-(arity g c1 t a)).(let TMP_2 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
-(a0: A).(\forall (d1: C).(\forall (is: PList).((drop1 is d1 c) \to (\forall
-(c2: C).((csubc g d1 c2) \to (let TMP_1 \def (lift1 is t0) in (sc3 g a0 c2
-TMP_1)))))))))) in (let TMP_21 \def (\lambda (c: C).(\lambda (n:
-nat).(\lambda (d1: C).(\lambda (is: PList).(\lambda (_: (drop1 is d1
-c)).(\lambda (c2: C).(\lambda (_: (csubc g d1 c2)).(let TMP_3 \def (TSort n)
-in (let TMP_7 \def (\lambda (t0: T).(let TMP_4 \def (ASort O n) in (let TMP_5
-\def (arity g c2 t0 TMP_4) in (let TMP_6 \def (sn3 c2 t0) in (land TMP_5
-TMP_6))))) in (let TMP_8 \def (TSort n) in (let TMP_9 \def (ASort O n) in
-(let TMP_10 \def (arity g c2 TMP_8 TMP_9) in (let TMP_11 \def (TSort n) in
-(let TMP_12 \def (sn3 c2 TMP_11) in (let TMP_13 \def (arity_sort g c2 n) in
-(let TMP_14 \def (TSort n) in (let TMP_15 \def (nf2_sort c2 n) in (let TMP_16
-\def (sn3_nf2 c2 TMP_14 TMP_15) in (let TMP_17 \def (conj TMP_10 TMP_12
-TMP_13 TMP_16) in (let TMP_18 \def (TSort n) in (let TMP_19 \def (lift1 is
-TMP_18) in (let TMP_20 \def (lift1_sort n is) in (eq_ind_r T TMP_3 TMP_7
-TMP_17 TMP_19 TMP_20))))))))))))))))))))))) in (let TMP_191 \def (\lambda (c:
-C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c
-(CHead d (Bind Abbr) u))).(\lambda (a0: A).(\lambda (_: (arity g d u
-a0)).(\lambda (H2: ((\forall (d1: C).(\forall (is: PList).((drop1 is d1 d)
-\to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g a0 c2 (lift1 is
-u))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda (H3: (drop1 is d1
-c)).(\lambda (c2: C).(\lambda (H4: (csubc g d1 c2)).(let H_x \def
-(drop1_getl_trans is c d1 H3 Abbr d u i H0) in (let H5 \def H_x in (let
-TMP_23 \def (\lambda (e2: C).(let TMP_22 \def (ptrans is i) in (drop1 TMP_22
-e2 d))) in (let TMP_29 \def (\lambda (e2: C).(let TMP_24 \def (trans is i) in
-(let TMP_25 \def (Bind Abbr) in (let TMP_26 \def (ptrans is i) in (let TMP_27
-\def (lift1 TMP_26 u) in (let TMP_28 \def (CHead e2 TMP_25 TMP_27) in (getl
-TMP_24 d1 TMP_28))))))) in (let TMP_30 \def (TLRef i) in (let TMP_31 \def
-(lift1 is TMP_30) in (let TMP_32 \def (sc3 g a0 c2 TMP_31) in (let TMP_190
-\def (\lambda (x: C).(\lambda (_: (drop1 (ptrans is i) x d)).(\lambda (H7:
-(getl (trans is i) d1 (CHead x (Bind Abbr) (lift1 (ptrans is i) u)))).(let
-TMP_33 \def (Bind Abbr) in (let TMP_34 \def (ptrans is i) in (let TMP_35 \def
-(lift1 TMP_34 u) in (let TMP_36 \def (CHead x TMP_33 TMP_35) in (let TMP_37
-\def (trans is i) in (let H_x0 \def (csubc_getl_conf g d1 TMP_36 TMP_37 H7 c2
-H4) in (let H8 \def H_x0 in (let TMP_39 \def (\lambda (e2: C).(let TMP_38
-\def (trans is i) in (getl TMP_38 c2 e2))) in (let TMP_44 \def (\lambda (e2:
-C).(let TMP_40 \def (Bind Abbr) in (let TMP_41 \def (ptrans is i) in (let
-TMP_42 \def (lift1 TMP_41 u) in (let TMP_43 \def (CHead x TMP_40 TMP_42) in
-(csubc g TMP_43 e2)))))) in (let TMP_45 \def (TLRef i) in (let TMP_46 \def
