C).(\lambda (v: T).(\lambda (a: A).(let TMP_110 \def (asucc g a) in (sc3 g
626 TMP_110 c1 v))))) in (let TMP_112 \def (\lambda (_: C).(\lambda (_:
627 T).(\lambda (a: A).(sc3 g a x0 x1)))) in (let TMP_113 \def (ex5_3 C T A
628 TMP_105 TMP_108 TMP_109 TMP_111 TMP_112) in (let TMP_116 \def (\lambda (_:
629 B).(\lambda (c1: C).(\lambda (v1: T).(let TMP_114 \def (Bind Void) in (let
630 TMP_115 \def (CHead c1 TMP_114 v1) in (eq C e1 TMP_115)))))) in (let TMP_118
631 \def (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(let TMP_117 \def (Bind
632 b) in (eq K k TMP_117))))) in (let TMP_120 \def (\lambda (b: B).(\lambda (_:
633 C).(\lambda (_: T).(let TMP_119 \def (eq B b Void) in (not TMP_119))))) in
634 (let TMP_121 \def (\lambda (_: B).(\lambda (c1: C).(\lambda (_: T).(csubc g
635 c1 x0)))) in (let TMP_122 \def (ex4_3 B C T TMP_116 TMP_118 TMP_120 TMP_121)
636 in (let TMP_124 \def (\lambda (c1: C).(let TMP_123 \def (S n) in (drop h
637 TMP_123 c1 e1))) in (let TMP_128 \def (\lambda (c1: C).(let TMP_125 \def (r k
638 n) in (let TMP_126 \def (lift h TMP_125 x1) in (let TMP_127 \def (CHead c k
639 TMP_126) in (csubc g c1 TMP_127))))) in (let TMP_129 \def (ex2 C TMP_124
640 TMP_128) in (let TMP_177 \def (\lambda (H10: (ex2 C (\lambda (c1: C).(eq C e1
641 (CHead c1 k x1))) (\lambda (c1: C).(csubc g c1 x0)))).(let TMP_131 \def
642 (\lambda (c1: C).(let TMP_130 \def (CHead c1 k x1) in (eq C e1 TMP_130))) in
643 (let TMP_132 \def (\lambda (c1: C).(csubc g c1 x0)) in (let TMP_134 \def
644 (\lambda (c1: C).(let TMP_133 \def (S n) in (drop h TMP_133 c1 e1))) in (let
645 TMP_138 \def (\lambda (c1: C).(let TMP_135 \def (r k n) in (let TMP_136 \def
646 (lift h TMP_135 x1) in (let TMP_137 \def (CHead c k TMP_136) in (csubc g c1
647 TMP_137))))) in (let TMP_139 \def (ex2 C TMP_134 TMP_138) in (let TMP_176
648 \def (\lambda (x: C).(\lambda (H11: (eq C e1 (CHead x k x1))).(\lambda (H12:
649 (csubc g x x0)).(let TMP_140 \def (CHead x k x1) in (let TMP_147 \def
650 (\lambda (c0: C).(let TMP_142 \def (\lambda (c1: C).(let TMP_141 \def (S n)
651 in (drop h TMP_141 c1 c0))) in (let TMP_146 \def (\lambda (c1: C).(let
652 TMP_143 \def (r k n) in (let TMP_144 \def (lift h TMP_143 x1) in (let TMP_145
653 \def (CHead c k TMP_144) in (csubc g c1 TMP_145))))) in (ex2 C TMP_142
654 TMP_146)))) in (let TMP_148 \def (r k n) in (let H_x0 \def (H x0 TMP_148 h H5
655 x H12) in (let H13 \def H_x0 in (let TMP_150 \def (\lambda (c1: C).(let
656 TMP_149 \def (r k n) in (drop h TMP_149 c1 x))) in (let TMP_151 \def (\lambda
657 (c1: C).(csubc g c1 c)) in (let TMP_154 \def (\lambda (c1: C).(let TMP_152
658 \def (S n) in (let TMP_153 \def (CHead x k x1) in (drop h TMP_152 c1
659 TMP_153)))) in (let TMP_158 \def (\lambda (c1: C).(let TMP_155 \def (r k n)
660 in (let TMP_156 \def (lift h TMP_155 x1) in (let TMP_157 \def (CHead c k
661 TMP_156) in (csubc g c1 TMP_157))))) in (let TMP_159 \def (ex2 C TMP_154
662 TMP_158) in (let TMP_174 \def (\lambda (x2: C).(\lambda (H14: (drop h (r k n)
663 x2 x)).(\lambda (H15: (csubc g x2 c)).(let TMP_162 \def (\lambda (c1: C).(let
