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/lift/props.ma".
19 theorem lift_gen_sort:
20 \forall (h: nat).(\forall (d: nat).(\forall (n: nat).(\forall (t: T).((eq T
21 (TSort n) (lift h d t)) \to (eq T t (TSort n))))))
23 \lambda (h: nat).(\lambda (d: nat).(\lambda (n: nat).(\lambda (t: T).(let
24 TMP_2 \def (\lambda (t0: T).((eq T (TSort n) (lift h d t0)) \to (let TMP_1
25 \def (TSort n) in (eq T t0 TMP_1)))) in (let TMP_5 \def (\lambda (n0:
26 nat).(\lambda (H: (eq T (TSort n) (lift h d (TSort n0)))).(let TMP_3 \def
27 (TSort n) in (let TMP_4 \def (TSort n0) in (sym_eq T TMP_3 TMP_4 H))))) in
28 (let TMP_49 \def (\lambda (n0: nat).(\lambda (H: (eq T (TSort n) (lift h d
29 (TLRef n0)))).(let TMP_6 \def (TLRef n0) in (let TMP_7 \def (TSort n) in (let
30 TMP_8 \def (eq T TMP_6 TMP_7) in (let TMP_27 \def (\lambda (_: (lt n0
31 d)).(let TMP_9 \def (TLRef n0) in (let TMP_10 \def (lift h d TMP_9) in (let
32 TMP_12 \def (\lambda (t0: T).(let TMP_11 \def (TSort n) in (eq T TMP_11 t0)))
33 in (let TMP_13 \def (TLRef n0) in (let TMP_14 \def (TSort n) in (let TMP_15
34 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _)
35 \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let TMP_16 \def
36 (TLRef n0) in (let TMP_17 \def (lift h d TMP_16) in (let H1 \def (eq_ind T
37 TMP_14 TMP_15 I TMP_17 H) in (let TMP_18 \def (lt n0 d) in (let TMP_19 \def
38 (False_ind TMP_18 H1) in (let TMP_20 \def (lift_lref_lt n0 h d TMP_19) in
39 (let H1 \def (eq_ind T TMP_10 TMP_12 H TMP_13 TMP_20) in (let TMP_21 \def
40 (TSort n) in (let TMP_22 \def (\lambda (ee: T).(match ee with [(TSort _)
41 \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
42 False])) in (let TMP_23 \def (TLRef n0) in (let H2 \def (eq_ind T TMP_21
43 TMP_22 I TMP_23 H1) in (let TMP_24 \def (TLRef n0) in (let TMP_25 \def (TSort
44 n) in (let TMP_26 \def (eq T TMP_24 TMP_25) in (False_ind TMP_26
45 H2)))))))))))))))))))))) in (let TMP_48 \def (\lambda (_: (le d n0)).(let
46 TMP_28 \def (TLRef n0) in (let TMP_29 \def (lift h d TMP_28) in (let TMP_31
47 \def (\lambda (t0: T).(let TMP_30 \def (TSort n) in (eq T TMP_30 t0))) in
48 (let TMP_32 \def (plus n0 h) in (let TMP_33 \def (TLRef TMP_32) in (let
49 TMP_34 \def (TSort n) in (let TMP_35 \def (\lambda (ee: T).(match ee with
50 [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _)
51 \Rightarrow False])) in (let TMP_36 \def (TLRef n0) in (let TMP_37 \def (lift
52 h d TMP_36) in (let H1 \def (eq_ind T TMP_34 TMP_35 I TMP_37 H) in (let
53 TMP_38 \def (le d n0) in (let TMP_39 \def (False_ind TMP_38 H1) in (let
54 TMP_40 \def (lift_lref_ge n0 h d TMP_39) in (let H1 \def (eq_ind T TMP_29
55 TMP_31 H TMP_33 TMP_40) in (let TMP_41 \def (TSort n) in (let TMP_42 \def
56 (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _)
57 \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let TMP_43 \def
58 (plus n0 h) in (let TMP_44 \def (TLRef TMP_43) in (let H2 \def (eq_ind T
59 TMP_41 TMP_42 I TMP_44 H1) in (let TMP_45 \def (TLRef n0) in (let TMP_46 \def
60 (TSort n) in (let TMP_47 \def (eq T TMP_45 TMP_46) in (False_ind TMP_47
61 H2)))))))))))))))))))))))) in (lt_le_e n0 d TMP_8 TMP_27 TMP_48)))))))) in
62 (let TMP_68 \def (\lambda (k: K).(\lambda (t0: T).(\lambda (_: (((eq T (TSort
63 n) (lift h d t0)) \to (eq T t0 (TSort n))))).(\lambda (t1: T).(\lambda (_:
64 (((eq T (TSort n) (lift h d t1)) \to (eq T t1 (TSort n))))).(\lambda (H1: (eq
65 T (TSort n) (lift h d (THead k t0 t1)))).(let TMP_50 \def (THead k t0 t1) in
66 (let TMP_51 \def (lift h d TMP_50) in (let TMP_53 \def (\lambda (t2: T).(let
67 TMP_52 \def (TSort n) in (eq T TMP_52 t2))) in (let TMP_54 \def (lift h d t0)
68 in (let TMP_55 \def (s k d) in (let TMP_56 \def (lift h TMP_55 t1) in (let
69 TMP_57 \def (THead k TMP_54 TMP_56) in (let TMP_58 \def (lift_head k t0 t1 h
70 d) in (let H2 \def (eq_ind T TMP_51 TMP_53 H1 TMP_57 TMP_58) in (let TMP_59
71 \def (TSort n) in (let TMP_60 \def (\lambda (ee: T).(match ee with [(TSort _)
72 \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
73 False])) in (let TMP_61 \def (lift h d t0) in (let TMP_62 \def (s k d) in
74 (let TMP_63 \def (lift h TMP_62 t1) in (let TMP_64 \def (THead k TMP_61
75 TMP_63) in (let H3 \def (eq_ind T TMP_59 TMP_60 I TMP_64 H2) in (let TMP_65
76 \def (THead k t0 t1) in (let TMP_66 \def (TSort n) in (let TMP_67 \def (eq T
77 TMP_65 TMP_66) in (False_ind TMP_67 H3)))))))))))))))))))))))))) in (T_ind
78 TMP_2 TMP_5 TMP_49 TMP_68 t)))))))).
80 theorem lift_gen_lref:
81 \forall (t: T).(\forall (d: nat).(\forall (h: nat).(\forall (i: nat).((eq T
82 (TLRef i) (lift h d t)) \to (or (land (lt i d) (eq T t (TLRef i))) (land (le
83 (plus d h) i) (eq T t (TLRef (minus i h)))))))))
85 \lambda (t: T).(let TMP_11 \def (\lambda (t0: T).(\forall (d: nat).(\forall
86 (h: nat).(\forall (i: nat).((eq T (TLRef i) (lift h d t0)) \to (let TMP_1
87 \def (lt i d) in (let TMP_2 \def (TLRef i) in (let TMP_3 \def (eq T t0 TMP_2)
88 in (let TMP_4 \def (land TMP_1 TMP_3) in (let TMP_5 \def (plus d h) in (let
89 TMP_6 \def (le TMP_5 i) in (let TMP_7 \def (minus i h) in (let TMP_8 \def
90 (TLRef TMP_7) in (let TMP_9 \def (eq T t0 TMP_8) in (let TMP_10 \def (land
91 TMP_6 TMP_9) in (or TMP_4 TMP_10)))))))))))))))) in (let TMP_34 \def (\lambda
92 (n: nat).(\lambda (d: nat).(\lambda (h: nat).(\lambda (i: nat).(\lambda (H:
93 (eq T (TLRef i) (lift h d (TSort n)))).(let TMP_12 \def (TSort n) in (let
94 TMP_13 \def (lift h d TMP_12) in (let TMP_15 \def (\lambda (t0: T).(let
95 TMP_14 \def (TLRef i) in (eq T TMP_14 t0))) in (let TMP_16 \def (TSort n) in
96 (let TMP_17 \def (lift_sort n h d) in (let H0 \def (eq_ind T TMP_13 TMP_15 H
97 TMP_16 TMP_17) in (let TMP_18 \def (TLRef i) in (let TMP_19 \def (\lambda
98 (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow
99 True | (THead _ _ _) \Rightarrow False])) in (let TMP_20 \def (TSort n) in
100 (let H1 \def (eq_ind T TMP_18 TMP_19 I TMP_20 H0) in (let TMP_21 \def (lt i
101 d) in (let TMP_22 \def (TSort n) in (let TMP_23 \def (TLRef i) in (let TMP_24
102 \def (eq T TMP_22 TMP_23) in (let TMP_25 \def (land TMP_21 TMP_24) in (let
103 TMP_26 \def (plus d h) in (let TMP_27 \def (le TMP_26 i) in (let TMP_28 \def
104 (TSort n) in (let TMP_29 \def (minus i h) in (let TMP_30 \def (TLRef TMP_29)
105 in (let TMP_31 \def (eq T TMP_28 TMP_30) in (let TMP_32 \def (land TMP_27
106 TMP_31) in (let TMP_33 \def (or TMP_25 TMP_32) in (False_ind TMP_33
107 H1))))))))))))))))))))))))))))) in (let TMP_162 \def (\lambda (n:
108 nat).(\lambda (d: nat).(\lambda (h: nat).(\lambda (i: nat).(\lambda (H: (eq T
109 (TLRef i) (lift h d (TLRef n)))).(let TMP_35 \def (lt i d) in (let TMP_36
110 \def (TLRef n) in (let TMP_37 \def (TLRef i) in (let TMP_38 \def (eq T TMP_36
111 TMP_37) in (let TMP_39 \def (land TMP_35 TMP_38) in (let TMP_40 \def (plus d
112 h) in (let TMP_41 \def (le TMP_40 i) in (let TMP_42 \def (TLRef n) in (let
113 TMP_43 \def (minus i h) in (let TMP_44 \def (TLRef TMP_43) in (let TMP_45
114 \def (eq T TMP_42 TMP_44) in (let TMP_46 \def (land TMP_41 TMP_45) in (let
115 TMP_47 \def (or TMP_39 TMP_46) in (let TMP_90 \def (\lambda (H0: (lt n
116 d)).(let TMP_48 \def (TLRef n) in (let TMP_49 \def (lift h d TMP_48) in (let
117 TMP_51 \def (\lambda (t0: T).(let TMP_50 \def (TLRef i) in (eq T TMP_50 t0)))
118 in (let TMP_52 \def (TLRef n) in (let TMP_53 \def (lift_lref_lt n h d H0) in
119 (let H1 \def (eq_ind T TMP_49 TMP_51 H TMP_52 TMP_53) in (let TMP_54 \def
120 (\lambda (e: T).(match e with [(TSort _) \Rightarrow i | (TLRef n0)
121 \Rightarrow n0 | (THead _ _ _) \Rightarrow i])) in (let TMP_55 \def (TLRef i)
122 in (let TMP_56 \def (TLRef n) in (let H2 \def (f_equal T nat TMP_54 TMP_55
123 TMP_56 H1) in (let TMP_69 \def (\lambda (n0: nat).(let TMP_57 \def (lt n0 d)
124 in (let TMP_58 \def (TLRef n) in (let TMP_59 \def (TLRef n0) in (let TMP_60
125 \def (eq T TMP_58 TMP_59) in (let TMP_61 \def (land TMP_57 TMP_60) in (let
126 TMP_62 \def (plus d h) in (let TMP_63 \def (le TMP_62 n0) in (let TMP_64 \def
127 (TLRef n) in (let TMP_65 \def (minus n0 h) in (let TMP_66 \def (TLRef TMP_65)
128 in (let TMP_67 \def (eq T TMP_64 TMP_66) in (let TMP_68 \def (land TMP_63
129 TMP_67) in (or TMP_61 TMP_68)))))))))))))) in (let TMP_70 \def (lt n d) in
130 (let TMP_71 \def (TLRef n) in (let TMP_72 \def (TLRef n) in (let TMP_73 \def
131 (eq T TMP_71 TMP_72) in (let TMP_74 \def (land TMP_70 TMP_73) in (let TMP_75
132 \def (plus d h) in (let TMP_76 \def (le TMP_75 n) in (let TMP_77 \def (TLRef
133 n) in (let TMP_78 \def (minus n h) in (let TMP_79 \def (TLRef TMP_78) in (let
134 TMP_80 \def (eq T TMP_77 TMP_79) in (let TMP_81 \def (land TMP_76 TMP_80) in
135 (let TMP_82 \def (lt n d) in (let TMP_83 \def (TLRef n) in (let TMP_84 \def
136 (TLRef n) in (let TMP_85 \def (eq T TMP_83 TMP_84) in (let TMP_86 \def (TLRef
137 n) in (let TMP_87 \def (refl_equal T TMP_86) in (let TMP_88 \def (conj TMP_82
138 TMP_85 H0 TMP_87) in (let TMP_89 \def (or_introl TMP_74 TMP_81 TMP_88) in
139 (eq_ind_r nat n TMP_69 TMP_89 i H2))))))))))))))))))))))))))))))))) in (let
140 TMP_161 \def (\lambda (H0: (le d n)).(let TMP_91 \def (TLRef n) in (let
141 TMP_92 \def (lift h d TMP_91) in (let TMP_94 \def (\lambda (t0: T).(let
142 TMP_93 \def (TLRef i) in (eq T TMP_93 t0))) in (let TMP_95 \def (plus n h) in
143 (let TMP_96 \def (TLRef TMP_95) in (let TMP_97 \def (lift_lref_ge n h d H0)
144 in (let H1 \def (eq_ind T TMP_92 TMP_94 H TMP_96 TMP_97) in (let TMP_98 \def
145 (\lambda (e: T).(match e with [(TSort _) \Rightarrow i | (TLRef n0)
146 \Rightarrow n0 | (THead _ _ _) \Rightarrow i])) in (let TMP_99 \def (TLRef i)
147 in (let TMP_100 \def (plus n h) in (let TMP_101 \def (TLRef TMP_100) in (let
148 H2 \def (f_equal T nat TMP_98 TMP_99 TMP_101 H1) in (let TMP_102 \def (plus n
149 h) in (let TMP_115 \def (\lambda (n0: nat).(let TMP_103 \def (lt n0 d) in
150 (let TMP_104 \def (TLRef n) in (let TMP_105 \def (TLRef n0) in (let TMP_106
151 \def (eq T TMP_104 TMP_105) in (let TMP_107 \def (land TMP_103 TMP_106) in
152 (let TMP_108 \def (plus d h) in (let TMP_109 \def (le TMP_108 n0) in (let
153 TMP_110 \def (TLRef n) in (let TMP_111 \def (minus n0 h) in (let TMP_112 \def
154 (TLRef TMP_111) in (let TMP_113 \def (eq T TMP_110 TMP_112) in (let TMP_114
155 \def (land TMP_109 TMP_113) in (or TMP_107 TMP_114)))))))))))))) in (let
156 TMP_130 \def (\lambda (n0: nat).(let TMP_116 \def (plus n h) in (let TMP_117
157 \def (lt TMP_116 d) in (let TMP_118 \def (TLRef n) in (let TMP_119 \def (plus
158 n h) in (let TMP_120 \def (TLRef TMP_119) in (let TMP_121 \def (eq T TMP_118
159 TMP_120) in (let TMP_122 \def (land TMP_117 TMP_121) in (let TMP_123 \def
160 (plus d h) in (let TMP_124 \def (plus n h) in (let TMP_125 \def (le TMP_123
161 TMP_124) in (let TMP_126 \def (TLRef n) in (let TMP_127 \def (TLRef n0) in
162 (let TMP_128 \def (eq T TMP_126 TMP_127) in (let TMP_129 \def (land TMP_125
163 TMP_128) in (or TMP_122 TMP_129)))))))))))))))) in (let TMP_131 \def (plus n
164 h) in (let TMP_132 \def (lt TMP_131 d) in (let TMP_133 \def (TLRef n) in (let
165 TMP_134 \def (plus n h) in (let TMP_135 \def (TLRef TMP_134) in (let TMP_136
166 \def (eq T TMP_133 TMP_135) in (let TMP_137 \def (land TMP_132 TMP_136) in
167 (let TMP_138 \def (plus d h) in (let TMP_139 \def (plus n h) in (let TMP_140
168 \def (le TMP_138 TMP_139) in (let TMP_141 \def (TLRef n) in (let TMP_142 \def
169 (TLRef n) in (let TMP_143 \def (eq T TMP_141 TMP_142) in (let TMP_144 \def
170 (land TMP_140 TMP_143) in (let TMP_145 \def (plus d h) in (let TMP_146 \def
171 (plus n h) in (let TMP_147 \def (le TMP_145 TMP_146) in (let TMP_148 \def
172 (TLRef n) in (let TMP_149 \def (TLRef n) in (let TMP_150 \def (eq T TMP_148
173 TMP_149) in (let TMP_151 \def (le_n h) in (let TMP_152 \def (le_plus_plus d n
174 h h H0 TMP_151) in (let TMP_153 \def (TLRef n) in (let TMP_154 \def
175 (refl_equal T TMP_153) in (let TMP_155 \def (conj TMP_147 TMP_150 TMP_152
176 TMP_154) in (let TMP_156 \def (or_intror TMP_137 TMP_144 TMP_155) in (let
177 TMP_157 \def (plus n h) in (let TMP_158 \def (minus TMP_157 h) in (let
178 TMP_159 \def (minus_plus_r n h) in (let TMP_160 \def (eq_ind_r nat n TMP_130
179 TMP_156 TMP_158 TMP_159) in (eq_ind_r nat TMP_102 TMP_115 TMP_160 i
180 H2))))))))))))))))))))))))))))))))))))))))))))))) in (lt_le_e n d TMP_47
181 TMP_90 TMP_161))))))))))))))))))))) in (let TMP_191 \def (\lambda (k:
182 K).(\lambda (t0: T).(\lambda (_: ((\forall (d: nat).(\forall (h:
183 nat).(\forall (i: nat).((eq T (TLRef i) (lift h d t0)) \to (or (land (lt i d)
184 (eq T t0 (TLRef i))) (land (le (plus d h) i) (eq T t0 (TLRef (minus i
185 h))))))))))).(\lambda (t1: T).(\lambda (_: ((\forall (d: nat).(\forall (h:
186 nat).(\forall (i: nat).((eq T (TLRef i) (lift h d t1)) \to (or (land (lt i d)
187 (eq T t1 (TLRef i))) (land (le (plus d h) i) (eq T t1 (TLRef (minus i
188 h))))))))))).(\lambda (d: nat).(\lambda (h: nat).(\lambda (i: nat).(\lambda
189 (H1: (eq T (TLRef i) (lift h d (THead k t0 t1)))).(let TMP_163 \def (THead k
190 t0 t1) in (let TMP_164 \def (lift h d TMP_163) in (let TMP_166 \def (\lambda
191 (t2: T).(let TMP_165 \def (TLRef i) in (eq T TMP_165 t2))) in (let TMP_167
192 \def (lift h d t0) in (let TMP_168 \def (s k d) in (let TMP_169 \def (lift h
193 TMP_168 t1) in (let TMP_170 \def (THead k TMP_167 TMP_169) in (let TMP_171
194 \def (lift_head k t0 t1 h d) in (let H2 \def (eq_ind T TMP_164 TMP_166 H1
195 TMP_170 TMP_171) in (let TMP_172 \def (TLRef i) in (let TMP_173 \def (\lambda
196 (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow
197 True | (THead _ _ _) \Rightarrow False])) in (let TMP_174 \def (lift h d t0)
198 in (let TMP_175 \def (s k d) in (let TMP_176 \def (lift h TMP_175 t1) in (let
199 TMP_177 \def (THead k TMP_174 TMP_176) in (let H3 \def (eq_ind T TMP_172
200 TMP_173 I TMP_177 H2) in (let TMP_178 \def (lt i d) in (let TMP_179 \def
201 (THead k t0 t1) in (let TMP_180 \def (TLRef i) in (let TMP_181 \def (eq T
202 TMP_179 TMP_180) in (let TMP_182 \def (land TMP_178 TMP_181) in (let TMP_183
203 \def (plus d h) in (let TMP_184 \def (le TMP_183 i) in (let TMP_185 \def
204 (THead k t0 t1) in (let TMP_186 \def (minus i h) in (let TMP_187 \def (TLRef
205 TMP_186) in (let TMP_188 \def (eq T TMP_185 TMP_187) in (let TMP_189 \def
206 (land TMP_184 TMP_188) in (let TMP_190 \def (or TMP_182 TMP_189) in
207 (False_ind TMP_190 H3))))))))))))))))))))))))))))))))))))))) in (T_ind TMP_11