-(lift1 is TMP_45) in (let TMP_47 \def (sc3 g a0 c2 TMP_46) in (let TMP_189
-\def (\lambda (x0: C).(\lambda (H9: (getl (trans is i) c2 x0)).(\lambda (H10:
-(csubc g (CHead x (Bind Abbr) (lift1 (ptrans is i) u)) x0)).(let TMP_48 \def
-(ptrans is i) in (let TMP_49 \def (lift1 TMP_48 u) in (let TMP_50 \def (Bind
-Abbr) in (let H_x1 \def (csubc_gen_head_l g x x0 TMP_49 TMP_50 H10) in (let
-H11 \def H_x1 in (let TMP_55 \def (\lambda (c3: C).(let TMP_51 \def (Bind
-Abbr) in (let TMP_52 \def (ptrans is i) in (let TMP_53 \def (lift1 TMP_52 u)
-in (let TMP_54 \def (CHead c3 TMP_51 TMP_53) in (eq C x0 TMP_54)))))) in (let
-TMP_56 \def (\lambda (c3: C).(csubc g x c3)) in (let TMP_57 \def (ex2 C
-TMP_55 TMP_56) in (let TMP_60 \def (\lambda (_: C).(\lambda (_: T).(\lambda
-(_: A).(let TMP_58 \def (Bind Abbr) in (let TMP_59 \def (Bind Abst) in (eq K
-TMP_58 TMP_59)))))) in (let TMP_63 \def (\lambda (c3: C).(\lambda (w:
-T).(\lambda (_: A).(let TMP_61 \def (Bind Abbr) in (let TMP_62 \def (CHead c3
-TMP_61 w) in (eq C x0 TMP_62)))))) in (let TMP_64 \def (\lambda (c3:
-C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) in (let TMP_68 \def
-(\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(let TMP_65 \def (asucc g
-a1) in (let TMP_66 \def (ptrans is i) in (let TMP_67 \def (lift1 TMP_66 u) in
-(sc3 g TMP_65 x TMP_67))))))) in (let TMP_69 \def (\lambda (c3: C).(\lambda
-(w: T).(\lambda (a1: A).(sc3 g a1 c3 w)))) in (let TMP_70 \def (ex5_3 C T A
-TMP_60 TMP_63 TMP_64 TMP_68 TMP_69) in (let TMP_73 \def (\lambda (b:
-B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_71 \def (Bind b) in (let TMP_72
-\def (CHead c3 TMP_71 v2) in (eq C x0 TMP_72)))))) in (let TMP_76 \def
-(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_74 \def (Bind Abbr)
-in (let TMP_75 \def (Bind Void) in (eq K TMP_74 TMP_75)))))) in (let TMP_78
-\def (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(let TMP_77 \def (eq B b
-Void) in (not TMP_77))))) in (let TMP_79 \def (\lambda (_: B).(\lambda (c3:
-C).(\lambda (_: T).(csubc g x c3)))) in (let TMP_80 \def (ex4_3 B C T TMP_73
-TMP_76 TMP_78 TMP_79) in (let TMP_81 \def (TLRef i) in (let TMP_82 \def
-(lift1 is TMP_81) in (let TMP_83 \def (sc3 g a0 c2 TMP_82) in (let TMP_137
-\def (\lambda (H12: (ex2 C (\lambda (c3: C).(eq C x0 (CHead c3 (Bind Abbr)
-(lift1 (ptrans is i) u)))) (\lambda (c3: C).(csubc g x c3)))).(let TMP_88
-\def (\lambda (c3: C).(let TMP_84 \def (Bind Abbr) in (let TMP_85 \def
-(ptrans is i) in (let TMP_86 \def (lift1 TMP_85 u) in (let TMP_87 \def (CHead
-c3 TMP_84 TMP_86) in (eq C x0 TMP_87)))))) in (let TMP_89 \def (\lambda (c3:
-C).(csubc g x c3)) in (let TMP_90 \def (TLRef i) in (let TMP_91 \def (lift1
-is TMP_90) in (let TMP_92 \def (sc3 g a0 c2 TMP_91) in (let TMP_136 \def
-(\lambda (x1: C).(\lambda (H13: (eq C x0 (CHead x1 (Bind Abbr) (lift1 (ptrans
-is i) u)))).(\lambda (_: (csubc g x x1)).(let TMP_94 \def (\lambda (c0:
-C).(let TMP_93 \def (trans is i) in (getl TMP_93 c2 c0))) in (let TMP_95 \def
-(Bind Abbr) in (let TMP_96 \def (ptrans is i) in (let TMP_97 \def (lift1
-TMP_96 u) in (let TMP_98 \def (CHead x1 TMP_95 TMP_97) in (let H15 \def
-(eq_ind C x0 TMP_94 H9 TMP_98 H13) in (let H_y \def (sc3_abbr g a0 TNil) in
-(let TMP_99 \def (trans is i) in (let TMP_100 \def (TLRef TMP_99) in (let
-TMP_101 \def (\lambda (t0: T).(sc3 g a0 c2 t0)) in (let TMP_102 \def (trans
-is i) in (let TMP_103 \def (ptrans is i) in (let TMP_104 \def (lift1 TMP_103
-u) in (let TMP_105 \def (S i) in (let TMP_106 \def (lift TMP_105 O u) in (let
-TMP_107 \def (lift1 is TMP_106) in (let TMP_108 \def (\lambda (t0: T).(sc3 g
-a0 c2 t0)) in (let TMP_109 \def (S i) in (let TMP_110 \def (PConsTail is
-TMP_109 O) in (let TMP_111 \def (lift1 TMP_110 u) in (let TMP_112 \def
-(\lambda (t0: T).(sc3 g a0 c2 t0)) in (let TMP_113 \def (S i) in (let TMP_114
-\def (PConsTail is TMP_113 O) in (let TMP_115 \def (S i) in (let TMP_116 \def
-(getl_drop Abbr c d u i H0) in (let TMP_117 \def (drop1_cons_tail c d TMP_115
-O TMP_116 is d1 H3) in (let TMP_118 \def (H2 d1 TMP_114 TMP_117 c2 H4) in
-(let TMP_119 \def (S i) in (let TMP_120 \def (lift TMP_119 O u) in (let
-TMP_121 \def (lift1 is TMP_120) in (let TMP_122 \def (S i) in (let TMP_123
-\def (lift1_cons_tail u TMP_122 O is) in (let TMP_124 \def (eq_ind T TMP_111
-TMP_112 TMP_118 TMP_121 TMP_123) in (let TMP_125 \def (trans is i) in (let
-TMP_126 \def (S TMP_125) in (let TMP_127 \def (ptrans is i) in (let TMP_128
-\def (lift1 TMP_127 u) in (let TMP_129 \def (lift TMP_126 O TMP_128) in (let
-TMP_130 \def (lift1_free is i u) in (let TMP_131 \def (eq_ind T TMP_107
-TMP_108 TMP_124 TMP_129 TMP_130) in (let TMP_132 \def (H_y TMP_102 x1 TMP_104
-c2 TMP_131 H15) in (let TMP_133 \def (TLRef i) in (let TMP_134 \def (lift1 is
-TMP_133) in (let TMP_135 \def (lift1_lref is i) in (eq_ind_r T TMP_100
-TMP_101 TMP_132 TMP_134
-TMP_135)))))))))))))))))))))))))))))))))))))))))))))))) in (ex2_ind C TMP_88
-TMP_89 TMP_92 TMP_136 H12)))))))) in (let TMP_164 \def (\lambda (H12: (ex5_3
-C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K (Bind Abbr) (Bind
-Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C x0 (CHead c3
-(Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g
-x c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(sc3 g (asucc g a1)
-x (lift1 (ptrans is i) u))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a1:
-A).(sc3 g a1 c3 w)))))).(let TMP_140 \def (\lambda (_: C).(\lambda (_:
-T).(\lambda (_: A).(let TMP_138 \def (Bind Abbr) in (let TMP_139 \def (Bind
-Abst) in (eq K TMP_138 TMP_139)))))) in (let TMP_143 \def (\lambda (c3:
-C).(\lambda (w: T).(\lambda (_: A).(let TMP_141 \def (Bind Abbr) in (let
-TMP_142 \def (CHead c3 TMP_141 w) in (eq C x0 TMP_142)))))) in (let TMP_144
-\def (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) in