664 TMP_160 \def (S n) in (let TMP_161 \def (CHead x k x1) in (drop h TMP_160 c1
665 TMP_161)))) in (let TMP_166 \def (\lambda (c1: C).(let TMP_163 \def (r k n)
666 in (let TMP_164 \def (lift h TMP_163 x1) in (let TMP_165 \def (CHead c k
667 TMP_164) in (csubc g c1 TMP_165))))) in (let TMP_167 \def (r k n) in (let
668 TMP_168 \def (lift h TMP_167 x1) in (let TMP_169 \def (CHead x2 k TMP_168) in
669 (let TMP_170 \def (drop_skip k h n x2 x H14 x1) in (let TMP_171 \def (r k n)
670 in (let TMP_172 \def (lift h TMP_171 x1) in (let TMP_173 \def (csubc_head g
671 x2 c H15 k TMP_172) in (ex_intro2 C TMP_162 TMP_166 TMP_169 TMP_170
672 TMP_173))))))))))))) in (let TMP_175 \def (ex2_ind C TMP_150 TMP_151 TMP_159
673 TMP_174 H13) in (eq_ind_r C TMP_140 TMP_147 TMP_175 e1 H11)))))))))))))))) in
674 (ex2_ind C TMP_131 TMP_132 TMP_139 TMP_176 H10)))))))) in (let TMP_266 \def
675 (\lambda (H10: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_:
676 A).(eq K k (Bind Abbr))))) (\lambda (c1: C).(\lambda (v: T).(\lambda (_:
677 A).(eq C e1 (CHead c1 (Bind Abst) v))))) (\lambda (c1: C).(\lambda (_:
678 T).(\lambda (_: A).(csubc g c1 x0)))) (\lambda (c1: C).(\lambda (v:
679 T).(\lambda (a: A).(sc3 g (asucc g a) c1 v)))) (\lambda (_: C).(\lambda (_:
680 T).(\lambda (a: A).(sc3 g a x0 x1)))))).(let TMP_179 \def (\lambda (_:
681 C).(\lambda (_: T).(\lambda (_: A).(let TMP_178 \def (Bind Abbr) in (eq K k
682 TMP_178))))) in (let TMP_182 \def (\lambda (c1: C).(\lambda (v: T).(\lambda
683 (_: A).(let TMP_180 \def (Bind Abst) in (let TMP_181 \def (CHead c1 TMP_180
684 v) in (eq C e1 TMP_181)))))) in (let TMP_183 \def (\lambda (c1: C).(\lambda
685 (_: T).(\lambda (_: A).(csubc g c1 x0)))) in (let TMP_185 \def (\lambda (c1:
686 C).(\lambda (v: T).(\lambda (a: A).(let TMP_184 \def (asucc g a) in (sc3 g
687 TMP_184 c1 v))))) in (let TMP_186 \def (\lambda (_: C).(\lambda (_:
688 T).(\lambda (a: A).(sc3 g a x0 x1)))) in (let TMP_188 \def (\lambda (c1:
689 C).(let TMP_187 \def (S n) in (drop h TMP_187 c1 e1))) in (let TMP_192 \def
690 (\lambda (c1: C).(let TMP_189 \def (r k n) in (let TMP_190 \def (lift h
691 TMP_189 x1) in (let TMP_191 \def (CHead c k TMP_190) in (csubc g c1
692 TMP_191))))) in (let TMP_193 \def (ex2 C TMP_188 TMP_192) in (let TMP_265
693 \def (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H11: (eq K
694 k (Bind Abbr))).(\lambda (H12: (eq C e1 (CHead x2 (Bind Abst) x3))).(\lambda
695 (H13: (csubc g x2 x0)).(\lambda (H14: (sc3 g (asucc g x4) x2 x3)).(\lambda
696 (H15: (sc3 g x4 x0 x1)).(let TMP_194 \def (Bind Abst) in (let TMP_195 \def
697 (CHead x2 TMP_194 x3) in (let TMP_202 \def (\lambda (c0: C).(let TMP_197 \def
698 (\lambda (c1: C).(let TMP_196 \def (S n) in (drop h TMP_196 c1 c0))) in (let
699 TMP_201 \def (\lambda (c1: C).(let TMP_198 \def (r k n) in (let TMP_199 \def
700 (lift h TMP_198 x1) in (let TMP_200 \def (CHead c k TMP_199) in (csubc g c1
701 TMP_200))))) in (ex2 C TMP_197 TMP_201)))) in (let TMP_208 \def (\lambda (k0:
702 K).(\forall (h0: nat).((drop h0 n (CHead c k0 (lift h (r k0 n) x1)) (CHead x0
703 k0 x1)) \to (\forall (e3: C).((csubc g e3 (CHead x0 k0 x1)) \to (let TMP_203
704 \def (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_207 \def (\lambda (c1:
705 C).(let TMP_204 \def (r k0 n) in (let TMP_205 \def (lift h TMP_204 x1) in
706 (let TMP_206 \def (CHead c k0 TMP_205) in (csubc g c1 TMP_206))))) in (ex2 C
707 TMP_203 TMP_207)))))))) in (let TMP_209 \def (Bind Abbr) in (let H16 \def
708 (eq_ind K k TMP_208 H8 TMP_209 H11) in (let TMP_211 \def (\lambda (k0:
709 K).(let TMP_210 \def (r k0 n) in (drop h TMP_210 c x0))) in (let TMP_212 \def
710 (Bind Abbr) in (let H17 \def (eq_ind K k TMP_211 H5 TMP_212 H11) in (let
711 TMP_213 \def (Bind Abbr) in (let TMP_222 \def (\lambda (k0: K).(let TMP_217
712 \def (\lambda (c1: C).(let TMP_214 \def (S n) in (let TMP_215 \def (Bind
713 Abst) in (let TMP_216 \def (CHead x2 TMP_215 x3) in (drop h TMP_214 c1
714 TMP_216))))) in (let TMP_221 \def (\lambda (c1: C).(let TMP_218 \def (r k0 n)
715 in (let TMP_219 \def (lift h TMP_218 x1) in (let TMP_220 \def (CHead c k0
716 TMP_219) in (csubc g c1 TMP_220))))) in (ex2 C TMP_217 TMP_221)))) in (let
717 TMP_223 \def (Bind Abbr) in (let TMP_224 \def (r TMP_223 n) in (let H_x0 \def
718 (H x0 TMP_224 h H17 x2 H13) in (let H18 \def H_x0 in (let TMP_225 \def
719 (\lambda (c1: C).(drop h n c1 x2)) in (let TMP_226 \def (\lambda (c1:
720 C).(csubc g c1 c)) in (let TMP_230 \def (\lambda (c1: C).(let TMP_227 \def (S
721 n) in (let TMP_228 \def (Bind Abst) in (let TMP_229 \def (CHead x2 TMP_228
722 x3) in (drop h TMP_227 c1 TMP_229))))) in (let TMP_236 \def (\lambda (c1:
723 C).(let TMP_231 \def (Bind Abbr) in (let TMP_232 \def (Bind Abbr) in (let
724 TMP_233 \def (r TMP_232 n) in (let TMP_234 \def (lift h TMP_233 x1) in (let
725 TMP_235 \def (CHead c TMP_231 TMP_234) in (csubc g c1 TMP_235))))))) in (let
726 TMP_237 \def (ex2 C TMP_230 TMP_236) in (let TMP_262 \def (\lambda (x:
727 C).(\lambda (H19: (drop h n x x2)).(\lambda (H20: (csubc g x c)).(let TMP_241
728 \def (\lambda (c1: C).(let TMP_238 \def (S n) in (let TMP_239 \def (Bind
729 Abst) in (let TMP_240 \def (CHead x2 TMP_239 x3) in (drop h TMP_238 c1
730 TMP_240))))) in (let TMP_247 \def (\lambda (c1: C).(let TMP_242 \def (Bind
731 Abbr) in (let TMP_243 \def (Bind Abbr) in (let TMP_244 \def (r TMP_243 n) in
732 (let TMP_245 \def (lift h TMP_244 x1) in (let TMP_246 \def (CHead c TMP_242
733 TMP_245) in (csubc g c1 TMP_246))))))) in (let TMP_248 \def (Bind Abst) in
734 (let TMP_249 \def (lift h n x3) in (let TMP_250 \def (CHead x TMP_248
735 TMP_249) in (let TMP_251 \def (drop_skip_bind h n x x2 H19 Abst x3) in (let
736 TMP_252 \def (lift h n x3) in (let TMP_253 \def (asucc g x4) in (let TMP_254
737 \def (sc3_lift g TMP_253 x2 x3 H14 x h n H19) in (let TMP_255 \def (Bind
738 Abbr) in (let TMP_256 \def (r TMP_255 n) in (let TMP_257 \def (lift h TMP_256
739 x1) in (let TMP_258 \def (Bind Abbr) in (let TMP_259 \def (r TMP_258 n) in
740 (let TMP_260 \def (sc3_lift g x4 x0 x1 H15 c h TMP_259 H17) in (let TMP_261