208 TMP_34 TMP_162 TMP_191 t))))).
210 theorem lift_gen_lref_lt:
211 \forall (h: nat).(\forall (d: nat).(\forall (n: nat).((lt n d) \to (\forall
212 (t: T).((eq T (TLRef n) (lift h d t)) \to (eq T t (TLRef n)))))))
214 \lambda (h: nat).(\lambda (d: nat).(\lambda (n: nat).(\lambda (H: (lt n
215 d)).(\lambda (t: T).(\lambda (H0: (eq T (TLRef n) (lift h d t))).(let H_x
216 \def (lift_gen_lref t d h n H0) in (let H1 \def H_x in (let TMP_1 \def (lt n
217 d) in (let TMP_2 \def (TLRef n) in (let TMP_3 \def (eq T t TMP_2) in (let
218 TMP_4 \def (land TMP_1 TMP_3) in (let TMP_5 \def (plus d h) in (let TMP_6
219 \def (le TMP_5 n) in (let TMP_7 \def (minus n h) in (let TMP_8 \def (TLRef
220 TMP_7) in (let TMP_9 \def (eq T t TMP_8) in (let TMP_10 \def (land TMP_6
221 TMP_9) in (let TMP_11 \def (TLRef n) in (let TMP_12 \def (eq T t TMP_11) in
222 (let TMP_24 \def (\lambda (H2: (land (lt n d) (eq T t (TLRef n)))).(let
223 TMP_13 \def (lt n d) in (let TMP_14 \def (TLRef n) in (let TMP_15 \def (eq T
224 t TMP_14) in (let TMP_16 \def (TLRef n) in (let TMP_17 \def (eq T t TMP_16)
225 in (let TMP_23 \def (\lambda (_: (lt n d)).(\lambda (H4: (eq T t (TLRef
226 n))).(let TMP_18 \def (TLRef n) in (let TMP_20 \def (\lambda (t0: T).(let
227 TMP_19 \def (TLRef n) in (eq T t0 TMP_19))) in (let TMP_21 \def (TLRef n) in
228 (let TMP_22 \def (refl_equal T TMP_21) in (eq_ind_r T TMP_18 TMP_20 TMP_22 t
229 H4))))))) in (land_ind TMP_13 TMP_15 TMP_17 TMP_23 H2)))))))) in (let TMP_47
230 \def (\lambda (H2: (land (le (plus d h) n) (eq T t (TLRef (minus n
231 h))))).(let TMP_25 \def (plus d h) in (let TMP_26 \def (le TMP_25 n) in (let
232 TMP_27 \def (minus n h) in (let TMP_28 \def (TLRef TMP_27) in (let TMP_29
233 \def (eq T t TMP_28) in (let TMP_30 \def (TLRef n) in (let TMP_31 \def (eq T
234 t TMP_30) in (let TMP_46 \def (\lambda (H3: (le (plus d h) n)).(\lambda (H4:
235 (eq T t (TLRef (minus n h)))).(let TMP_32 \def (minus n h) in (let TMP_33
236 \def (TLRef TMP_32) in (let TMP_35 \def (\lambda (t0: T).(let TMP_34 \def
237 (TLRef n) in (eq T t0 TMP_34))) in (let TMP_36 \def (plus d h) in (let TMP_37
238 \def (minus n h) in (let TMP_38 \def (TLRef TMP_37) in (let TMP_39 \def
239 (TLRef n) in (let TMP_40 \def (eq T TMP_38 TMP_39) in (let TMP_41 \def (plus
240 d h) in (let TMP_42 \def (S n) in (let TMP_43 \def (le_plus_trans TMP_42 d h
241 H) in (let TMP_44 \def (lt_le_S n TMP_41 TMP_43) in (let TMP_45 \def
242 (le_false TMP_36 n TMP_40 H3 TMP_44) in (eq_ind_r T TMP_33 TMP_35 TMP_45 t
243 H4)))))))))))))))) in (land_ind TMP_26 TMP_29 TMP_31 TMP_46 H2)))))))))) in
244 (or_ind TMP_4 TMP_10 TMP_12 TMP_24 TMP_47 H1)))))))))))))))))))))).
246 theorem lift_gen_lref_false:
247 \forall (h: nat).(\forall (d: nat).(\forall (n: nat).((le d n) \to ((lt n
248 (plus d h)) \to (\forall (t: T).((eq T (TLRef n) (lift h d t)) \to (\forall
251 \lambda (h: nat).(\lambda (d: nat).(\lambda (n: nat).(\lambda (H: (le d
252 n)).(\lambda (H0: (lt n (plus d h))).(\lambda (t: T).(\lambda (H1: (eq T
253 (TLRef n) (lift h d t))).(\lambda (P: Prop).(let H_x \def (lift_gen_lref t d
254 h n H1) in (let H2 \def H_x in (let TMP_1 \def (lt n d) in (let TMP_2 \def
255 (TLRef n) in (let TMP_3 \def (eq T t TMP_2) in (let TMP_4 \def (land TMP_1
256 TMP_3) in (let TMP_5 \def (plus d h) in (let TMP_6 \def (le TMP_5 n) in (let
257 TMP_7 \def (minus n h) in (let TMP_8 \def (TLRef TMP_7) in (let TMP_9 \def
258 (eq T t TMP_8) in (let TMP_10 \def (land TMP_6 TMP_9) in (let TMP_15 \def
259 (\lambda (H3: (land (lt n d) (eq T t (TLRef n)))).(let TMP_11 \def (lt n d)
260 in (let TMP_12 \def (TLRef n) in (let TMP_13 \def (eq T t TMP_12) in (let
261 TMP_14 \def (\lambda (H4: (lt n d)).(\lambda (_: (eq T t (TLRef
262 n))).(le_false d n P H H4))) in (land_ind TMP_11 TMP_13 P TMP_14 H3)))))) in
263 (let TMP_23 \def (\lambda (H3: (land (le (plus d h) n) (eq T t (TLRef (minus
264 n h))))).(let TMP_16 \def (plus d h) in (let TMP_17 \def (le TMP_16 n) in
265 (let TMP_18 \def (minus n h) in (let TMP_19 \def (TLRef TMP_18) in (let
266 TMP_20 \def (eq T t TMP_19) in (let TMP_22 \def (\lambda (H4: (le (plus d h)
267 n)).(\lambda (_: (eq T t (TLRef (minus n h)))).(let TMP_21 \def (plus d h) in
268 (le_false TMP_21 n P H4 H0)))) in (land_ind TMP_17 TMP_20 P TMP_22 H3))))))))
269 in (or_ind TMP_4 TMP_10 P TMP_15 TMP_23 H2)))))))))))))))))))))).
271 theorem lift_gen_lref_ge:
272 \forall (h: nat).(\forall (d: nat).(\forall (n: nat).((le d n) \to (\forall
273 (t: T).((eq T (TLRef (plus n h)) (lift h d t)) \to (eq T t (TLRef n)))))))
275 \lambda (h: nat).(\lambda (d: nat).(\lambda (n: nat).(\lambda (H: (le d
276 n)).(\lambda (t: T).(\lambda (H0: (eq T (TLRef (plus n h)) (lift h d
277 t))).(let TMP_1 \def (plus n h) in (let H_x \def (lift_gen_lref t d h TMP_1
278 H0) in (let H1 \def H_x in (let TMP_2 \def (plus n h) in (let TMP_3 \def (lt
279 TMP_2 d) in (let TMP_4 \def (plus n h) in (let TMP_5 \def (TLRef TMP_4) in
280 (let TMP_6 \def (eq T t TMP_5) in (let TMP_7 \def (land TMP_3 TMP_6) in (let
281 TMP_8 \def (plus d h) in (let TMP_9 \def (plus n h) in (let TMP_10 \def (le
282 TMP_8 TMP_9) in (let TMP_11 \def (plus n h) in (let TMP_12 \def (minus TMP_11
283 h) in (let TMP_13 \def (TLRef TMP_12) in (let TMP_14 \def (eq T t TMP_13) in
284 (let TMP_15 \def (land TMP_10 TMP_14) in (let TMP_16 \def (TLRef n) in (let
285 TMP_17 \def (eq T t TMP_16) in (let TMP_41 \def (\lambda (H2: (land (lt (plus
286 n h) d) (eq T t (TLRef (plus n h))))).(let TMP_18 \def (plus n h) in (let
287 TMP_19 \def (lt TMP_18 d) in (let TMP_20 \def (plus n h) in (let TMP_21 \def
288 (TLRef TMP_20) in (let TMP_22 \def (eq T t TMP_21) in (let TMP_23 \def (TLRef
289 n) in (let TMP_24 \def (eq T t TMP_23) in (let TMP_40 \def (\lambda (H3: (lt
290 (plus n h) d)).(\lambda (H4: (eq T t (TLRef (plus n h)))).(let TMP_25 \def
291 (plus n h) in (let TMP_26 \def (TLRef TMP_25) in (let TMP_28 \def (\lambda
292 (t0: T).(let TMP_27 \def (TLRef n) in (eq T t0 TMP_27))) in (let TMP_29 \def
293 (plus n h) in (let TMP_30 \def (TLRef TMP_29) in (let TMP_31 \def (TLRef n)