-(let TMP_148 \def (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(let
-TMP_145 \def (asucc g a1) in (let TMP_146 \def (ptrans is i) in (let TMP_147
-\def (lift1 TMP_146 u) in (sc3 g TMP_145 x TMP_147))))))) in (let TMP_149
-\def (\lambda (c3: C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w)))) in
-(let TMP_150 \def (TLRef i) in (let TMP_151 \def (lift1 is TMP_150) in (let
-TMP_152 \def (sc3 g a0 c2 TMP_151) in (let TMP_163 \def (\lambda (x1:
-C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H13: (eq K (Bind Abbr) (Bind
-Abst))).(\lambda (H14: (eq C x0 (CHead x1 (Bind Abbr) x2))).(\lambda (_:
-(csubc g x x1)).(\lambda (_: (sc3 g (asucc g x3) x (lift1 (ptrans is i)
-u))).(\lambda (_: (sc3 g x3 x1 x2)).(let TMP_154 \def (\lambda (c0: C).(let
-TMP_153 \def (trans is i) in (getl TMP_153 c2 c0))) in (let TMP_155 \def
-(Bind Abbr) in (let TMP_156 \def (CHead x1 TMP_155 x2) in (let H18 \def
-(eq_ind C x0 TMP_154 H9 TMP_156 H14) in (let TMP_157 \def (Bind Abbr) in (let
-TMP_158 \def (\lambda (ee: K).(match ee with [(Bind b) \Rightarrow (match b
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
-False]) | (Flat _) \Rightarrow False])) in (let TMP_159 \def (Bind Abst) in
-(let H19 \def (eq_ind K TMP_157 TMP_158 I TMP_159 H13) in (let TMP_160 \def
-(TLRef i) in (let TMP_161 \def (lift1 is TMP_160) in (let TMP_162 \def (sc3 g
-a0 c2 TMP_161) in (False_ind TMP_162 H19)))))))))))))))))))) in (ex5_3_ind C
-T A TMP_140 TMP_143 TMP_144 TMP_148 TMP_149 TMP_152 TMP_163 H12))))))))))) in
-(let TMP_188 \def (\lambda (H12: (ex4_3 B C T (\lambda (b: B).(\lambda (c3:
-C).(\lambda (v2: T).(eq C x0 (CHead c3 (Bind b) v2))))) (\lambda (_:
-B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind Abbr) (Bind Void))))) (\lambda
-(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_:
-B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3)))))).(let TMP_167 \def
-(\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_165 \def (Bind b)
-in (let TMP_166 \def (CHead c3 TMP_165 v2) in (eq C x0 TMP_166)))))) in (let
-TMP_170 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_168
-\def (Bind Abbr) in (let TMP_169 \def (Bind Void) in (eq K TMP_168
-TMP_169)))))) in (let TMP_172 \def (\lambda (b: B).(\lambda (_: C).(\lambda
-(_: T).(let TMP_171 \def (eq B b Void) in (not TMP_171))))) in (let TMP_173
-\def (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3)))) in
-(let TMP_174 \def (TLRef i) in (let TMP_175 \def (lift1 is TMP_174) in (let
-TMP_176 \def (sc3 g a0 c2 TMP_175) in (let TMP_187 \def (\lambda (x1:
-B).(\lambda (x2: C).(\lambda (x3: T).(\lambda (H13: (eq C x0 (CHead x2 (Bind
-x1) x3))).(\lambda (H14: (eq K (Bind Abbr) (Bind Void))).(\lambda (_: (not
-(eq B x1 Void))).(\lambda (_: (csubc g x x2)).(let TMP_178 \def (\lambda (c0:
-C).(let TMP_177 \def (trans is i) in (getl TMP_177 c2 c0))) in (let TMP_179
-\def (Bind x1) in (let TMP_180 \def (CHead x2 TMP_179 x3) in (let H17 \def