741 \def (csubc_abst g x c H20 TMP_252 x4 TMP_254 TMP_257 TMP_260) in (ex_intro2
742 C TMP_241 TMP_247 TMP_250 TMP_251 TMP_261)))))))))))))))))))) in (let TMP_263
743 \def (ex2_ind C TMP_225 TMP_226 TMP_237 TMP_262 H18) in (let TMP_264 \def
744 (eq_ind_r K TMP_213 TMP_222 TMP_263 k H11) in (eq_ind_r C TMP_195 TMP_202
745 TMP_264 e1 H12)))))))))))))))))))))))))))))))) in (ex5_3_ind C T A TMP_179
746 TMP_182 TMP_183 TMP_185 TMP_186 TMP_193 TMP_265 H10))))))))))) in (let
747 TMP_349 \def (\lambda (H10: (ex4_3 B C T (\lambda (_: B).(\lambda (c1:
748 C).(\lambda (v1: T).(eq C e1 (CHead c1 (Bind Void) v1))))) (\lambda (b:
749 B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind b))))) (\lambda (b:
750 B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
751 B).(\lambda (c1: C).(\lambda (_: T).(csubc g c1 x0)))))).(let TMP_269 \def
752 (\lambda (_: B).(\lambda (c1: C).(\lambda (v1: T).(let TMP_267 \def (Bind
753 Void) in (let TMP_268 \def (CHead c1 TMP_267 v1) in (eq C e1 TMP_268)))))) in
754 (let TMP_271 \def (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(let
755 TMP_270 \def (Bind b) in (eq K k TMP_270))))) in (let TMP_273 \def (\lambda
756 (b: B).(\lambda (_: C).(\lambda (_: T).(let TMP_272 \def (eq B b Void) in
757 (not TMP_272))))) in (let TMP_274 \def (\lambda (_: B).(\lambda (c1:
758 C).(\lambda (_: T).(csubc g c1 x0)))) in (let TMP_276 \def (\lambda (c1:
759 C).(let TMP_275 \def (S n) in (drop h TMP_275 c1 e1))) in (let TMP_280 \def
760 (\lambda (c1: C).(let TMP_277 \def (r k n) in (let TMP_278 \def (lift h
761 TMP_277 x1) in (let TMP_279 \def (CHead c k TMP_278) in (csubc g c1
762 TMP_279))))) in (let TMP_281 \def (ex2 C TMP_276 TMP_280) in (let TMP_348
763 \def (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H11: (eq C
764 e1 (CHead x3 (Bind Void) x4))).(\lambda (H12: (eq K k (Bind x2))).(\lambda
765 (H13: (not (eq B x2 Void))).(\lambda (H14: (csubc g x3 x0)).(let TMP_282 \def
766 (Bind Void) in (let TMP_283 \def (CHead x3 TMP_282 x4) in (let TMP_290 \def
767 (\lambda (c0: C).(let TMP_285 \def (\lambda (c1: C).(let TMP_284 \def (S n)
768 in (drop h TMP_284 c1 c0))) in (let TMP_289 \def (\lambda (c1: C).(let
769 TMP_286 \def (r k n) in (let TMP_287 \def (lift h TMP_286 x1) in (let TMP_288
770 \def (CHead c k TMP_287) in (csubc g c1 TMP_288))))) in (ex2 C TMP_285
771 TMP_289)))) in (let TMP_296 \def (\lambda (k0: K).(\forall (h0: nat).((drop
772 h0 n (CHead c k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to (\forall (e3:
773 C).((csubc g e3 (CHead x0 k0 x1)) \to (let TMP_291 \def (\lambda (c1:
774 C).(drop h0 n c1 e3)) in (let TMP_295 \def (\lambda (c1: C).(let TMP_292 \def
775 (r k0 n) in (let TMP_293 \def (lift h TMP_292 x1) in (let TMP_294 \def (CHead
776 c k0 TMP_293) in (csubc g c1 TMP_294))))) in (ex2 C TMP_291 TMP_295))))))))
777 in (let TMP_297 \def (Bind x2) in (let H15 \def (eq_ind K k TMP_296 H8
778 TMP_297 H12) in (let TMP_299 \def (\lambda (k0: K).(let TMP_298 \def (r k0 n)
779 in (drop h TMP_298 c x0))) in (let TMP_300 \def (Bind x2) in (let H16 \def