294 in (let TMP_32 \def (eq T TMP_30 TMP_31) in (let TMP_33 \def (plus n h) in
295 (let TMP_34 \def (plus d h) in (let TMP_35 \def (le_plus_l d h) in (let
296 TMP_36 \def (lt_le_trans TMP_33 d TMP_34 H3 TMP_35) in (let TMP_37 \def
297 (simpl_lt_plus_r h n d TMP_36) in (let TMP_38 \def (lt_le_S n d TMP_37) in
298 (let TMP_39 \def (le_false d n TMP_32 H TMP_38) in (eq_ind_r T TMP_26 TMP_28
299 TMP_39 t H4))))))))))))))))) in (land_ind TMP_19 TMP_22 TMP_24 TMP_40
300 H2)))))))))) in (let TMP_61 \def (\lambda (H2: (land (le (plus d h) (plus n
301 h)) (eq T t (TLRef (minus (plus n h) h))))).(let TMP_42 \def (plus d h) in
302 (let TMP_43 \def (plus n h) in (let TMP_44 \def (le TMP_42 TMP_43) in (let
303 TMP_45 \def (plus n h) in (let TMP_46 \def (minus TMP_45 h) in (let TMP_47
304 \def (TLRef TMP_46) in (let TMP_48 \def (eq T t TMP_47) in (let TMP_49 \def
305 (TLRef n) in (let TMP_50 \def (eq T t TMP_49) in (let TMP_60 \def (\lambda
306 (_: (le (plus d h) (plus n h))).(\lambda (H4: (eq T t (TLRef (minus (plus n
307 h) h)))).(let TMP_51 \def (plus n h) in (let TMP_52 \def (minus TMP_51 h) in
308 (let TMP_53 \def (TLRef TMP_52) in (let TMP_55 \def (\lambda (t0: T).(let
309 TMP_54 \def (TLRef n) in (eq T t0 TMP_54))) in (let TMP_56 \def (plus n h) in
310 (let TMP_57 \def (minus TMP_56 h) in (let TMP_58 \def (minus_plus_r n h) in
311 (let TMP_59 \def (f_equal nat T TLRef TMP_57 n TMP_58) in (eq_ind_r T TMP_53
312 TMP_55 TMP_59 t H4))))))))))) in (land_ind TMP_44 TMP_48 TMP_50 TMP_60
313 H2)))))))))))) in (or_ind TMP_7 TMP_15 TMP_17 TMP_41 TMP_61
314 H1))))))))))))))))))))))))))).
316 theorem lift_gen_head:
317 \forall (k: K).(\forall (u: T).(\forall (t: T).(\forall (x: T).(\forall (h:
318 nat).(\forall (d: nat).((eq T (THead k u t) (lift h d x)) \to (ex3_2 T T
319 (\lambda (y: T).(\lambda (z: T).(eq T x (THead k y z)))) (\lambda (y:
320 T).(\lambda (_: T).(eq T u (lift h d y)))) (\lambda (_: T).(\lambda (z:
321 T).(eq T t (lift h (s k d) z)))))))))))
323 \lambda (k: K).(\lambda (u: T).(\lambda (t: T).(\lambda (x: T).(let TMP_8
324 \def (\lambda (t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (THead k u
325 t) (lift h d t0)) \to (let TMP_2 \def (\lambda (y: T).(\lambda (z: T).(let
326 TMP_1 \def (THead k y z) in (eq T t0 TMP_1)))) in (let TMP_4 \def (\lambda
327 (y: T).(\lambda (_: T).(let TMP_3 \def (lift h d y) in (eq T u TMP_3)))) in
328 (let TMP_7 \def (\lambda (_: T).(\lambda (z: T).(let TMP_5 \def (s k d) in
329 (let TMP_6 \def (lift h TMP_5 z) in (eq T t TMP_6))))) in (ex3_2 T T TMP_2
330 TMP_4 TMP_7)))))))) in (let TMP_27 \def (\lambda (n: nat).(\lambda (h:
331 nat).(\lambda (d: nat).(\lambda (H: (eq T (THead k u t) (lift h d (TSort
332 n)))).(let TMP_9 \def (TSort n) in (let TMP_10 \def (lift h d TMP_9) in (let
333 TMP_12 \def (\lambda (t0: T).(let TMP_11 \def (THead k u t) in (eq T TMP_11
334 t0))) in (let TMP_13 \def (TSort n) in (let TMP_14 \def (lift_sort n h d) in
335 (let H0 \def (eq_ind T TMP_10 TMP_12 H TMP_13 TMP_14) in (let TMP_15 \def
336 (THead k u t) in (let TMP_16 \def (\lambda (ee: T).(match ee with [(TSort _)
337 \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
338 True])) in (let TMP_17 \def (TSort n) in (let H1 \def (eq_ind T TMP_15 TMP_16
339 I TMP_17 H0) in (let TMP_20 \def (\lambda (y: T).(\lambda (z: T).(let TMP_18
340 \def (TSort n) in (let TMP_19 \def (THead k y z) in (eq T TMP_18 TMP_19)))))
341 in (let TMP_22 \def (\lambda (y: T).(\lambda (_: T).(let TMP_21 \def (lift h
342 d y) in (eq T u TMP_21)))) in (let TMP_25 \def (\lambda (_: T).(\lambda (z:
343 T).(let TMP_23 \def (s k d) in (let TMP_24 \def (lift h TMP_23 z) in (eq T t
344 TMP_24))))) in (let TMP_26 \def (ex3_2 T T TMP_20 TMP_22 TMP_25) in
345 (False_ind TMP_26 H1))))))))))))))))))) in (let TMP_77 \def (\lambda (n:
346 nat).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H: (eq T (THead k u t)
347 (lift h d (TLRef n)))).(let TMP_30 \def (\lambda (y: T).(\lambda (z: T).(let
348 TMP_28 \def (TLRef n) in (let TMP_29 \def (THead k y z) in (eq T TMP_28
349 TMP_29))))) in (let TMP_32 \def (\lambda (y: T).(\lambda (_: T).(let TMP_31
350 \def (lift h d y) in (eq T u TMP_31)))) in (let TMP_35 \def (\lambda (_:
351 T).(\lambda (z: T).(let TMP_33 \def (s k d) in (let TMP_34 \def (lift h
352 TMP_33 z) in (eq T t TMP_34))))) in (let TMP_36 \def (ex3_2 T T TMP_30 TMP_32
353 TMP_35) in (let TMP_55 \def (\lambda (H0: (lt n d)).(let TMP_37 \def (TLRef
354 n) in (let TMP_38 \def (lift h d TMP_37) in (let TMP_40 \def (\lambda (t0:
355 T).(let TMP_39 \def (THead k u t) in (eq T TMP_39 t0))) in (let TMP_41 \def
356 (TLRef n) in (let TMP_42 \def (lift_lref_lt n h d H0) in (let H1 \def (eq_ind
357 T TMP_38 TMP_40 H TMP_41 TMP_42) in (let TMP_43 \def (THead k u t) in (let
358 TMP_44 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False |
359 (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let
360 TMP_45 \def (TLRef n) in (let H2 \def (eq_ind T TMP_43 TMP_44 I TMP_45 H1) in
361 (let TMP_48 \def (\lambda (y: T).(\lambda (z: T).(let TMP_46 \def (TLRef n)
362 in (let TMP_47 \def (THead k y z) in (eq T TMP_46 TMP_47))))) in (let TMP_50
363 \def (\lambda (y: T).(\lambda (_: T).(let TMP_49 \def (lift h d y) in (eq T u
364 TMP_49)))) in (let TMP_53 \def (\lambda (_: T).(\lambda (z: T).(let TMP_51
365 \def (s k d) in (let TMP_52 \def (lift h TMP_51 z) in (eq T t TMP_52))))) in
366 (let TMP_54 \def (ex3_2 T T TMP_48 TMP_50 TMP_53) in (False_ind TMP_54
367 H2)))))))))))))))) in (let TMP_76 \def (\lambda (H0: (le d n)).(let TMP_56
368 \def (TLRef n) in (let TMP_57 \def (lift h d TMP_56) in (let TMP_59 \def
369 (\lambda (t0: T).(let TMP_58 \def (THead k u t) in (eq T TMP_58 t0))) in (let
370 TMP_60 \def (plus n h) in (let TMP_61 \def (TLRef TMP_60) in (let TMP_62 \def
371 (lift_lref_ge n h d H0) in (let H1 \def (eq_ind T TMP_57 TMP_59 H TMP_61
372 TMP_62) in (let TMP_63 \def (THead k u t) in (let TMP_64 \def (\lambda (ee:
373 T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
374 | (THead _ _ _) \Rightarrow True])) in (let TMP_65 \def (plus n h) in (let
375 TMP_66 \def (TLRef TMP_65) in (let H2 \def (eq_ind T TMP_63 TMP_64 I TMP_66
376 H1) in (let TMP_69 \def (\lambda (y: T).(\lambda (z: T).(let TMP_67 \def
377 (TLRef n) in (let TMP_68 \def (THead k y z) in (eq T TMP_67 TMP_68))))) in
378 (let TMP_71 \def (\lambda (y: T).(\lambda (_: T).(let TMP_70 \def (lift h d
379 y) in (eq T u TMP_70)))) in (let TMP_74 \def (\lambda (_: T).(\lambda (z:
380 T).(let TMP_72 \def (s k d) in (let TMP_73 \def (lift h TMP_72 z) in (eq T t
381 TMP_73))))) in (let TMP_75 \def (ex3_2 T T TMP_69 TMP_71 TMP_74) in
382 (False_ind TMP_75 H2)))))))))))))))))) in (lt_le_e n d TMP_36 TMP_55
383 TMP_76))))))))))) in (let TMP_205 \def (\lambda (k0: K).(\lambda (t0:
384 T).(\lambda (H: ((\forall (h: nat).(\forall (d: nat).((eq T (THead k u t)
385 (lift h d t0)) \to (ex3_2 T T (\lambda (y: T).(\lambda (z: T).(eq T t0 (THead
386 k y z)))) (\lambda (y: T).(\lambda (_: T).(eq T u (lift h d y)))) (\lambda
387 (_: T).(\lambda (z: T).(eq T t (lift h (s k d) z)))))))))).(\lambda (t1:
388 T).(\lambda (H0: ((\forall (h: nat).(\forall (d: nat).((eq T (THead k u t)
389 (lift h d t1)) \to (ex3_2 T T (\lambda (y: T).(\lambda (z: T).(eq T t1 (THead
390 k y z)))) (\lambda (y: T).(\lambda (_: T).(eq T u (lift h d y)))) (\lambda
391 (_: T).(\lambda (z: T).(eq T t (lift h (s k d) z)))))))))).(\lambda (h:
392 nat).(\lambda (d: nat).(\lambda (H1: (eq T (THead k u t) (lift h d (THead k0
393 t0 t1)))).(let TMP_78 \def (THead k0 t0 t1) in (let TMP_79 \def (lift h d
394 TMP_78) in (let TMP_81 \def (\lambda (t2: T).(let TMP_80 \def (THead k u t)
395 in (eq T TMP_80 t2))) in (let TMP_82 \def (lift h d t0) in (let TMP_83 \def
396 (s k0 d) in (let TMP_84 \def (lift h TMP_83 t1) in (let TMP_85 \def (THead k0
397 TMP_82 TMP_84) in (let TMP_86 \def (lift_head k0 t0 t1 h d) in (let H2 \def
398 (eq_ind T TMP_79 TMP_81 H1 TMP_85 TMP_86) in (let TMP_87 \def (\lambda (e:
399 T).(match e with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead
400 k1 _ _) \Rightarrow k1])) in (let TMP_88 \def (THead k u t) in (let TMP_89
401 \def (lift h d t0) in (let TMP_90 \def (s k0 d) in (let TMP_91 \def (lift h
402 TMP_90 t1) in (let TMP_92 \def (THead k0 TMP_89 TMP_91) in (let H3 \def
403 (f_equal T K TMP_87 TMP_88 TMP_92 H2) in (let TMP_93 \def (\lambda (e:
404 T).(match e with [(TSort _) \Rightarrow u | (TLRef _) \Rightarrow u | (THead
405 _ t2 _) \Rightarrow t2])) in (let TMP_94 \def (THead k u t) in (let TMP_95
406 \def (lift h d t0) in (let TMP_96 \def (s k0 d) in (let TMP_97 \def (lift h
407 TMP_96 t1) in (let TMP_98 \def (THead k0 TMP_95 TMP_97) in (let H4 \def
408 (f_equal T T TMP_93 TMP_94 TMP_98 H2) in (let TMP_99 \def (\lambda (e:
409 T).(match e with [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead
410 _ _ t2) \Rightarrow t2])) in (let TMP_100 \def (THead k u t) in (let TMP_101
411 \def (lift h d t0) in (let TMP_102 \def (s k0 d) in (let TMP_103 \def (lift h
412 TMP_102 t1) in (let TMP_104 \def (THead k0 TMP_101 TMP_103) in (let H5 \def
413 (f_equal T T TMP_99 TMP_100 TMP_104 H2) in (let TMP_203 \def (\lambda (H6:
414 (eq T u (lift h d t0))).(\lambda (H7: (eq K k k0)).(let TMP_107 \def (\lambda
415 (k1: K).(let TMP_105 \def (s k1 d) in (let TMP_106 \def (lift h TMP_105 t1)
416 in (eq T t TMP_106)))) in (let H8 \def (eq_ind_r K k0 TMP_107 H5 k H7) in
417 (let TMP_116 \def (\lambda (k1: K).(let TMP_110 \def (\lambda (y: T).(\lambda
418 (z: T).(let TMP_108 \def (THead k1 t0 t1) in (let TMP_109 \def (THead k y z)
419 in (eq T TMP_108 TMP_109))))) in (let TMP_112 \def (\lambda (y: T).(\lambda
420 (_: T).(let TMP_111 \def (lift h d y) in (eq T u TMP_111)))) in (let TMP_115
421 \def (\lambda (_: T).(\lambda (z: T).(let TMP_113 \def (s k d) in (let
422 TMP_114 \def (lift h TMP_113 z) in (eq T t TMP_114))))) in (ex3_2 T T TMP_110
423 TMP_112 TMP_115))))) in (let TMP_124 \def (\lambda (t2: T).(\forall (h0:
424 nat).(\forall (d0: nat).((eq T (THead k u t2) (lift h0 d0 t1)) \to (let
425 TMP_118 \def (\lambda (y: T).(\lambda (z: T).(let TMP_117 \def (THead k y z)
426 in (eq T t1 TMP_117)))) in (let TMP_120 \def (\lambda (y: T).(\lambda (_:
427 T).(let TMP_119 \def (lift h0 d0 y) in (eq T u TMP_119)))) in (let TMP_123
428 \def (\lambda (_: T).(\lambda (z: T).(let TMP_121 \def (s k d0) in (let
429 TMP_122 \def (lift h0 TMP_121 z) in (eq T t2 TMP_122))))) in (ex3_2 T T
430 TMP_118 TMP_120 TMP_123)))))))) in (let TMP_125 \def (s k d) in (let TMP_126
431 \def (lift h TMP_125 t1) in (let H9 \def (eq_ind T t TMP_124 H0 TMP_126 H8)
432 in (let TMP_134 \def (\lambda (t2: T).(\forall (h0: nat).(\forall (d0:
433 nat).((eq T (THead k u t2) (lift h0 d0 t0)) \to (let TMP_128 \def (\lambda
434 (y: T).(\lambda (z: T).(let TMP_127 \def (THead k y z) in (eq T t0
435 TMP_127)))) in (let TMP_130 \def (\lambda (y: T).(\lambda (_: T).(let TMP_129
436 \def (lift h0 d0 y) in (eq T u TMP_129)))) in (let TMP_133 \def (\lambda (_:
437 T).(\lambda (z: T).(let TMP_131 \def (s k d0) in (let TMP_132 \def (lift h0
438 TMP_131 z) in (eq T t2 TMP_132))))) in (ex3_2 T T TMP_128 TMP_130
439 TMP_133)))))))) in (let TMP_135 \def (s k d) in (let TMP_136 \def (lift h
440 TMP_135 t1) in (let H10 \def (eq_ind T t TMP_134 H TMP_136 H8) in (let
441 TMP_137 \def (s k d) in (let TMP_138 \def (lift h TMP_137 t1) in (let TMP_147
442 \def (\lambda (t2: T).(let TMP_141 \def (\lambda (y: T).(\lambda (z: T).(let
443 TMP_139 \def (THead k t0 t1) in (let TMP_140 \def (THead k y z) in (eq T
444 TMP_139 TMP_140))))) in (let TMP_143 \def (\lambda (y: T).(\lambda (_:
445 T).(let TMP_142 \def (lift h d y) in (eq T u TMP_142)))) in (let TMP_146 \def
446 (\lambda (_: T).(\lambda (z: T).(let TMP_144 \def (s k d) in (let TMP_145
447 \def (lift h TMP_144 z) in (eq T t2 TMP_145))))) in (ex3_2 T T TMP_141
448 TMP_143 TMP_146))))) in (let TMP_157 \def (\lambda (t2: T).(\forall (h0:
449 nat).(\forall (d0: nat).((eq T (THead k t2 (lift h (s k d) t1)) (lift h0 d0
450 t0)) \to (let TMP_149 \def (\lambda (y: T).(\lambda (z: T).(let TMP_148 \def
451 (THead k y z) in (eq T t0 TMP_148)))) in (let TMP_151 \def (\lambda (y:
452 T).(\lambda (_: T).(let TMP_150 \def (lift h0 d0 y) in (eq T t2 TMP_150))))
453 in (let TMP_156 \def (\lambda (_: T).(\lambda (z: T).(let TMP_152 \def (s k
454 d) in (let TMP_153 \def (lift h TMP_152 t1) in (let TMP_154 \def (s k d0) in
455 (let TMP_155 \def (lift h0 TMP_154 z) in (eq T TMP_153 TMP_155))))))) in
456 (ex3_2 T T TMP_149 TMP_151 TMP_156)))))))) in (let TMP_158 \def (lift h d t0)
457 in (let H11 \def (eq_ind T u TMP_157 H10 TMP_158 H6) in (let TMP_168 \def
458 (\lambda (t2: T).(\forall (h0: nat).(\forall (d0: nat).((eq T (THead k t2
459 (lift h (s k d) t1)) (lift h0 d0 t1)) \to (let TMP_160 \def (\lambda (y:
460 T).(\lambda (z: T).(let TMP_159 \def (THead k y z) in (eq T t1 TMP_159)))) in
461 (let TMP_162 \def (\lambda (y: T).(\lambda (_: T).(let TMP_161 \def (lift h0
462 d0 y) in (eq T t2 TMP_161)))) in (let TMP_167 \def (\lambda (_: T).(\lambda
463 (z: T).(let TMP_163 \def (s k d) in (let TMP_164 \def (lift h TMP_163 t1) in
464 (let TMP_165 \def (s k d0) in (let TMP_166 \def (lift h0 TMP_165 z) in (eq T
465 TMP_164 TMP_166))))))) in (ex3_2 T T TMP_160 TMP_162 TMP_167)))))))) in (let
466 TMP_169 \def (lift h d t0) in (let H12 \def (eq_ind T u TMP_168 H9 TMP_169
467 H6) in (let TMP_170 \def (lift h d t0) in (let TMP_181 \def (\lambda (t2:
468 T).(let TMP_173 \def (\lambda (y: T).(\lambda (z: T).(let TMP_171 \def (THead
469 k t0 t1) in (let TMP_172 \def (THead k y z) in (eq T TMP_171 TMP_172))))) in
470 (let TMP_175 \def (\lambda (y: T).(\lambda (_: T).(let TMP_174 \def (lift h d
471 y) in (eq T t2 TMP_174)))) in (let TMP_180 \def (\lambda (_: T).(\lambda (z:
472 T).(let TMP_176 \def (s k d) in (let TMP_177 \def (lift h TMP_176 t1) in (let
473 TMP_178 \def (s k d) in (let TMP_179 \def (lift h TMP_178 z) in (eq T TMP_177
474 TMP_179))))))) in (ex3_2 T T TMP_173 TMP_175 TMP_180))))) in (let TMP_184
475 \def (\lambda (y: T).(\lambda (z: T).(let TMP_182 \def (THead k t0 t1) in
476 (let TMP_183 \def (THead k y z) in (eq T TMP_182 TMP_183))))) in (let TMP_187
477 \def (\lambda (y: T).(\lambda (_: T).(let TMP_185 \def (lift h d t0) in (let
478 TMP_186 \def (lift h d y) in (eq T TMP_185 TMP_186))))) in (let TMP_192 \def
479 (\lambda (_: T).(\lambda (z: T).(let TMP_188 \def (s k d) in (let TMP_189
480 \def (lift h TMP_188 t1) in (let TMP_190 \def (s k d) in (let TMP_191 \def
481 (lift h TMP_190 z) in (eq T TMP_189 TMP_191))))))) in (let TMP_193 \def
482 (THead k t0 t1) in (let TMP_194 \def (refl_equal T TMP_193) in (let TMP_195
483 \def (lift h d t0) in (let TMP_196 \def (refl_equal T TMP_195) in (let
484 TMP_197 \def (s k d) in (let TMP_198 \def (lift h TMP_197 t1) in (let TMP_199
485 \def (refl_equal T TMP_198) in (let TMP_200 \def (ex3_2_intro T T TMP_184
486 TMP_187 TMP_192 t0 t1 TMP_194 TMP_196 TMP_199) in (let TMP_201 \def (eq_ind_r
487 T TMP_170 TMP_181 TMP_200 u H6) in (let TMP_202 \def (eq_ind_r T TMP_138
488 TMP_147 TMP_201 t H8) in (eq_ind K k TMP_116 TMP_202 k0
489 H7)))))))))))))))))))))))))))))))))))))) in (let TMP_204 \def (TMP_203 H4) in
490 (TMP_204 H3))))))))))))))))))))))))))))))))))))))))) in (T_ind TMP_8 TMP_27
491 TMP_77 TMP_205 x)))))))).
493 theorem lift_gen_bind:
494 \forall (b: B).(\forall (u: T).(\forall (t: T).(\forall (x: T).(\forall (h:
495 nat).(\forall (d: nat).((eq T (THead (Bind b) u t) (lift h d x)) \to (ex3_2 T
496 T (\lambda (y: T).(\lambda (z: T).(eq T x (THead (Bind b) y z)))) (\lambda
497 (y: T).(\lambda (_: T).(eq T u (lift h d y)))) (\lambda (_: T).(\lambda (z:
498 T).(eq T t (lift h (S d) z)))))))))))
500 \lambda (b: B).(\lambda (u: T).(\lambda (t: T).(\lambda (x: T).(\lambda (h:
501 nat).(\lambda (d: nat).(\lambda (H: (eq T (THead (Bind b) u t) (lift h d
502 x))).(let TMP_1 \def (Bind b) in (let H_x \def (lift_gen_head TMP_1 u t x h d
503 H) in (let H0 \def H_x in (let TMP_4 \def (\lambda (y: T).(\lambda (z:
504 T).(let TMP_2 \def (Bind b) in (let TMP_3 \def (THead TMP_2 y z) in (eq T x
505 TMP_3))))) in (let TMP_6 \def (\lambda (y: T).(\lambda (_: T).(let TMP_5 \def
506 (lift h d y) in (eq T u TMP_5)))) in (let TMP_9 \def (\lambda (_: T).(\lambda
507 (z: T).(let TMP_7 \def (S d) in (let TMP_8 \def (lift h TMP_7 z) in (eq T t
508 TMP_8))))) in (let TMP_12 \def (\lambda (y: T).(\lambda (z: T).(let TMP_10
509 \def (Bind b) in (let TMP_11 \def (THead TMP_10 y z) in (eq T x TMP_11)))))
510 in (let TMP_14 \def (\lambda (y: T).(\lambda (_: T).(let TMP_13 \def (lift h
511 d y) in (eq T u TMP_13)))) in (let TMP_17 \def (\lambda (_: T).(\lambda (z:
512 T).(let TMP_15 \def (S d) in (let TMP_16 \def (lift h TMP_15 z) in (eq T t
513 TMP_16))))) in (let TMP_18 \def (ex3_2 T T TMP_12 TMP_14 TMP_17) in (let
514 TMP_81 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: (eq T x (THead
515 (Bind b) x0 x1))).(\lambda (H2: (eq T u (lift h d x0))).(\lambda (H3: (eq T t
516 (lift h (S d) x1))).(let TMP_19 \def (Bind b) in (let TMP_20 \def (THead
517 TMP_19 x0 x1) in (let TMP_29 \def (\lambda (t0: T).(let TMP_23 \def (\lambda
518 (y: T).(\lambda (z: T).(let TMP_21 \def (Bind b) in (let TMP_22 \def (THead
519 TMP_21 y z) in (eq T t0 TMP_22))))) in (let TMP_25 \def (\lambda (y:
520 T).(\lambda (_: T).(let TMP_24 \def (lift h d y) in (eq T u TMP_24)))) in
521 (let TMP_28 \def (\lambda (_: T).(\lambda (z: T).(let TMP_26 \def (S d) in
522 (let TMP_27 \def (lift h TMP_26 z) in (eq T t TMP_27))))) in (ex3_2 T T
523 TMP_23 TMP_25 TMP_28))))) in (let TMP_30 \def (S d) in (let TMP_31 \def (lift
524 h TMP_30 x1) in (let TMP_42 \def (\lambda (t0: T).(let TMP_36 \def (\lambda
525 (y: T).(\lambda (z: T).(let TMP_32 \def (Bind b) in (let TMP_33 \def (THead
526 TMP_32 x0 x1) in (let TMP_34 \def (Bind b) in (let TMP_35 \def (THead TMP_34
527 y z) in (eq T TMP_33 TMP_35))))))) in (let TMP_38 \def (\lambda (y:
528 T).(\lambda (_: T).(let TMP_37 \def (lift h d y) in (eq T u TMP_37)))) in
529 (let TMP_41 \def (\lambda (_: T).(\lambda (z: T).(let TMP_39 \def (S d) in
530 (let TMP_40 \def (lift h TMP_39 z) in (eq T t0 TMP_40))))) in (ex3_2 T T
531 TMP_36 TMP_38 TMP_41))))) in (let TMP_43 \def (lift h d x0) in (let TMP_56
532 \def (\lambda (t0: T).(let TMP_48 \def (\lambda (y: T).(\lambda (z: T).(let
533 TMP_44 \def (Bind b) in (let TMP_45 \def (THead TMP_44 x0 x1) in (let TMP_46
534 \def (Bind b) in (let TMP_47 \def (THead TMP_46 y z) in (eq T TMP_45
535 TMP_47))))))) in (let TMP_50 \def (\lambda (y: T).(\lambda (_: T).(let TMP_49
536 \def (lift h d y) in (eq T t0 TMP_49)))) in (let TMP_55 \def (\lambda (_:
537 T).(\lambda (z: T).(let TMP_51 \def (S d) in (let TMP_52 \def (lift h TMP_51
538 x1) in (let TMP_53 \def (S d) in (let TMP_54 \def (lift h TMP_53 z) in (eq T
539 TMP_52 TMP_54))))))) in (ex3_2 T T TMP_48 TMP_50 TMP_55))))) in (let TMP_61
540 \def (\lambda (y: T).(\lambda (z: T).(let TMP_57 \def (Bind b) in (let TMP_58
541 \def (THead TMP_57 x0 x1) in (let TMP_59 \def (Bind b) in (let TMP_60 \def
542 (THead TMP_59 y z) in (eq T TMP_58 TMP_60))))))) in (let TMP_64 \def (\lambda
543 (y: T).(\lambda (_: T).(let TMP_62 \def (lift h d x0) in (let TMP_63 \def
544 (lift h d y) in (eq T TMP_62 TMP_63))))) in (let TMP_69 \def (\lambda (_:
545 T).(\lambda (z: T).(let TMP_65 \def (S d) in (let TMP_66 \def (lift h TMP_65
546 x1) in (let TMP_67 \def (S d) in (let TMP_68 \def (lift h TMP_67 z) in (eq T
547 TMP_66 TMP_68))))))) in (let TMP_70 \def (Bind b) in (let TMP_71 \def (THead
548 TMP_70 x0 x1) in (let TMP_72 \def (refl_equal T TMP_71) in (let TMP_73 \def
549 (lift h d x0) in (let TMP_74 \def (refl_equal T TMP_73) in (let TMP_75 \def
550 (S d) in (let TMP_76 \def (lift h TMP_75 x1) in (let TMP_77 \def (refl_equal
551 T TMP_76) in (let TMP_78 \def (ex3_2_intro T T TMP_61 TMP_64 TMP_69 x0 x1
552 TMP_72 TMP_74 TMP_77) in (let TMP_79 \def (eq_ind_r T TMP_43 TMP_56 TMP_78 u
553 H2) in (let TMP_80 \def (eq_ind_r T TMP_31 TMP_42 TMP_79 t H3) in (eq_ind_r T
554 TMP_20 TMP_29 TMP_80 x H1)))))))))))))))))))))))))))) in (ex3_2_ind T T TMP_4
555 TMP_6 TMP_9 TMP_18 TMP_81 H0)))))))))))))))))).
557 theorem lift_gen_flat:
558 \forall (f: F).(\forall (u: T).(\forall (t: T).(\forall (x: T).(\forall (h:
559 nat).(\forall (d: nat).((eq T (THead (Flat f) u t) (lift h d x)) \to (ex3_2 T
560 T (\lambda (y: T).(\lambda (z: T).(eq T x (THead (Flat f) y z)))) (\lambda
561 (y: T).(\lambda (_: T).(eq T u (lift h d y)))) (\lambda (_: T).(\lambda (z:
562 T).(eq T t (lift h d z)))))))))))
564 \lambda (f: F).(\lambda (u: T).(\lambda (t: T).(\lambda (x: T).(\lambda (h:
565 nat).(\lambda (d: nat).(\lambda (H: (eq T (THead (Flat f) u t) (lift h d
566 x))).(let TMP_1 \def (Flat f) in (let H_x \def (lift_gen_head TMP_1 u t x h d
567 H) in (let H0 \def H_x in (let TMP_4 \def (\lambda (y: T).(\lambda (z:
568 T).(let TMP_2 \def (Flat f) in (let TMP_3 \def (THead TMP_2 y z) in (eq T x
569 TMP_3))))) in (let TMP_6 \def (\lambda (y: T).(\lambda (_: T).(let TMP_5 \def
570 (lift h d y) in (eq T u TMP_5)))) in (let TMP_8 \def (\lambda (_: T).(\lambda
571 (z: T).(let TMP_7 \def (lift h d z) in (eq T t TMP_7)))) in (let TMP_11 \def
572 (\lambda (y: T).(\lambda (z: T).(let TMP_9 \def (Flat f) in (let TMP_10 \def
573 (THead TMP_9 y z) in (eq T x TMP_10))))) in (let TMP_13 \def (\lambda (y:
574 T).(\lambda (_: T).(let TMP_12 \def (lift h d y) in (eq T u TMP_12)))) in
575 (let TMP_15 \def (\lambda (_: T).(\lambda (z: T).(let TMP_14 \def (lift h d
576 z) in (eq T t TMP_14)))) in (let TMP_16 \def (ex3_2 T T TMP_11 TMP_13 TMP_15)
577 in (let TMP_71 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: (eq T x
578 (THead (Flat f) x0 x1))).(\lambda (H2: (eq T u (lift h d x0))).(\lambda (H3:
579 (eq T t (lift h d x1))).(let TMP_17 \def (Flat f) in (let TMP_18 \def (THead
580 TMP_17 x0 x1) in (let TMP_26 \def (\lambda (t0: T).(let TMP_21 \def (\lambda
581 (y: T).(\lambda (z: T).(let TMP_19 \def (Flat f) in (let TMP_20 \def (THead
582 TMP_19 y z) in (eq T t0 TMP_20))))) in (let TMP_23 \def (\lambda (y:
583 T).(\lambda (_: T).(let TMP_22 \def (lift h d y) in (eq T u TMP_22)))) in
584 (let TMP_25 \def (\lambda (_: T).(\lambda (z: T).(let TMP_24 \def (lift h d
585 z) in (eq T t TMP_24)))) in (ex3_2 T T TMP_21 TMP_23 TMP_25))))) in (let
586 TMP_27 \def (lift h d x1) in (let TMP_37 \def (\lambda (t0: T).(let TMP_32
587 \def (\lambda (y: T).(\lambda (z: T).(let TMP_28 \def (Flat f) in (let TMP_29
588 \def (THead TMP_28 x0 x1) in (let TMP_30 \def (Flat f) in (let TMP_31 \def
589 (THead TMP_30 y z) in (eq T TMP_29 TMP_31))))))) in (let TMP_34 \def (\lambda
590 (y: T).(\lambda (_: T).(let TMP_33 \def (lift h d y) in (eq T u TMP_33)))) in
591 (let TMP_36 \def (\lambda (_: T).(\lambda (z: T).(let TMP_35 \def (lift h d
592 z) in (eq T t0 TMP_35)))) in (ex3_2 T T TMP_32 TMP_34 TMP_36))))) in (let
593 TMP_38 \def (lift h d x0) in (let TMP_49 \def (\lambda (t0: T).(let TMP_43
594 \def (\lambda (y: T).(\lambda (z: T).(let TMP_39 \def (Flat f) in (let TMP_40
595 \def (THead TMP_39 x0 x1) in (let TMP_41 \def (Flat f) in (let TMP_42 \def
596 (THead TMP_41 y z) in (eq T TMP_40 TMP_42))))))) in (let TMP_45 \def (\lambda
597 (y: T).(\lambda (_: T).(let TMP_44 \def (lift h d y) in (eq T t0 TMP_44))))