780 (eq_ind K k TMP_299 H5 TMP_300 H12) in (let TMP_301 \def (Bind x2) in (let
781 TMP_310 \def (\lambda (k0: K).(let TMP_305 \def (\lambda (c1: C).(let TMP_302
782 \def (S n) in (let TMP_303 \def (Bind Void) in (let TMP_304 \def (CHead x3
783 TMP_303 x4) in (drop h TMP_302 c1 TMP_304))))) in (let TMP_309 \def (\lambda
784 (c1: C).(let TMP_306 \def (r k0 n) in (let TMP_307 \def (lift h TMP_306 x1)
785 in (let TMP_308 \def (CHead c k0 TMP_307) in (csubc g c1 TMP_308))))) in (ex2
786 C TMP_305 TMP_309)))) in (let TMP_311 \def (Bind x2) in (let TMP_312 \def (r
787 TMP_311 n) in (let H_x0 \def (H x0 TMP_312 h H16 x3 H14) in (let H17 \def
788 H_x0 in (let TMP_313 \def (\lambda (c1: C).(drop h n c1 x3)) in (let TMP_314
789 \def (\lambda (c1: C).(csubc g c1 c)) in (let TMP_318 \def (\lambda (c1:
790 C).(let TMP_315 \def (S n) in (let TMP_316 \def (Bind Void) in (let TMP_317
791 \def (CHead x3 TMP_316 x4) in (drop h TMP_315 c1 TMP_317))))) in (let TMP_324
792 \def (\lambda (c1: C).(let TMP_319 \def (Bind x2) in (let TMP_320 \def (Bind
793 x2) in (let TMP_321 \def (r TMP_320 n) in (let TMP_322 \def (lift h TMP_321
794 x1) in (let TMP_323 \def (CHead c TMP_319 TMP_322) in (csubc g c1
795 TMP_323))))))) in (let TMP_325 \def (ex2 C TMP_318 TMP_324) in (let TMP_345
796 \def (\lambda (x: C).(\lambda (H18: (drop h n x x3)).(\lambda (H19: (csubc g
797 x c)).(let TMP_329 \def (\lambda (c1: C).(let TMP_326 \def (S n) in (let
798 TMP_327 \def (Bind Void) in (let TMP_328 \def (CHead x3 TMP_327 x4) in (drop
799 h TMP_326 c1 TMP_328))))) in (let TMP_335 \def (\lambda (c1: C).(let TMP_330
800 \def (Bind x2) in (let TMP_331 \def (Bind x2) in (let TMP_332 \def (r TMP_331
801 n) in (let TMP_333 \def (lift h TMP_332 x1) in (let TMP_334 \def (CHead c
802 TMP_330 TMP_333) in (csubc g c1 TMP_334))))))) in (let TMP_336 \def (Bind
803 Void) in (let TMP_337 \def (lift h n x4) in (let TMP_338 \def (CHead x
804 TMP_336 TMP_337) in (let TMP_339 \def (drop_skip_bind h n x x3 H18 Void x4)
805 in (let TMP_340 \def (lift h n x4) in (let TMP_341 \def (Bind x2) in (let
806 TMP_342 \def (r TMP_341 n) in (let TMP_343 \def (lift h TMP_342 x1) in (let
807 TMP_344 \def (csubc_void g x c H19 x2 H13 TMP_340 TMP_343) in (ex_intro2 C
808 TMP_329 TMP_335 TMP_338 TMP_339 TMP_344))))))))))))))) in (let TMP_346 \def
809 (ex2_ind C TMP_313 TMP_314 TMP_325 TMP_345 H17) in (let TMP_347 \def
810 (eq_ind_r K TMP_301 TMP_310 TMP_346 k H12) in (eq_ind_r C TMP_283 TMP_290
811 TMP_347 e1 H11))))))))))))))))))))))))))))))) in (ex4_3_ind B C T TMP_269
812 TMP_271 TMP_273 TMP_274 TMP_281 TMP_348 H10)))))))))) in (let TMP_350 \def
813 (or3_ind TMP_103 TMP_113 TMP_122 TMP_129 TMP_177 TMP_266 TMP_349 H9) in
814 (eq_ind_r T TMP_94 TMP_99 TMP_350 t
815 H4)))))))))))))))))))))))))))))))))))))))))) in (let TMP_352 \def
816 (drop_gen_skip_l c e2 t h n k H1) in (ex3_2_ind C T TMP_69 TMP_72 TMP_74
817 TMP_79 TMP_351 TMP_352))))))))))))))) in (nat_ind TMP_34 TMP_67 TMP_353
818 d)))))))))) in (C_ind TMP_3 TMP_30 TMP_354 c2))))).
projects / helm.git / blob