598 in (let TMP_48 \def (\lambda (_: T).(\lambda (z: T).(let TMP_46 \def (lift h
599 d x1) in (let TMP_47 \def (lift h d z) in (eq T TMP_46 TMP_47))))) in (ex3_2
600 T T TMP_43 TMP_45 TMP_48))))) in (let TMP_54 \def (\lambda (y: T).(\lambda
601 (z: T).(let TMP_50 \def (Flat f) in (let TMP_51 \def (THead TMP_50 x0 x1) in
602 (let TMP_52 \def (Flat f) in (let TMP_53 \def (THead TMP_52 y z) in (eq T
603 TMP_51 TMP_53))))))) in (let TMP_57 \def (\lambda (y: T).(\lambda (_: T).(let
604 TMP_55 \def (lift h d x0) in (let TMP_56 \def (lift h d y) in (eq T TMP_55
605 TMP_56))))) in (let TMP_60 \def (\lambda (_: T).(\lambda (z: T).(let TMP_58
606 \def (lift h d x1) in (let TMP_59 \def (lift h d z) in (eq T TMP_58
607 TMP_59))))) in (let TMP_61 \def (Flat f) in (let TMP_62 \def (THead TMP_61 x0
608 x1) in (let TMP_63 \def (refl_equal T TMP_62) in (let TMP_64 \def (lift h d
609 x0) in (let TMP_65 \def (refl_equal T TMP_64) in (let TMP_66 \def (lift h d
610 x1) in (let TMP_67 \def (refl_equal T TMP_66) in (let TMP_68 \def
611 (ex3_2_intro T T TMP_54 TMP_57 TMP_60 x0 x1 TMP_63 TMP_65 TMP_67) in (let
612 TMP_69 \def (eq_ind_r T TMP_38 TMP_49 TMP_68 u H2) in (let TMP_70 \def
613 (eq_ind_r T TMP_27 TMP_37 TMP_69 t H3) in (eq_ind_r T TMP_18 TMP_26 TMP_70 x
614 H1)))))))))))))))))))))))))) in (ex3_2_ind T T TMP_4 TMP_6 TMP_8 TMP_16
615 TMP_71 H0)))))))))))))))))).
618 \forall (x: T).(\forall (t: T).(\forall (h: nat).(\forall (d: nat).((eq T
619 (lift h d x) (lift h d t)) \to (eq T x t)))))
621 \lambda (x: T).(let TMP_1 \def (\lambda (t: T).(\forall (t0: T).(\forall (h:
622 nat).(\forall (d: nat).((eq T (lift h d t) (lift h d t0)) \to (eq T t
623 t0)))))) in (let TMP_10 \def (\lambda (n: nat).(\lambda (t: T).(\lambda (h:
624 nat).(\lambda (d: nat).(\lambda (H: (eq T (lift h d (TSort n)) (lift h d
625 t))).(let TMP_2 \def (TSort n) in (let TMP_3 \def (lift h d TMP_2) in (let
626 TMP_5 \def (\lambda (t0: T).(let TMP_4 \def (lift h d t) in (eq T t0 TMP_4)))
627 in (let TMP_6 \def (TSort n) in (let TMP_7 \def (lift_sort n h d) in (let H0
628 \def (eq_ind T TMP_3 TMP_5 H TMP_6 TMP_7) in (let TMP_8 \def (TSort n) in
629 (let TMP_9 \def (lift_gen_sort h d n t H0) in (sym_eq T t TMP_8
630 TMP_9)))))))))))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda (t:
631 T).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H: (eq T (lift h d (TLRef
632 n)) (lift h d t))).(let TMP_11 \def (TLRef n) in (let TMP_12 \def (eq T
633 TMP_11 t) in (let TMP_23 \def (\lambda (H0: (lt n d)).(let TMP_13 \def (TLRef
634 n) in (let TMP_14 \def (lift h d TMP_13) in (let TMP_16 \def (\lambda (t0:
635 T).(let TMP_15 \def (lift h d t) in (eq T t0 TMP_15))) in (let TMP_17 \def
636 (TLRef n) in (let TMP_18 \def (lift_lref_lt n h d H0) in (let H1 \def (eq_ind
637 T TMP_14 TMP_16 H TMP_17 TMP_18) in (let TMP_19 \def (TLRef n) in (let TMP_20
638 \def (le_n d) in (let TMP_21 \def (lt_le_trans n d d H0 TMP_20) in (let
639 TMP_22 \def (lift_gen_lref_lt h d n TMP_21 t H1) in (sym_eq T t TMP_19
640 TMP_22)))))))))))) in (let TMP_33 \def (\lambda (H0: (le d n)).(let TMP_24
641 \def (TLRef n) in (let TMP_25 \def (lift h d TMP_24) in (let TMP_27 \def
642 (\lambda (t0: T).(let TMP_26 \def (lift h d t) in (eq T t0 TMP_26))) in (let
643 TMP_28 \def (plus n h) in (let TMP_29 \def (TLRef TMP_28) in (let TMP_30 \def
644 (lift_lref_ge n h d H0) in (let H1 \def (eq_ind T TMP_25 TMP_27 H TMP_29
645 TMP_30) in (let TMP_31 \def (TLRef n) in (let TMP_32 \def (lift_gen_lref_ge h
646 d n H0 t H1) in (sym_eq T t TMP_31 TMP_32))))))))))) in (lt_le_e n d TMP_12
647 TMP_23 TMP_33)))))))))) in (let TMP_140 \def (\lambda (k: K).(let TMP_36 \def
648 (\lambda (k0: K).(\forall (t: T).(((\forall (t0: T).(\forall (h:
649 nat).(\forall (d: nat).((eq T (lift h d t) (lift h d t0)) \to (eq T t
650 t0)))))) \to (\forall (t0: T).(((\forall (t1: T).(\forall (h: nat).(\forall
651 (d: nat).((eq T (lift h d t0) (lift h d t1)) \to (eq T t0 t1)))))) \to
652 (\forall (t1: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d (THead
653 k0 t t0)) (lift h d t1)) \to (let TMP_35 \def (THead k0 t t0) in (eq T TMP_35
654 t1))))))))))) in (let TMP_90 \def (\lambda (b: B).(\lambda (t: T).(\lambda
655 (H: ((\forall (t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t)
656 (lift h d t0)) \to (eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall
657 (t1: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d
658 t1)) \to (eq T t0 t1))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d:
659 nat).(\lambda (H1: (eq T (lift h d (THead (Bind b) t t0)) (lift h d
660 t1))).(let TMP_37 \def (Bind b) in (let TMP_38 \def (THead TMP_37 t t0) in
661 (let TMP_39 \def (lift h d TMP_38) in (let TMP_41 \def (\lambda (t2: T).(let
662 TMP_40 \def (lift h d t1) in (eq T t2 TMP_40))) in (let TMP_42 \def (Bind b)
663 in (let TMP_43 \def (lift h d t) in (let TMP_44 \def (S d) in (let TMP_45
664 \def (lift h TMP_44 t0) in (let TMP_46 \def (THead TMP_42 TMP_43 TMP_45) in
665 (let TMP_47 \def (lift_bind b t t0 h d) in (let H2 \def (eq_ind T TMP_39
666 TMP_41 H1 TMP_46 TMP_47) in (let TMP_50 \def (\lambda (y: T).(\lambda (z:
667 T).(let TMP_48 \def (Bind b) in (let TMP_49 \def (THead TMP_48 y z) in (eq T
668 t1 TMP_49))))) in (let TMP_53 \def (\lambda (y: T).(\lambda (_: T).(let
669 TMP_51 \def (lift h d t) in (let TMP_52 \def (lift h d y) in (eq T TMP_51
670 TMP_52))))) in (let TMP_58 \def (\lambda (_: T).(\lambda (z: T).(let TMP_54
671 \def (S d) in (let TMP_55 \def (lift h TMP_54 t0) in (let TMP_56 \def (S d)
672 in (let TMP_57 \def (lift h TMP_56 z) in (eq T TMP_55 TMP_57))))))) in (let
673 TMP_59 \def (Bind b) in (let TMP_60 \def (THead TMP_59 t t0) in (let TMP_61
674 \def (eq T TMP_60 t1) in (let TMP_85 \def (\lambda (x0: T).(\lambda (x1:
675 T).(\lambda (H3: (eq T t1 (THead (Bind b) x0 x1))).(\lambda (H4: (eq T (lift
676 h d t) (lift h d x0))).(\lambda (H5: (eq T (lift h (S d) t0) (lift h (S d)
677 x1))).(let TMP_62 \def (Bind b) in (let TMP_63 \def (THead TMP_62 x0 x1) in
678 (let TMP_66 \def (\lambda (t2: T).(let TMP_64 \def (Bind b) in (let TMP_65
679 \def (THead TMP_64 t t0) in (eq T TMP_65 t2)))) in (let TMP_67 \def (Bind b)
680 in (let TMP_68 \def (THead TMP_67 x0 x1) in (let TMP_69 \def (Bind b) in (let
681 TMP_70 \def (THead TMP_69 t t0) in (let TMP_71 \def (Bind b) in (let TMP_72
682 \def (THead TMP_71 t t0) in (let TMP_73 \def (Bind b) in (let TMP_74 \def
683 (THead TMP_73 x0 x1) in (let TMP_75 \def (Bind b) in (let TMP_76 \def (Bind
684 b) in (let TMP_77 \def (Bind b) in (let TMP_78 \def (refl_equal K TMP_77) in
685 (let TMP_79 \def (H x0 h d H4) in (let TMP_80 \def (S d) in (let TMP_81 \def
686 (H0 x1 h TMP_80 H5) in (let TMP_82 \def (f_equal3 K T T T THead TMP_75 TMP_76
687 t x0 t0 x1 TMP_78 TMP_79 TMP_81) in (let TMP_83 \def (sym_eq T TMP_72 TMP_74
688 TMP_82) in (let TMP_84 \def (sym_eq T TMP_68 TMP_70 TMP_83) in (eq_ind_r T
689 TMP_63 TMP_66 TMP_84 t1 H3))))))))))))))))))))))))))) in (let TMP_86 \def
690 (lift h d t) in (let TMP_87 \def (S d) in (let TMP_88 \def (lift h TMP_87 t0)
691 in (let TMP_89 \def (lift_gen_bind b TMP_86 TMP_88 t1 h d H2) in (ex3_2_ind T
692 T TMP_50 TMP_53 TMP_58 TMP_61 TMP_85 TMP_89))))))))))))))))))))))))))))))))
693 in (let TMP_139 \def (\lambda (f: F).(\lambda (t: T).(\lambda (H: ((\forall
694 (t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t) (lift h d
695 t0)) \to (eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (t1:
696 T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t1))
697 \to (eq T t0 t1))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d:
698 nat).(\lambda (H1: (eq T (lift h d (THead (Flat f) t t0)) (lift h d
699 t1))).(let TMP_91 \def (Flat f) in (let TMP_92 \def (THead TMP_91 t t0) in
700 (let TMP_93 \def (lift h d TMP_92) in (let TMP_95 \def (\lambda (t2: T).(let
701 TMP_94 \def (lift h d t1) in (eq T t2 TMP_94))) in (let TMP_96 \def (Flat f)
702 in (let TMP_97 \def (lift h d t) in (let TMP_98 \def (lift h d t0) in (let
703 TMP_99 \def (THead TMP_96 TMP_97 TMP_98) in (let TMP_100 \def (lift_flat f t
704 t0 h d) in (let H2 \def (eq_ind T TMP_93 TMP_95 H1 TMP_99 TMP_100) in (let
705 TMP_103 \def (\lambda (y: T).(\lambda (z: T).(let TMP_101 \def (Flat f) in
706 (let TMP_102 \def (THead TMP_101 y z) in (eq T t1 TMP_102))))) in (let
707 TMP_106 \def (\lambda (y: T).(\lambda (_: T).(let TMP_104 \def (lift h d t)
708 in (let TMP_105 \def (lift h d y) in (eq T TMP_104 TMP_105))))) in (let
709 TMP_109 \def (\lambda (_: T).(\lambda (z: T).(let TMP_107 \def (lift h d t0)
710 in (let TMP_108 \def (lift h d z) in (eq T TMP_107 TMP_108))))) in (let
711 TMP_110 \def (Flat f) in (let TMP_111 \def (THead TMP_110 t t0) in (let
712 TMP_112 \def (eq T TMP_111 t1) in (let TMP_135 \def (\lambda (x0: T).(\lambda
713 (x1: T).(\lambda (H3: (eq T t1 (THead (Flat f) x0 x1))).(\lambda (H4: (eq T
714 (lift h d t) (lift h d x0))).(\lambda (H5: (eq T (lift h d t0) (lift h d
715 x1))).(let TMP_113 \def (Flat f) in (let TMP_114 \def (THead TMP_113 x0 x1)
716 in (let TMP_117 \def (\lambda (t2: T).(let TMP_115 \def (Flat f) in (let
717 TMP_116 \def (THead TMP_115 t t0) in (eq T TMP_116 t2)))) in (let TMP_118
718 \def (Flat f) in (let TMP_119 \def (THead TMP_118 x0 x1) in (let TMP_120 \def
719 (Flat f) in (let TMP_121 \def (THead TMP_120 t t0) in (let TMP_122 \def (Flat
720 f) in (let TMP_123 \def (THead TMP_122 t t0) in (let TMP_124 \def (Flat f) in
721 (let TMP_125 \def (THead TMP_124 x0 x1) in (let TMP_126 \def (Flat f) in (let
722 TMP_127 \def (Flat f) in (let TMP_128 \def (Flat f) in (let TMP_129 \def
723 (refl_equal K TMP_128) in (let TMP_130 \def (H x0 h d H4) in (let TMP_131
724 \def (H0 x1 h d H5) in (let TMP_132 \def (f_equal3 K T T T THead TMP_126
725 TMP_127 t x0 t0 x1 TMP_129 TMP_130 TMP_131) in (let TMP_133 \def (sym_eq T
726 TMP_123 TMP_125 TMP_132) in (let TMP_134 \def (sym_eq T TMP_119 TMP_121
727 TMP_133) in (eq_ind_r T TMP_114 TMP_117 TMP_134 t1
728 H3)))))))))))))))))))))))))) in (let TMP_136 \def (lift h d t) in (let
729 TMP_137 \def (lift h d t0) in (let TMP_138 \def (lift_gen_flat f TMP_136
730 TMP_137 t1 h d H2) in (ex3_2_ind T T TMP_103 TMP_106 TMP_109 TMP_112 TMP_135
731 TMP_138)))))))))))))))))))))))))))))) in (K_ind TMP_36 TMP_90 TMP_139 k)))))
732 in (T_ind TMP_1 TMP_10 TMP_34 TMP_140 x))))).
734 theorem lift_gen_lift:
735 \forall (t1: T).(\forall (x: T).(\forall (h1: nat).(\forall (h2:
736 nat).(\forall (d1: nat).(\forall (d2: nat).((le d1 d2) \to ((eq T (lift h1 d1
737 t1) (lift h2 (plus d2 h1) x)) \to (ex2 T (\lambda (t2: T).(eq T x (lift h1 d1
738 t2))) (\lambda (t2: T).(eq T t1 (lift h2 d2 t2)))))))))))
740 \lambda (t1: T).(let TMP_5 \def (\lambda (t: T).(\forall (x: T).(\forall
741 (h1: nat).(\forall (h2: nat).(\forall (d1: nat).(\forall (d2: nat).((le d1
742 d2) \to ((eq T (lift h1 d1 t) (lift h2 (plus d2 h1) x)) \to (let TMP_2 \def
743 (\lambda (t2: T).(let TMP_1 \def (lift h1 d1 t2) in (eq T x TMP_1))) in (let
744 TMP_4 \def (\lambda (t2: T).(let TMP_3 \def (lift h2 d2 t2) in (eq T t
745 TMP_3))) in (ex2 T TMP_2 TMP_4))))))))))) in (let TMP_48 \def (\lambda (n:
746 nat).(\lambda (x: T).(\lambda (h1: nat).(\lambda (h2: nat).(\lambda (d1:
747 nat).(\lambda (d2: nat).(\lambda (_: (le d1 d2)).(\lambda (H0: (eq T (lift h1
748 d1 (TSort n)) (lift h2 (plus d2 h1) x))).(let TMP_6 \def (TSort n) in (let
749 TMP_7 \def (lift h1 d1 TMP_6) in (let TMP_10 \def (\lambda (t: T).(let TMP_8
750 \def (plus d2 h1) in (let TMP_9 \def (lift h2 TMP_8 x) in (eq T t TMP_9))))
751 in (let TMP_11 \def (TSort n) in (let TMP_12 \def (lift_sort n h1 d1) in (let
752 H1 \def (eq_ind T TMP_7 TMP_10 H0 TMP_11 TMP_12) in (let TMP_13 \def (TSort
753 n) in (let TMP_19 \def (\lambda (t: T).(let TMP_15 \def (\lambda (t2: T).(let
754 TMP_14 \def (lift h1 d1 t2) in (eq T t TMP_14))) in (let TMP_18 \def (\lambda
755 (t2: T).(let TMP_16 \def (TSort n) in (let TMP_17 \def (lift h2 d2 t2) in (eq
756 T TMP_16 TMP_17)))) in (ex2 T TMP_15 TMP_18)))) in (let TMP_22 \def (\lambda
757 (t2: T).(let TMP_20 \def (TSort n) in (let TMP_21 \def (lift h1 d1 t2) in (eq
758 T TMP_20 TMP_21)))) in (let TMP_25 \def (\lambda (t2: T).(let TMP_23 \def
759 (TSort n) in (let TMP_24 \def (lift h2 d2 t2) in (eq T TMP_23 TMP_24)))) in
760 (let TMP_26 \def (TSort n) in (let TMP_27 \def (TSort n) in (let TMP_29 \def
761 (\lambda (t: T).(let TMP_28 \def (TSort n) in (eq T TMP_28 t))) in (let
762 TMP_30 \def (TSort n) in (let TMP_31 \def (refl_equal T TMP_30) in (let
763 TMP_32 \def (TSort n) in (let TMP_33 \def (lift h1 d1 TMP_32) in (let TMP_34
764 \def (lift_sort n h1 d1) in (let TMP_35 \def (eq_ind_r T TMP_27 TMP_29 TMP_31
765 TMP_33 TMP_34) in (let TMP_36 \def (TSort n) in (let TMP_38 \def (\lambda (t:
766 T).(let TMP_37 \def (TSort n) in (eq T TMP_37 t))) in (let TMP_39 \def (TSort
767 n) in (let TMP_40 \def (refl_equal T TMP_39) in (let TMP_41 \def (TSort n) in
768 (let TMP_42 \def (lift h2 d2 TMP_41) in (let TMP_43 \def (lift_sort n h2 d2)
769 in (let TMP_44 \def (eq_ind_r T TMP_36 TMP_38 TMP_40 TMP_42 TMP_43) in (let
770 TMP_45 \def (ex_intro2 T TMP_22 TMP_25 TMP_26 TMP_35 TMP_44) in (let TMP_46
771 \def (plus d2 h1) in (let TMP_47 \def (lift_gen_sort h2 TMP_46 n x H1) in
772 (eq_ind_r T TMP_13 TMP_19 TMP_45 x
773 TMP_47))))))))))))))))))))))))))))))))))))))) in (let TMP_325 \def (\lambda
774 (n: nat).(\lambda (x: T).(\lambda (h1: nat).(\lambda (h2: nat).(\lambda (d1:
775 nat).(\lambda (d2: nat).(\lambda (H: (le d1 d2)).(\lambda (H0: (eq T (lift h1
776 d1 (TLRef n)) (lift h2 (plus d2 h1) x))).(let TMP_50 \def (\lambda (t2:
777 T).(let TMP_49 \def (lift h1 d1 t2) in (eq T x TMP_49))) in (let TMP_53 \def
778 (\lambda (t2: T).(let TMP_51 \def (TLRef n) in (let TMP_52 \def (lift h2 d2
779 t2) in (eq T TMP_51 TMP_52)))) in (let TMP_54 \def (ex2 T TMP_50 TMP_53) in
780 (let TMP_101 \def (\lambda (H1: (lt n d1)).(let TMP_55 \def (TLRef n) in (let
781 TMP_56 \def (lift h1 d1 TMP_55) in (let TMP_59 \def (\lambda (t: T).(let
782 TMP_57 \def (plus d2 h1) in (let TMP_58 \def (lift h2 TMP_57 x) in (eq T t
783 TMP_58)))) in (let TMP_60 \def (TLRef n) in (let TMP_61 \def (lift_lref_lt n
784 h1 d1 H1) in (let H2 \def (eq_ind T TMP_56 TMP_59 H0 TMP_60 TMP_61) in (let
785 TMP_62 \def (TLRef n) in (let TMP_68 \def (\lambda (t: T).(let TMP_64 \def
786 (\lambda (t2: T).(let TMP_63 \def (lift h1 d1 t2) in (eq T t TMP_63))) in
787 (let TMP_67 \def (\lambda (t2: T).(let TMP_65 \def (TLRef n) in (let TMP_66
788 \def (lift h2 d2 t2) in (eq T TMP_65 TMP_66)))) in (ex2 T TMP_64 TMP_67))))
789 in (let TMP_71 \def (\lambda (t2: T).(let TMP_69 \def (TLRef n) in (let
790 TMP_70 \def (lift h1 d1 t2) in (eq T TMP_69 TMP_70)))) in (let TMP_74 \def
791 (\lambda (t2: T).(let TMP_72 \def (TLRef n) in (let TMP_73 \def (lift h2 d2
792 t2) in (eq T TMP_72 TMP_73)))) in (let TMP_75 \def (TLRef n) in (let TMP_76
793 \def (TLRef n) in (let TMP_78 \def (\lambda (t: T).(let TMP_77 \def (TLRef n)
794 in (eq T TMP_77 t))) in (let TMP_79 \def (TLRef n) in (let TMP_80 \def
795 (refl_equal T TMP_79) in (let TMP_81 \def (TLRef n) in (let TMP_82 \def (lift
796 h1 d1 TMP_81) in (let TMP_83 \def (lift_lref_lt n h1 d1 H1) in (let TMP_84
797 \def (eq_ind_r T TMP_76 TMP_78 TMP_80 TMP_82 TMP_83) in (let TMP_85 \def
798 (TLRef n) in (let TMP_87 \def (\lambda (t: T).(let TMP_86 \def (TLRef n) in
799 (eq T TMP_86 t))) in (let TMP_88 \def (TLRef n) in (let TMP_89 \def
800 (refl_equal T TMP_88) in (let TMP_90 \def (TLRef n) in (let TMP_91 \def (lift
801 h2 d2 TMP_90) in (let TMP_92 \def (lt_le_trans n d1 d2 H1 H) in (let TMP_93
802 \def (lift_lref_lt n h2 d2 TMP_92) in (let TMP_94 \def (eq_ind_r T TMP_85
803 TMP_87 TMP_89 TMP_91 TMP_93) in (let TMP_95 \def (ex_intro2 T TMP_71 TMP_74
804 TMP_75 TMP_84 TMP_94) in (let TMP_96 \def (plus d2 h1) in (let TMP_97 \def
805 (plus d2 h1) in (let TMP_98 \def (le_plus_trans d1 d2 h1 H) in (let TMP_99
806 \def (lt_le_trans n d1 TMP_97 H1 TMP_98) in (let TMP_100 \def
807 (lift_gen_lref_lt h2 TMP_96 n TMP_99 x H2) in (eq_ind_r T TMP_62 TMP_68
808 TMP_95 x TMP_100)))))))))))))))))))))))))))))))))))) in (let TMP_324 \def
809 (\lambda (H1: (le d1 n)).(let TMP_102 \def (TLRef n) in (let TMP_103 \def
810 (lift h1 d1 TMP_102) in (let TMP_106 \def (\lambda (t: T).(let TMP_104 \def
811 (plus d2 h1) in (let TMP_105 \def (lift h2 TMP_104 x) in (eq T t TMP_105))))
812 in (let TMP_107 \def (plus n h1) in (let TMP_108 \def (TLRef TMP_107) in (let
813 TMP_109 \def (lift_lref_ge n h1 d1 H1) in (let H2 \def (eq_ind T TMP_103
814 TMP_106 H0 TMP_108 TMP_109) in (let TMP_111 \def (\lambda (t2: T).(let
815 TMP_110 \def (lift h1 d1 t2) in (eq T x TMP_110))) in (let TMP_114 \def
816 (\lambda (t2: T).(let TMP_112 \def (TLRef n) in (let TMP_113 \def (lift h2 d2
817 t2) in (eq T TMP_112 TMP_113)))) in (let TMP_115 \def (ex2 T TMP_111 TMP_114)
818 in (let TMP_158 \def (\lambda (H3: (lt n d2)).(let TMP_116 \def (plus n h1)
819 in (let TMP_117 \def (TLRef TMP_116) in (let TMP_123 \def (\lambda (t:
820 T).(let TMP_119 \def (\lambda (t2: T).(let TMP_118 \def (lift h1 d1 t2) in
821 (eq T t TMP_118))) in (let TMP_122 \def (\lambda (t2: T).(let TMP_120 \def
822 (TLRef n) in (let TMP_121 \def (lift h2 d2 t2) in (eq T TMP_120 TMP_121))))
823 in (ex2 T TMP_119 TMP_122)))) in (let TMP_127 \def (\lambda (t2: T).(let
824 TMP_124 \def (plus n h1) in (let TMP_125 \def (TLRef TMP_124) in (let TMP_126
825 \def (lift h1 d1 t2) in (eq T TMP_125 TMP_126))))) in (let TMP_130 \def
826 (\lambda (t2: T).(let TMP_128 \def (TLRef n) in (let TMP_129 \def (lift h2 d2
827 t2) in (eq T TMP_128 TMP_129)))) in (let TMP_131 \def (TLRef n) in (let
828 TMP_132 \def (plus n h1) in (let TMP_133 \def (TLRef TMP_132) in (let TMP_136
829 \def (\lambda (t: T).(let TMP_134 \def (plus n h1) in (let TMP_135 \def
830 (TLRef TMP_134) in (eq T TMP_135 t)))) in (let TMP_137 \def (plus n h1) in
831 (let TMP_138 \def (TLRef TMP_137) in (let TMP_139 \def (refl_equal T TMP_138)
832 in (let TMP_140 \def (TLRef n) in (let TMP_141 \def (lift h1 d1 TMP_140) in
833 (let TMP_142 \def (lift_lref_ge n h1 d1 H1) in (let TMP_143 \def (eq_ind_r T
834 TMP_133 TMP_136 TMP_139 TMP_141 TMP_142) in (let TMP_144 \def (TLRef n) in
835 (let TMP_146 \def (\lambda (t: T).(let TMP_145 \def (TLRef n) in (eq T
836 TMP_145 t))) in (let TMP_147 \def (TLRef n) in (let TMP_148 \def (refl_equal
837 T TMP_147) in (let TMP_149 \def (TLRef n) in (let TMP_150 \def (lift h2 d2
838 TMP_149) in (let TMP_151 \def (lift_lref_lt n h2 d2 H3) in (let TMP_152 \def
839 (eq_ind_r T TMP_144 TMP_146 TMP_148 TMP_150 TMP_151) in (let TMP_153 \def
840 (ex_intro2 T TMP_127 TMP_130 TMP_131 TMP_143 TMP_152) in (let TMP_154 \def
841 (plus d2 h1) in (let TMP_155 \def (plus n h1) in (let TMP_156 \def (lt_reg_r
842 n d2 h1 H3) in (let TMP_157 \def (lift_gen_lref_lt h2 TMP_154 TMP_155 TMP_156
843 x H2) in (eq_ind_r T TMP_117 TMP_123 TMP_153 x
844 TMP_157))))))))))))))))))))))))))))))) in (let TMP_323 \def (\lambda (H3: (le
845 d2 n)).(let TMP_159 \def (plus d2 h2) in (let TMP_161 \def (\lambda (t2:
846 T).(let TMP_160 \def (lift h1 d1 t2) in (eq T x TMP_160))) in (let TMP_164
847 \def (\lambda (t2: T).(let TMP_162 \def (TLRef n) in (let TMP_163 \def (lift
848 h2 d2 t2) in (eq T TMP_162 TMP_163)))) in (let TMP_165 \def (ex2 T TMP_161
849 TMP_164) in (let TMP_186 \def (\lambda (H4: (lt n (plus d2 h2))).(let TMP_166
850 \def (plus d2 h1) in (let TMP_167 \def (plus n h1) in (let TMP_168 \def (le_n
851 h1) in (let TMP_169 \def (le_plus_plus d2 n h1 h1 H3 TMP_168) in (let TMP_170
852 \def (plus d2 h2) in (let TMP_171 \def (plus TMP_170 h1) in (let TMP_173 \def
853 (\lambda (n0: nat).(let TMP_172 \def (plus n h1) in (lt TMP_172 n0))) in (let
854 TMP_174 \def (plus d2 h2) in (let TMP_175 \def (lt_reg_r n TMP_174 h1 H4) in
855 (let TMP_176 \def (plus d2 h1) in (let TMP_177 \def (plus TMP_176 h2) in (let
856 TMP_178 \def (plus_permute_2_in_3 d2 h1 h2) in (let TMP_179 \def (eq_ind_r
857 nat TMP_171 TMP_173 TMP_175 TMP_177 TMP_178) in (let TMP_181 \def (\lambda
858 (t2: T).(let TMP_180 \def (lift h1 d1 t2) in (eq T x TMP_180))) in (let
859 TMP_184 \def (\lambda (t2: T).(let TMP_182 \def (TLRef n) in (let TMP_183
860 \def (lift h2 d2 t2) in (eq T TMP_182 TMP_183)))) in (let TMP_185 \def (ex2 T
861 TMP_181 TMP_184) in (lift_gen_lref_false h2 TMP_166 TMP_167 TMP_169 TMP_179 x
862 H2 TMP_185)))))))))))))))))) in (let TMP_322 \def (\lambda (H4: (le (plus d2
863 h2) n)).(let TMP_187 \def (plus n h1) in (let TMP_191 \def (\lambda (n0:
864 nat).(let TMP_188 \def (TLRef n0) in (let TMP_189 \def (plus d2 h1) in (let
865 TMP_190 \def (lift h2 TMP_189 x) in (eq T TMP_188 TMP_190))))) in (let
866 TMP_192 \def (plus n h1) in (let TMP_193 \def (minus TMP_192 h2) in (let
867 TMP_194 \def (plus TMP_193 h2) in (let TMP_195 \def (plus n h1) in (let
868 TMP_196 \def (plus d2 h2) in (let TMP_197 \def (le_plus_r d2 h2) in (let
869 TMP_198 \def (le_trans h2 TMP_196 n TMP_197 H4) in (let TMP_199 \def
870 (le_plus_trans h2 n h1 TMP_198) in (let TMP_200 \def (le_plus_minus_sym h2
871 TMP_195 TMP_199) in (let H5 \def (eq_ind nat TMP_187 TMP_191 H2 TMP_194
872 TMP_200) in (let TMP_201 \def (plus n h1) in (let TMP_202 \def (minus TMP_201
873 h2) in (let TMP_203 \def (TLRef TMP_202) in (let TMP_209 \def (\lambda (t:
874 T).(let TMP_205 \def (\lambda (t2: T).(let TMP_204 \def (lift h1 d1 t2) in
875 (eq T t TMP_204))) in (let TMP_208 \def (\lambda (t2: T).(let TMP_206 \def
876 (TLRef n) in (let TMP_207 \def (lift h2 d2 t2) in (eq T TMP_206 TMP_207))))
877 in (ex2 T TMP_205 TMP_208)))) in (let TMP_214 \def (\lambda (t2: T).(let
878 TMP_210 \def (plus n h1) in (let TMP_211 \def (minus TMP_210 h2) in (let
879 TMP_212 \def (TLRef TMP_211) in (let TMP_213 \def (lift h1 d1 t2) in (eq T
880 TMP_212 TMP_213)))))) in (let TMP_217 \def (\lambda (t2: T).(let TMP_215 \def
881 (TLRef n) in (let TMP_216 \def (lift h2 d2 t2) in (eq T TMP_215 TMP_216))))
882 in (let TMP_218 \def (minus n h2) in (let TMP_219 \def (TLRef TMP_218) in
883 (let TMP_220 \def (minus n h2) in (let TMP_221 \def (plus TMP_220 h1) in (let
884 TMP_226 \def (\lambda (n0: nat).(let TMP_222 \def (TLRef n0) in (let TMP_223
885 \def (minus n h2) in (let TMP_224 \def (TLRef TMP_223) in (let TMP_225 \def
886 (lift h1 d1 TMP_224) in (eq T TMP_222 TMP_225)))))) in (let TMP_227 \def
887 (minus n h2) in (let TMP_228 \def (plus TMP_227 h1) in (let TMP_229 \def
888 (TLRef TMP_228) in (let TMP_233 \def (\lambda (t: T).(let TMP_230 \def (minus
889 n h2) in (let TMP_231 \def (plus TMP_230 h1) in (let TMP_232 \def (TLRef
890 TMP_231) in (eq T TMP_232 t))))) in (let TMP_234 \def (minus n h2) in (let
891 TMP_235 \def (plus TMP_234 h1) in (let TMP_236 \def (TLRef TMP_235) in (let
892 TMP_237 \def (refl_equal T TMP_236) in (let TMP_238 \def (minus n h2) in (let
893 TMP_239 \def (TLRef TMP_238) in (let TMP_240 \def (lift h1 d1 TMP_239) in
894 (let TMP_241 \def (minus n h2) in (let TMP_242 \def (minus n h2) in (let
895 TMP_243 \def (le_minus d2 n h2 H4) in (let TMP_244 \def (le_trans d1 d2
896 TMP_242 H TMP_243) in (let TMP_245 \def (lift_lref_ge TMP_241 h1 d1 TMP_244)
897 in (let TMP_246 \def (eq_ind_r T TMP_229 TMP_233 TMP_237 TMP_240 TMP_245) in
898 (let TMP_247 \def (plus n h1) in (let TMP_248 \def (minus TMP_247 h2) in (let
899 TMP_249 \def (plus d2 h2) in (let TMP_250 \def (le_plus_r d2 h2) in (let
900 TMP_251 \def (le_trans h2 TMP_249 n TMP_250 H4) in (let TMP_252 \def
901 (le_minus_plus h2 n TMP_251 h1) in (let TMP_253 \def (eq_ind_r nat TMP_221
902 TMP_226 TMP_246 TMP_248 TMP_252) in (let TMP_254 \def (minus n h2) in (let
903 TMP_255 \def (plus TMP_254 h2) in (let TMP_260 \def (\lambda (n0: nat).(let
904 TMP_256 \def (TLRef n0) in (let TMP_257 \def (minus n0 h2) in (let TMP_258
905 \def (TLRef TMP_257) in (let TMP_259 \def (lift h2 d2 TMP_258) in (eq T
906 TMP_256 TMP_259)))))) in (let TMP_261 \def (minus n h2) in (let TMP_262 \def
907 (plus TMP_261 h2) in (let TMP_263 \def (minus TMP_262 h2) in (let TMP_264
908 \def (plus TMP_263 h2) in (let TMP_265 \def (TLRef TMP_264) in (let TMP_269
909 \def (\lambda (t: T).(let TMP_266 \def (minus n h2) in (let TMP_267 \def
910 (plus TMP_266 h2) in (let TMP_268 \def (TLRef TMP_267) in (eq T TMP_268
911 t))))) in (let TMP_270 \def (minus n h2) in (let TMP_271 \def (plus TMP_270
912 h2) in (let TMP_272 \def (minus TMP_271 h2) in (let TMP_273 \def (plus
913 TMP_272 h2) in (let TMP_274 \def (TLRef TMP_273) in (let TMP_275 \def (minus
914 n h2) in (let TMP_276 \def (plus TMP_275 h2) in (let TMP_277 \def (TLRef
915 TMP_276) in (let TMP_278 \def (minus n h2) in (let TMP_279 \def (plus TMP_278
916 h2) in (let TMP_280 \def (minus TMP_279 h2) in (let TMP_281 \def (plus
917 TMP_280 h2) in (let TMP_282 \def (minus n h2) in (let TMP_283 \def (plus
918 TMP_282 h2) in (let TMP_284 \def (minus n h2) in (let TMP_285 \def (plus
919 TMP_284 h2) in (let TMP_286 \def (minus TMP_285 h2) in (let TMP_287 \def
920 (minus n h2) in (let TMP_288 \def (minus n h2) in (let TMP_289 \def
921 (minus_plus_r TMP_288 h2) in (let TMP_290 \def (refl_equal nat h2) in (let
922 TMP_291 \def (f_equal2 nat nat nat plus TMP_286 TMP_287 h2 h2 TMP_289
923 TMP_290) in (let TMP_292 \def (f_equal nat T TLRef TMP_281 TMP_283 TMP_291)
924 in (let TMP_293 \def (sym_eq T TMP_274 TMP_277 TMP_292) in (let TMP_294 \def
925 (minus n h2) in (let TMP_295 \def (plus TMP_294 h2) in (let TMP_296 \def
926 (minus TMP_295 h2) in (let TMP_297 \def (TLRef TMP_296) in (let TMP_298 \def
927 (lift h2 d2 TMP_297) in (let TMP_299 \def (minus n h2) in (let TMP_300 \def
928 (plus TMP_299 h2) in (let TMP_301 \def (minus TMP_300 h2) in (let TMP_302
929 \def (minus n h2) in (let TMP_303 \def (plus TMP_302 h2) in (let TMP_304 \def
930 (minus n h2) in (let TMP_305 \def (le_minus d2 n h2 H4) in (let TMP_306 \def
931 (le_n h2) in (let TMP_307 \def (le_plus_plus d2 TMP_304 h2 h2 TMP_305
932 TMP_306) in (let TMP_308 \def (le_minus d2 TMP_303 h2 TMP_307) in (let
933 TMP_309 \def (lift_lref_ge TMP_301 h2 d2 TMP_308) in (let TMP_310 \def
934 (eq_ind_r T TMP_265 TMP_269 TMP_293 TMP_298 TMP_309) in (let TMP_311 \def
935 (plus d2 h2) in (let TMP_312 \def (le_plus_r d2 h2) in (let TMP_313 \def
936 (le_trans h2 TMP_311 n TMP_312 H4) in (let TMP_314 \def (le_plus_minus_sym h2
937 n TMP_313) in (let TMP_315 \def (eq_ind_r nat TMP_255 TMP_260 TMP_310 n
938 TMP_314) in (let TMP_316 \def (ex_intro2 T TMP_214 TMP_217 TMP_219 TMP_253
939 TMP_315) in (let TMP_317 \def (plus d2 h1) in (let TMP_318 \def (plus n h1)
940 in (let TMP_319 \def (minus TMP_318 h2) in (let TMP_320 \def (arith0 h2 d2 n
941 H4 h1) in (let TMP_321 \def (lift_gen_lref_ge h2 TMP_317 TMP_319 TMP_320 x
942 H5) in (eq_ind_r T TMP_203 TMP_209 TMP_316 x
943 TMP_321)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
944 ))))))))))))))))))))))))))))))))))))))) in (lt_le_e n TMP_159 TMP_165 TMP_186
945 TMP_322)))))))) in (lt_le_e n d2 TMP_115 TMP_158 TMP_323)))))))))))))) in
946 (lt_le_e n d1 TMP_54 TMP_101 TMP_324)))))))))))))) in (let TMP_720 \def
947 (\lambda (k: K).(\lambda (t: T).(\lambda (H: ((\forall (x: T).(\forall (h1:
948 nat).(\forall (h2: nat).(\forall (d1: nat).(\forall (d2: nat).((le d1 d2) \to
949 ((eq T (lift h1 d1 t) (lift h2 (plus d2 h1) x)) \to (ex2 T (\lambda (t2:
950 T).(eq T x (lift h1 d1 t2))) (\lambda (t2: T).(eq T t (lift h2 d2
951 t2))))))))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (x: T).(\forall (h1:
952 nat).(\forall (h2: nat).(\forall (d1: nat).(\forall (d2: nat).((le d1 d2) \to
953 ((eq T (lift h1 d1 t0) (lift h2 (plus d2 h1) x)) \to (ex2 T (\lambda (t2:
954 T).(eq T x (lift h1 d1 t2))) (\lambda (t2: T).(eq T t0 (lift h2 d2
955 t2))))))))))))).(\lambda (x: T).(\lambda (h1: nat).(\lambda (h2:
956 nat).(\lambda (d1: nat).(\lambda (d2: nat).(\lambda (H1: (le d1 d2)).(\lambda
957 (H2: (eq T (lift h1 d1 (THead k t t0)) (lift h2 (plus d2 h1) x))).(let
958 TMP_331 \def (\lambda (k0: K).((eq T (lift h1 d1 (THead k0 t t0)) (lift h2
959 (plus d2 h1) x)) \to (let TMP_327 \def (\lambda (t2: T).(let TMP_326 \def
960 (lift h1 d1 t2) in (eq T x TMP_326))) in (let TMP_330 \def (\lambda (t2:
961 T).(let TMP_328 \def (THead k0 t t0) in (let TMP_329 \def (lift h2 d2 t2) in
962 (eq T TMP_328 TMP_329)))) in (ex2 T TMP_327 TMP_330))))) in (let TMP_540 \def
963 (\lambda (b: B).(\lambda (H3: (eq T (lift h1 d1 (THead (Bind b) t t0)) (lift
964 h2 (plus d2 h1) x))).(let TMP_332 \def (Bind b) in (let TMP_333 \def (THead
965 TMP_332 t t0) in (let TMP_334 \def (lift h1 d1 TMP_333) in (let TMP_337 \def
966 (\lambda (t2: T).(let TMP_335 \def (plus d2 h1) in (let TMP_336 \def (lift h2
967 TMP_335 x) in (eq T t2 TMP_336)))) in (let TMP_338 \def (Bind b) in (let
968 TMP_339 \def (lift h1 d1 t) in (let TMP_340 \def (S d1) in (let TMP_341 \def
969 (lift h1 TMP_340 t0) in (let TMP_342 \def (THead TMP_338 TMP_339 TMP_341) in
970 (let TMP_343 \def (lift_bind b t t0 h1 d1) in (let H4 \def (eq_ind T TMP_334
971 TMP_337 H3 TMP_342 TMP_343) in (let TMP_346 \def (\lambda (y: T).(\lambda (z:
972 T).(let TMP_344 \def (Bind b) in (let TMP_345 \def (THead TMP_344 y z) in (eq
973 T x TMP_345))))) in (let TMP_350 \def (\lambda (y: T).(\lambda (_: T).(let
974 TMP_347 \def (lift h1 d1 t) in (let TMP_348 \def (plus d2 h1) in (let TMP_349
975 \def (lift h2 TMP_348 y) in (eq T TMP_347 TMP_349)))))) in (let TMP_356 \def
976 (\lambda (_: T).(\lambda (z: T).(let TMP_351 \def (S d1) in (let TMP_352 \def
977 (lift h1 TMP_351 t0) in (let TMP_353 \def (plus d2 h1) in (let TMP_354 \def
978 (S TMP_353) in (let TMP_355 \def (lift h2 TMP_354 z) in (eq T TMP_352
979 TMP_355)))))))) in (let TMP_358 \def (\lambda (t2: T).(let TMP_357 \def (lift
980 h1 d1 t2) in (eq T x TMP_357))) in (let TMP_362 \def (\lambda (t2: T).(let
981 TMP_359 \def (Bind b) in (let TMP_360 \def (THead TMP_359 t t0) in (let
982 TMP_361 \def (lift h2 d2 t2) in (eq T TMP_360 TMP_361))))) in (let TMP_363
983 \def (ex2 T TMP_358 TMP_362) in (let TMP_534 \def (\lambda (x0: T).(\lambda
984 (x1: T).(\lambda (H5: (eq T x (THead (Bind b) x0 x1))).(\lambda (H6: (eq T
985 (lift h1 d1 t) (lift h2 (plus d2 h1) x0))).(\lambda (H7: (eq T (lift h1 (S
986 d1) t0) (lift h2 (S (plus d2 h1)) x1))).(let TMP_364 \def (Bind b) in (let
987 TMP_365 \def (THead TMP_364 x0 x1) in (let TMP_372 \def (\lambda (t2: T).(let
988 TMP_367 \def (\lambda (t3: T).(let TMP_366 \def (lift h1 d1 t3) in (eq T t2
989 TMP_366))) in (let TMP_371 \def (\lambda (t3: T).(let TMP_368 \def (Bind b)
990 in (let TMP_369 \def (THead TMP_368 t t0) in (let TMP_370 \def (lift h2 d2
991 t3) in (eq T TMP_369 TMP_370))))) in (ex2 T TMP_367 TMP_371)))) in (let
992 TMP_374 \def (\lambda (t2: T).(let TMP_373 \def (lift h1 d1 t2) in (eq T x0
993 TMP_373))) in (let TMP_376 \def (\lambda (t2: T).(let TMP_375 \def (lift h2
994 d2 t2) in (eq T t TMP_375))) in (let TMP_380 \def (\lambda (t2: T).(let
995 TMP_377 \def (Bind b) in (let TMP_378 \def (THead TMP_377 x0 x1) in (let
996 TMP_379 \def (lift h1 d1 t2) in (eq T TMP_378 TMP_379))))) in (let TMP_384
997 \def (\lambda (t2: T).(let TMP_381 \def (Bind b) in (let TMP_382 \def (THead
998 TMP_381 t t0) in (let TMP_383 \def (lift h2 d2 t2) in (eq T TMP_382
999 TMP_383))))) in (let TMP_385 \def (ex2 T TMP_380 TMP_384) in (let TMP_531
1000 \def (\lambda (x2: T).(\lambda (H8: (eq T x0 (lift h1 d1 x2))).(\lambda (H9:
1001 (eq T t (lift h2 d2 x2))).(let TMP_386 \def (lift h1 d1 x2) in (let TMP_395
1002 \def (\lambda (t2: T).(let TMP_390 \def (\lambda (t3: T).(let TMP_387 \def
1003 (Bind b) in (let TMP_388 \def (THead TMP_387 t2 x1) in (let TMP_389 \def
1004 (lift h1 d1 t3) in (eq T TMP_388 TMP_389))))) in (let TMP_394 \def (\lambda
1005 (t3: T).(let TMP_391 \def (Bind b) in (let TMP_392 \def (THead TMP_391 t t0)
1006 in (let TMP_393 \def (lift h2 d2 t3) in (eq T TMP_392 TMP_393))))) in (ex2 T
1007 TMP_390 TMP_394)))) in (let TMP_396 \def (lift h2 d2 x2) in (let TMP_406 \def
1008 (\lambda (t2: T).(let TMP_401 \def (\lambda (t3: T).(let TMP_397 \def (Bind
1009 b) in (let TMP_398 \def (lift h1 d1 x2) in (let TMP_399 \def (THead TMP_397
1010 TMP_398 x1) in (let TMP_400 \def (lift h1 d1 t3) in (eq T TMP_399
1011 TMP_400)))))) in (let TMP_405 \def (\lambda (t3: T).(let TMP_402 \def (Bind
1012 b) in (let TMP_403 \def (THead TMP_402 t2 t0) in (let TMP_404 \def (lift h2
1013 d2 t3) in (eq T TMP_403 TMP_404))))) in (ex2 T TMP_401 TMP_405)))) in (let
1014 TMP_407 \def (S d2) in (let TMP_408 \def (plus TMP_407 h1) in (let H10 \def
1015 (refl_equal nat TMP_408) in (let TMP_409 \def (plus d2 h1) in (let TMP_410
1016 \def (S TMP_409) in (let TMP_414 \def (\lambda (n: nat).(let TMP_411 \def (S
1017 d1) in (let TMP_412 \def (lift h1 TMP_411 t0) in (let TMP_413 \def (lift h2 n
1018 x1) in (eq T TMP_412 TMP_413))))) in (let TMP_415 \def (S d2) in (let TMP_416
1019 \def (plus TMP_415 h1) in (let H11 \def (eq_ind nat TMP_410 TMP_414 H7
1020 TMP_416 H10) in (let TMP_419 \def (\lambda (t2: T).(let TMP_417 \def (S d1)
1021 in (let TMP_418 \def (lift h1 TMP_417 t2) in (eq T x1 TMP_418)))) in (let
1022 TMP_422 \def (\lambda (t2: T).(let TMP_420 \def (S d2) in (let TMP_421 \def
1023 (lift h2 TMP_420 t2) in (eq T t0 TMP_421)))) in (let TMP_427 \def (\lambda
1024 (t2: T).(let TMP_423 \def (Bind b) in (let TMP_424 \def (lift h1 d1 x2) in
1025 (let TMP_425 \def (THead TMP_423 TMP_424 x1) in (let TMP_426 \def (lift h1 d1
1026 t2) in (eq T TMP_425 TMP_426)))))) in (let TMP_432 \def (\lambda (t2: T).(let
1027 TMP_428 \def (Bind b) in (let TMP_429 \def (lift h2 d2 x2) in (let TMP_430
1028 \def (THead TMP_428 TMP_429 t0) in (let TMP_431 \def (lift h2 d2 t2) in (eq T
1029 TMP_430 TMP_431)))))) in (let TMP_433 \def (ex2 T TMP_427 TMP_432) in (let
1030 TMP_524 \def (\lambda (x3: T).(\lambda (H12: (eq T x1 (lift h1 (S d1)
1031 x3))).(\lambda (H13: (eq T t0 (lift h2 (S d2) x3))).(let TMP_434 \def (S d1)
1032 in (let TMP_435 \def (lift h1 TMP_434 x3) in (let TMP_446 \def (\lambda (t2:
1033 T).(let TMP_440 \def (\lambda (t3: T).(let TMP_436 \def (Bind b) in (let
1034 TMP_437 \def (lift h1 d1 x2) in (let TMP_438 \def (THead TMP_436 TMP_437 t2)
1035 in (let TMP_439 \def (lift h1 d1 t3) in (eq T TMP_438 TMP_439)))))) in (let
1036 TMP_445 \def (\lambda (t3: T).(let TMP_441 \def (Bind b) in (let TMP_442 \def
1037 (lift h2 d2 x2) in (let TMP_443 \def (THead TMP_441 TMP_442 t0) in (let
1038 TMP_444 \def (lift h2 d2 t3) in (eq T TMP_443 TMP_444)))))) in (ex2 T TMP_440
1039 TMP_445)))) in (let TMP_447 \def (S d2) in (let TMP_448 \def (lift h2 TMP_447
1040 x3) in (let TMP_461 \def (\lambda (t2: T).(let TMP_455 \def (\lambda (t3:
1041 T).(let TMP_449 \def (Bind b) in (let TMP_450 \def (lift h1 d1 x2) in (let
1042 TMP_451 \def (S d1) in (let TMP_452 \def (lift h1 TMP_451 x3) in (let TMP_453
1043 \def (THead TMP_449 TMP_450 TMP_452) in (let TMP_454 \def (lift h1 d1 t3) in
1044 (eq T TMP_453 TMP_454)))))))) in (let TMP_460 \def (\lambda (t3: T).(let
1045 TMP_456 \def (Bind b) in (let TMP_457 \def (lift h2 d2 x2) in (let TMP_458
1046 \def (THead TMP_456 TMP_457 t2) in (let TMP_459 \def (lift h2 d2 t3) in (eq T
1047 TMP_458 TMP_459)))))) in (ex2 T TMP_455 TMP_460)))) in (let TMP_468 \def
1048 (\lambda (t2: T).(let TMP_462 \def (Bind b) in (let TMP_463 \def (lift h1 d1
1049 x2) in (let TMP_464 \def (S d1) in (let TMP_465 \def (lift h1 TMP_464 x3) in
1050 (let TMP_466 \def (THead TMP_462 TMP_463 TMP_465) in (let TMP_467 \def (lift
1051 h1 d1 t2) in (eq T TMP_466 TMP_467)))))))) in (let TMP_475 \def (\lambda (t2:
1052 T).(let TMP_469 \def (Bind b) in (let TMP_470 \def (lift h2 d2 x2) in (let
1053 TMP_471 \def (S d2) in (let TMP_472 \def (lift h2 TMP_471 x3) in (let TMP_473
1054 \def (THead TMP_469 TMP_470 TMP_472) in (let TMP_474 \def (lift h2 d2 t2) in
1055 (eq T TMP_473 TMP_474)))))))) in (let TMP_476 \def (Bind b) in (let TMP_477
1056 \def (THead TMP_476 x2 x3) in (let TMP_478 \def (Bind b) in (let TMP_479 \def
1057 (lift h1 d1 x2) in (let TMP_480 \def (S d1) in (let TMP_481 \def (lift h1
1058 TMP_480 x3) in (let TMP_482 \def (THead TMP_478 TMP_479 TMP_481) in (let
1059 TMP_488 \def (\lambda (t2: T).(let TMP_483 \def (Bind b) in (let TMP_484 \def
1060 (lift h1 d1 x2) in (let TMP_485 \def (S d1) in (let TMP_486 \def (lift h1
1061 TMP_485 x3) in (let TMP_487 \def (THead TMP_483 TMP_484 TMP_486) in (eq T
1062 TMP_487 t2))))))) in (let TMP_489 \def (Bind b) in (let TMP_490 \def (lift h1
1063 d1 x2) in (let TMP_491 \def (S d1) in (let TMP_492 \def (lift h1 TMP_491 x3)
1064 in (let TMP_493 \def (THead TMP_489 TMP_490 TMP_492) in (let TMP_494 \def
1065 (refl_equal T TMP_493) in (let TMP_495 \def (Bind b) in (let TMP_496 \def
1066 (THead TMP_495 x2 x3) in (let TMP_497 \def (lift h1 d1 TMP_496) in (let
1067 TMP_498 \def (lift_bind b x2 x3 h1 d1) in (let TMP_499 \def (eq_ind_r T
1068 TMP_482 TMP_488 TMP_494 TMP_497 TMP_498) in (let TMP_500 \def (Bind b) in
1069 (let TMP_501 \def (lift h2 d2 x2) in (let TMP_502 \def (S d2) in (let TMP_503
1070 \def (lift h2 TMP_502 x3) in (let TMP_504 \def (THead TMP_500 TMP_501
1071 TMP_503) in (let TMP_510 \def (\lambda (t2: T).(let TMP_505 \def (Bind b) in
1072 (let TMP_506 \def (lift h2 d2 x2) in (let TMP_507 \def (S d2) in (let TMP_508
1073 \def (lift h2 TMP_507 x3) in (let TMP_509 \def (THead TMP_505 TMP_506
1074 TMP_508) in (eq T TMP_509 t2))))))) in (let TMP_511 \def (Bind b) in (let
1075 TMP_512 \def (lift h2 d2 x2) in (let TMP_513 \def (S d2) in (let TMP_514 \def
1076 (lift h2 TMP_513 x3) in (let TMP_515 \def (THead TMP_511 TMP_512 TMP_514) in
1077 (let TMP_516 \def (refl_equal T TMP_515) in (let TMP_517 \def (Bind b) in
1078 (let TMP_518 \def (THead TMP_517 x2 x3) in (let TMP_519 \def (lift h2 d2
1079 TMP_518) in (let TMP_520 \def (lift_bind b x2 x3 h2 d2) in (let TMP_521 \def
1080 (eq_ind_r T TMP_504 TMP_510 TMP_516 TMP_519 TMP_520) in (let TMP_522 \def
1081 (ex_intro2 T TMP_468 TMP_475 TMP_477 TMP_499 TMP_521) in (let TMP_523 \def
1082 (eq_ind_r T TMP_448 TMP_461 TMP_522 t0 H13) in (eq_ind_r T TMP_435 TMP_446
1083 TMP_523 x1 H12)))))))))))))))))))))))))))))))))))))))))))))))))) in (let
1084 TMP_525 \def (S d1) in (let TMP_526 \def (S d2) in (let TMP_527 \def (le_n_S
1085 d1 d2 H1) in (let TMP_528 \def (H0 x1 h1 h2 TMP_525 TMP_526 TMP_527 H11) in
1086 (let TMP_529 \def (ex2_ind T TMP_419 TMP_422 TMP_433 TMP_524 TMP_528) in (let
1087 TMP_530 \def (eq_ind_r T TMP_396 TMP_406 TMP_529 t H9) in (eq_ind_r T TMP_386
1088 TMP_395 TMP_530 x0 H8))))))))))))))))))))))))))))) in (let TMP_532 \def (H x0
1089 h1 h2 d1 d2 H1 H6) in (let TMP_533 \def (ex2_ind T TMP_374 TMP_376 TMP_385
1090 TMP_531 TMP_532) in (eq_ind_r T TMP_365 TMP_372 TMP_533 x H5)))))))))))))))))
1091 in (let TMP_535 \def (lift h1 d1 t) in (let TMP_536 \def (S d1) in (let
1092 TMP_537 \def (lift h1 TMP_536 t0) in (let TMP_538 \def (plus d2 h1) in (let
1093 TMP_539 \def (lift_gen_bind b TMP_535 TMP_537 x h2 TMP_538 H4) in (ex3_2_ind
1094 T T TMP_346 TMP_350 TMP_356 TMP_363 TMP_534 TMP_539))))))))))))))))))))))))))
1095 in (let TMP_719 \def (\lambda (f: F).(\lambda (H3: (eq T (lift h1 d1 (THead
1096 (Flat f) t t0)) (lift h2 (plus d2 h1) x))).(let TMP_541 \def (Flat f) in (let
1097 TMP_542 \def (THead TMP_541 t t0) in (let TMP_543 \def (lift h1 d1 TMP_542)
1098 in (let TMP_546 \def (\lambda (t2: T).(let TMP_544 \def (plus d2 h1) in (let
1099 TMP_545 \def (lift h2 TMP_544 x) in (eq T t2 TMP_545)))) in (let TMP_547 \def
1100 (Flat f) in (let TMP_548 \def (lift h1 d1 t) in (let TMP_549 \def (lift h1 d1
1101 t0) in (let TMP_550 \def (THead TMP_547 TMP_548 TMP_549) in (let TMP_551 \def
1102 (lift_flat f t t0 h1 d1) in (let H4 \def (eq_ind T TMP_543 TMP_546 H3 TMP_550
1103 TMP_551) in (let TMP_554 \def (\lambda (y: T).(\lambda (z: T).(let TMP_552
1104 \def (Flat f) in (let TMP_553 \def (THead TMP_552 y z) in (eq T x
1105 TMP_553))))) in (let TMP_558 \def (\lambda (y: T).(\lambda (_: T).(let
1106 TMP_555 \def (lift h1 d1 t) in (let TMP_556 \def (plus d2 h1) in (let TMP_557
1107 \def (lift h2 TMP_556 y) in (eq T TMP_555 TMP_557)))))) in (let TMP_562 \def
1108 (\lambda (_: T).(\lambda (z: T).(let TMP_559 \def (lift h1 d1 t0) in (let
1109 TMP_560 \def (plus d2 h1) in (let TMP_561 \def (lift h2 TMP_560 z) in (eq T
1110 TMP_559 TMP_561)))))) in (let TMP_564 \def (\lambda (t2: T).(let TMP_563 \def
1111 (lift h1 d1 t2) in (eq T x TMP_563))) in (let TMP_568 \def (\lambda (t2:
1112 T).(let TMP_565 \def (Flat f) in (let TMP_566 \def (THead TMP_565 t t0) in
1113 (let TMP_567 \def (lift h2 d2 t2) in (eq T TMP_566 TMP_567))))) in (let
1114 TMP_569 \def (ex2 T TMP_564 TMP_568) in (let TMP_714 \def (\lambda (x0:
1115 T).(\lambda (x1: T).(\lambda (H5: (eq T x (THead (Flat f) x0 x1))).(\lambda
1116 (H6: (eq T (lift h1 d1 t) (lift h2 (plus d2 h1) x0))).(\lambda (H7: (eq T
1117 (lift h1 d1 t0) (lift h2 (plus d2 h1) x1))).(let TMP_570 \def (Flat f) in
1118 (let TMP_571 \def (THead TMP_570 x0 x1) in (let TMP_578 \def (\lambda (t2:
1119 T).(let TMP_573 \def (\lambda (t3: T).(let TMP_572 \def (lift h1 d1 t3) in
1120 (eq T t2 TMP_572))) in (let TMP_577 \def (\lambda (t3: T).(let TMP_574 \def
1121 (Flat f) in (let TMP_575 \def (THead TMP_574 t t0) in (let TMP_576 \def (lift
1122 h2 d2 t3) in (eq T TMP_575 TMP_576))))) in (ex2 T TMP_573 TMP_577)))) in (let
1123 TMP_580 \def (\lambda (t2: T).(let TMP_579 \def (lift h1 d1 t2) in (eq T x0
1124 TMP_579))) in (let TMP_582 \def (\lambda (t2: T).(let TMP_581 \def (lift h2
1125 d2 t2) in (eq T t TMP_581))) in (let TMP_586 \def (\lambda (t2: T).(let
1126 TMP_583 \def (Flat f) in (let TMP_584 \def (THead TMP_583 x0 x1) in (let
1127 TMP_585 \def (lift h1 d1 t2) in (eq T TMP_584 TMP_585))))) in (let TMP_590
1128 \def (\lambda (t2: T).(let TMP_587 \def (Flat f) in (let TMP_588 \def (THead
1129 TMP_587 t t0) in (let TMP_589 \def (lift h2 d2 t2) in (eq T TMP_588
1130 TMP_589))))) in (let TMP_591 \def (ex2 T TMP_586 TMP_590) in (let TMP_711
1131 \def (\lambda (x2: T).(\lambda (H8: (eq T x0 (lift h1 d1 x2))).(\lambda (H9:
1132 (eq T t (lift h2 d2 x2))).(let TMP_592 \def (lift h1 d1 x2) in (let TMP_601
1133 \def (\lambda (t2: T).(let TMP_596 \def (\lambda (t3: T).(let TMP_593 \def
1134 (Flat f) in (let TMP_594 \def (THead TMP_593 t2 x1) in (let TMP_595 \def
1135 (lift h1 d1 t3) in (eq T TMP_594 TMP_595))))) in (let TMP_600 \def (\lambda
1136 (t3: T).(let TMP_597 \def (Flat f) in (let TMP_598 \def (THead TMP_597 t t0)
1137 in (let TMP_599 \def (lift h2 d2 t3) in (eq T TMP_598 TMP_599))))) in (ex2 T
1138 TMP_596 TMP_600)))) in (let TMP_602 \def (lift h2 d2 x2) in (let TMP_612 \def
1139 (\lambda (t2: T).(let TMP_607 \def (\lambda (t3: T).(let TMP_603 \def (Flat
1140 f) in (let TMP_604 \def (lift h1 d1 x2) in (let TMP_605 \def (THead TMP_603
1141 TMP_604 x1) in (let TMP_606 \def (lift h1 d1 t3) in (eq T TMP_605
1142 TMP_606)))))) in (let TMP_611 \def (\lambda (t3: T).(let TMP_608 \def (Flat
1143 f) in (let TMP_609 \def (THead TMP_608 t2 t0) in (let TMP_610 \def (lift h2
1144 d2 t3) in (eq T TMP_609 TMP_610))))) in (ex2 T TMP_607 TMP_611)))) in (let
1145 TMP_614 \def (\lambda (t2: T).(let TMP_613 \def (lift h1 d1 t2) in (eq T x1
1146 TMP_613))) in (let TMP_616 \def (\lambda (t2: T).(let TMP_615 \def (lift h2
1147 d2 t2) in (eq T t0 TMP_615))) in (let TMP_621 \def (\lambda (t2: T).(let
1148 TMP_617 \def (Flat f) in (let TMP_618 \def (lift h1 d1 x2) in (let TMP_619
1149 \def (THead TMP_617 TMP_618 x1) in (let TMP_620 \def (lift h1 d1 t2) in (eq T
1150 TMP_619 TMP_620)))))) in (let TMP_626 \def (\lambda (t2: T).(let TMP_622 \def
1151 (Flat f) in (let TMP_623 \def (lift h2 d2 x2) in (let TMP_624 \def (THead
1152 TMP_622 TMP_623 t0) in (let TMP_625 \def (lift h2 d2 t2) in (eq T TMP_624
1153 TMP_625)))))) in (let TMP_627 \def (ex2 T TMP_621 TMP_626) in (let TMP_707
1154 \def (\lambda (x3: T).(\lambda (H10: (eq T x1 (lift h1 d1 x3))).(\lambda
1155 (H11: (eq T t0 (lift h2 d2 x3))).(let TMP_628 \def (lift h1 d1 x3) in (let
1156 TMP_639 \def (\lambda (t2: T).(let TMP_633 \def (\lambda (t3: T).(let TMP_629
1157 \def (Flat f) in (let TMP_630 \def (lift h1 d1 x2) in (let TMP_631 \def
1158 (THead TMP_629 TMP_630 t2) in (let TMP_632 \def (lift h1 d1 t3) in (eq T
1159 TMP_631 TMP_632)))))) in (let TMP_638 \def (\lambda (t3: T).(let TMP_634 \def
1160 (Flat f) in (let TMP_635 \def (lift h2 d2 x2) in (let TMP_636 \def (THead
1161 TMP_634 TMP_635 t0) in (let TMP_637 \def (lift h2 d2 t3) in (eq T TMP_636
1162 TMP_637)))))) in (ex2 T TMP_633 TMP_638)))) in (let TMP_640 \def (lift h2 d2
1163 x3) in (let TMP_652 \def (\lambda (t2: T).(let TMP_646 \def (\lambda (t3:
1164 T).(let TMP_641 \def (Flat f) in (let TMP_642 \def (lift h1 d1 x2) in (let
1165 TMP_643 \def (lift h1 d1 x3) in (let TMP_644 \def (THead TMP_641 TMP_642
1166 TMP_643) in (let TMP_645 \def (lift h1 d1 t3) in (eq T TMP_644 TMP_645)))))))
1167 in (let TMP_651 \def (\lambda (t3: T).(let TMP_647 \def (Flat f) in (let
1168 TMP_648 \def (lift h2 d2 x2) in (let TMP_649 \def (THead TMP_647 TMP_648 t2)
1169 in (let TMP_650 \def (lift h2 d2 t3) in (eq T TMP_649 TMP_650)))))) in (ex2 T
1170 TMP_646 TMP_651)))) in (let TMP_658 \def (\lambda (t2: T).(let TMP_653 \def
1171 (Flat f) in (let TMP_654 \def (lift h1 d1 x2) in (let TMP_655 \def (lift h1
1172 d1 x3) in (let TMP_656 \def (THead TMP_653 TMP_654 TMP_655) in (let TMP_657
1173 \def (lift h1 d1 t2) in (eq T TMP_656 TMP_657))))))) in (let TMP_664 \def
1174 (\lambda (t2: T).(let TMP_659 \def (Flat f) in (let TMP_660 \def (lift h2 d2
1175 x2) in (let TMP_661 \def (lift h2 d2 x3) in (let TMP_662 \def (THead TMP_659
1176 TMP_660 TMP_661) in (let TMP_663 \def (lift h2 d2 t2) in (eq T TMP_662
1177 TMP_663))))))) in (let TMP_665 \def (Flat f) in (let TMP_666 \def (THead
1178 TMP_665 x2 x3) in (let TMP_667 \def (Flat f) in (let TMP_668 \def (lift h1 d1
1179 x2) in (let TMP_669 \def (lift h1 d1 x3) in (let TMP_670 \def (THead TMP_667
1180 TMP_668 TMP_669) in (let TMP_675 \def (\lambda (t2: T).(let TMP_671 \def
1181 (Flat f) in (let TMP_672 \def (lift h1 d1 x2) in (let TMP_673 \def (lift h1
1182 d1 x3) in (let TMP_674 \def (THead TMP_671 TMP_672 TMP_673) in (eq T TMP_674
1183 t2)))))) in (let TMP_676 \def (Flat f) in (let TMP_677 \def (lift h1 d1 x2)
1184 in (let TMP_678 \def (lift h1 d1 x3) in (let TMP_679 \def (THead TMP_676
1185 TMP_677 TMP_678) in (let TMP_680 \def (refl_equal T TMP_679) in (let TMP_681
1186 \def (Flat f) in (let TMP_682 \def (THead TMP_681 x2 x3) in (let TMP_683 \def
1187 (lift h1 d1 TMP_682) in (let TMP_684 \def (lift_flat f x2 x3 h1 d1) in (let
1188 TMP_685 \def (eq_ind_r T TMP_670 TMP_675 TMP_680 TMP_683 TMP_684) in (let
1189 TMP_686 \def (Flat f) in (let TMP_687 \def (lift h2 d2 x2) in (let TMP_688
1190 \def (lift h2 d2 x3) in (let TMP_689 \def (THead TMP_686 TMP_687 TMP_688) in
1191 (let TMP_694 \def (\lambda (t2: T).(let TMP_690 \def (Flat f) in (let TMP_691
1192 \def (lift h2 d2 x2) in (let TMP_692 \def (lift h2 d2 x3) in (let TMP_693
1193 \def (THead TMP_690 TMP_691 TMP_692) in (eq T TMP_693 t2)))))) in (let
1194 TMP_695 \def (Flat f) in (let TMP_696 \def (lift h2 d2 x2) in (let TMP_697
1195 \def (lift h2 d2 x3) in (let TMP_698 \def (THead TMP_695 TMP_696 TMP_697) in
1196 (let TMP_699 \def (refl_equal T TMP_698) in (let TMP_700 \def (Flat f) in
1197 (let TMP_701 \def (THead TMP_700 x2 x3) in (let TMP_702 \def (lift h2 d2
1198 TMP_701) in (let TMP_703 \def (lift_flat f x2 x3 h2 d2) in (let TMP_704 \def
1199 (eq_ind_r T TMP_689 TMP_694 TMP_699 TMP_702 TMP_703) in (let TMP_705 \def
1200 (ex_intro2 T TMP_658 TMP_664 TMP_666 TMP_685 TMP_704) in (let TMP_706 \def
1201 (eq_ind_r T TMP_640 TMP_652 TMP_705 t0 H11) in (eq_ind_r T TMP_628 TMP_639
1202 TMP_706 x1 H10)))))))))))))))))))))))))))))))))))))))))))) in (let TMP_708
1203 \def (H0 x1 h1 h2 d1 d2 H1 H7) in (let TMP_709 \def (ex2_ind T TMP_614
1204 TMP_616 TMP_627 TMP_707 TMP_708) in (let TMP_710 \def (eq_ind_r T TMP_602
1205 TMP_612 TMP_709 t H9) in (eq_ind_r T TMP_592 TMP_601 TMP_710 x0
1206 H8))))))))))))))))) in (let TMP_712 \def (H x0 h1 h2 d1 d2 H1 H6) in (let
1207 TMP_713 \def (ex2_ind T TMP_580 TMP_582 TMP_591 TMP_711 TMP_712) in (eq_ind_r
1208 T TMP_571 TMP_578 TMP_713 x H5))))))))))))))))) in (let TMP_715 \def (lift h1
1209 d1 t) in (let TMP_716 \def (lift h1 d1 t0) in (let TMP_717 \def (plus d2 h1)
1210 in (let TMP_718 \def (lift_gen_flat f TMP_715 TMP_716 x h2 TMP_717 H4) in
1211 (ex3_2_ind T T TMP_554 TMP_558 TMP_562 TMP_569 TMP_714
1212 TMP_718)))))))))))))))))))))))) in (K_ind TMP_331 TMP_540 TMP_719 k
1213 H2)))))))))))))))) in (T_ind TMP_5 TMP_48 TMP_325 TMP_720 t1))))).
1216 \forall (xs: TList).(\forall (ts: TList).(\forall (h: nat).(\forall (d:
1217 nat).((eq TList (lifts h d xs) (lifts h d ts)) \to (eq TList xs ts)))))
1219 \lambda (xs: TList).(let TMP_1 \def (\lambda (t: TList).(\forall (ts:
1220 TList).(\forall (h: nat).(\forall (d: nat).((eq TList (lifts h d t) (lifts h
1221 d ts)) \to (eq TList t ts)))))) in (let TMP_11 \def (\lambda (ts: TList).(let
1222 TMP_2 \def (\lambda (t: TList).(\forall (h: nat).(\forall (d: nat).((eq TList
1223 (lifts h d TNil) (lifts h d t)) \to (eq TList TNil t))))) in (let TMP_3 \def
1224 (\lambda (_: nat).(\lambda (_: nat).(\lambda (_: (eq TList TNil
1225 TNil)).(refl_equal TList TNil)))) in (let TMP_10 \def (\lambda (t:
1226 T).(\lambda (t0: TList).(\lambda (_: ((\forall (h: nat).(\forall (d:
1227 nat).((eq TList TNil (lifts h d t0)) \to (eq TList TNil t0)))))).(\lambda (h:
1228 nat).(\lambda (d: nat).(\lambda (H0: (eq TList TNil (TCons (lift h d t)
1229 (lifts h d t0)))).(let TMP_4 \def (\lambda (ee: TList).(match ee with [TNil
1230 \Rightarrow True | (TCons _ _) \Rightarrow False])) in (let TMP_5 \def (lift
1231 h d t) in (let TMP_6 \def (lifts h d t0) in (let TMP_7 \def (TCons TMP_5
1232 TMP_6) in (let H1 \def (eq_ind TList TNil TMP_4 I TMP_7 H0) in (let TMP_8
1233 \def (TCons t t0) in (let TMP_9 \def (eq TList TNil TMP_8) in (False_ind
1234 TMP_9 H1)))))))))))))) in (TList_ind TMP_2 TMP_3 TMP_10 ts))))) in (let
1235 TMP_53 \def (\lambda (t: T).(\lambda (t0: TList).(\lambda (H: ((\forall (ts:
1236 TList).(\forall (h: nat).(\forall (d: nat).((eq TList (lifts h d t0) (lifts h
1237 d ts)) \to (eq TList t0 ts))))))).(\lambda (ts: TList).(let TMP_13 \def
1238 (\lambda (t1: TList).(\forall (h: nat).(\forall (d: nat).((eq TList (lifts h
1239 d (TCons t t0)) (lifts h d t1)) \to (let TMP_12 \def (TCons t t0) in (eq
1240 TList TMP_12 t1)))))) in (let TMP_20 \def (\lambda (h: nat).(\lambda (d:
1241 nat).(\lambda (H0: (eq TList (TCons (lift h d t) (lifts h d t0)) TNil)).(let
1242 TMP_14 \def (lift h d t) in (let TMP_15 \def (lifts h d t0) in (let TMP_16
1243 \def (TCons TMP_14 TMP_15) in (let TMP_17 \def (\lambda (ee: TList).(match ee
1244 with [TNil \Rightarrow False | (TCons _ _) \Rightarrow True])) in (let H1
1245 \def (eq_ind TList TMP_16 TMP_17 I TNil H0) in (let TMP_18 \def (TCons t t0)
1246 in (let TMP_19 \def (eq TList TMP_18 TNil) in (False_ind TMP_19 H1)))))))))))
1247 in (let TMP_52 \def (\lambda (t1: T).(\lambda (t2: TList).(\lambda (_:
1248 ((\forall (h: nat).(\forall (d: nat).((eq TList (TCons (lift h d t) (lifts h
1249 d t0)) (lifts h d t2)) \to (eq TList (TCons t t0) t2)))))).(\lambda (h:
1250 nat).(\lambda (d: nat).(\lambda (H1: (eq TList (TCons (lift h d t) (lifts h d
1251 t0)) (TCons (lift h d t1) (lifts h d t2)))).(let TMP_27 \def (\lambda (e:
1252 TList).(match e with [TNil \Rightarrow (let TMP_25 \def lref_map in (let
1253 TMP_26 \def (\lambda (x: nat).(plus x h)) in (TMP_25 TMP_26 d t))) | (TCons
1254 t3 _) \Rightarrow t3])) in (let TMP_28 \def (lift h d t) in (let TMP_29 \def
1255 (lifts h d t0) in (let TMP_30 \def (TCons TMP_28 TMP_29) in (let TMP_31 \def
1256 (lift h d t1) in (let TMP_32 \def (lifts h d t2) in (let TMP_33 \def (TCons
1257 TMP_31 TMP_32) in (let H2 \def (f_equal TList T TMP_27 TMP_30 TMP_33 H1) in
1258 (let TMP_37 \def (\lambda (e: TList).(match e with [TNil \Rightarrow (let
1259 TMP_36 \def lifts in (TMP_36 h d t0)) | (TCons _ t3) \Rightarrow t3])) in
1260 (let TMP_38 \def (lift h d t) in (let TMP_39 \def (lifts h d t0) in (let
1261 TMP_40 \def (TCons TMP_38 TMP_39) in (let TMP_41 \def (lift h d t1) in (let
1262 TMP_42 \def (lifts h d t2) in (let TMP_43 \def (TCons TMP_41 TMP_42) in (let
1263 H3 \def (f_equal TList TList TMP_37 TMP_40 TMP_43 H1) in (let TMP_51 \def
1264 (\lambda (H4: (eq T (lift h d t) (lift h d t1))).(let TMP_46 \def (\lambda
1265 (t3: T).(let TMP_44 \def (TCons t t0) in (let TMP_45 \def (TCons t3 t2) in
1266 (eq TList TMP_44 TMP_45)))) in (let TMP_47 \def (refl_equal T t) in (let
1267 TMP_48 \def (H t2 h d H3) in (let TMP_49 \def (f_equal2 T TList TList TCons t
1268 t t0 t2 TMP_47 TMP_48) in (let TMP_50 \def (lift_inj t t1 h d H4) in (eq_ind
1269 T t TMP_46 TMP_49 t1 TMP_50))))))) in (TMP_51 H2)))))))))))))))))))))))) in
1270 (TList_ind TMP_13 TMP_20 TMP_52 ts)))))))) in (TList_ind TMP_1 TMP_11 TMP_53
projects / helm.git / blob