-(eq_ind C x0 TMP_178 H9 TMP_180 H13) in (let TMP_181 \def (Bind Abbr) in (let
-TMP_182 \def (\lambda (ee: K).(match ee with [(Bind b) \Rightarrow (match b
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
-False]) | (Flat _) \Rightarrow False])) in (let TMP_183 \def (Bind Void) in
-(let H18 \def (eq_ind K TMP_181 TMP_182 I TMP_183 H14) in (let TMP_184 \def
-(TLRef i) in (let TMP_185 \def (lift1 is TMP_184) in (let TMP_186 \def (sc3 g
-a0 c2 TMP_185) in (False_ind TMP_186 H18))))))))))))))))))) in (ex4_3_ind B C
-T TMP_167 TMP_170 TMP_172 TMP_173 TMP_176 TMP_187 H12)))))))))) in (or3_ind
-TMP_57 TMP_70 TMP_80 TMP_83 TMP_137 TMP_164 TMP_188
-H11))))))))))))))))))))))))))))) in (ex2_ind C TMP_39 TMP_44 TMP_47 TMP_189
-H8))))))))))))))))) in (ex2_ind C TMP_23 TMP_29 TMP_32 TMP_190
-H5)))))))))))))))))))))) in (let TMP_371 \def (\lambda (c: C).(\lambda (d:
-C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind
-Abst) u))).(\lambda (a0: A).(\lambda (H1: (arity g d u (asucc g
-a0))).(\lambda (_: ((\forall (d1: C).(\forall (is: PList).((drop1 is d1 d)
-\to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g (asucc g a0) c2 (lift1 is
-u))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda (H3: (drop1 is d1
-c)).(\lambda (c2: C).(\lambda (H4: (csubc g d1 c2)).(let H5 \def H0 in (let
-H_x \def (drop1_getl_trans is c d1 H3 Abst d u i H5) in (let H6 \def H_x in
-(let TMP_193 \def (\lambda (e2: C).(let TMP_192 \def (ptrans is i) in (drop1
-TMP_192 e2 d))) in (let TMP_199 \def (\lambda (e2: C).(let TMP_194 \def
-(trans is i) in (let TMP_195 \def (Bind Abst) in (let TMP_196 \def (ptrans is
-i) in (let TMP_197 \def (lift1 TMP_196 u) in (let TMP_198 \def (CHead e2
-TMP_195 TMP_197) in (getl TMP_194 d1 TMP_198))))))) in (let TMP_200 \def
-(TLRef i) in (let TMP_201 \def (lift1 is TMP_200) in (let TMP_202 \def (sc3 g
-a0 c2 TMP_201) in (let TMP_370 \def (\lambda (x: C).(\lambda (H7: (drop1
-(ptrans is i) x d)).(\lambda (H8: (getl (trans is i) d1 (CHead x (Bind Abst)
-(lift1 (ptrans is i) u)))).(let TMP_203 \def (Bind Abst) in (let TMP_204 \def
-(ptrans is i) in (let TMP_205 \def (lift1 TMP_204 u) in (let TMP_206 \def
-(CHead x TMP_203 TMP_205) in (let TMP_207 \def (trans is i) in (let H_x0 \def
-(csubc_getl_conf g d1 TMP_206 TMP_207 H8 c2 H4) in (let H9 \def H_x0 in (let
-TMP_209 \def (\lambda (e2: C).(let TMP_208 \def (trans is i) in (getl TMP_208
-c2 e2))) in (let TMP_214 \def (\lambda (e2: C).(let TMP_210 \def (Bind Abst)
-in (let TMP_211 \def (ptrans is i) in (let TMP_212 \def (lift1 TMP_211 u) in
-(let TMP_213 \def (CHead x TMP_210 TMP_212) in (csubc g TMP_213 e2)))))) in
-(let TMP_215 \def (TLRef i) in (let TMP_216 \def (lift1 is TMP_215) in (let
-TMP_217 \def (sc3 g a0 c2 TMP_216) in (let TMP_369 \def (\lambda (x0:
-C).(\lambda (H10: (getl (trans is i) c2 x0)).(\lambda (H11: (csubc g (CHead x
-(Bind Abst) (lift1 (ptrans is i) u)) x0)).(let TMP_218 \def (ptrans is i) in
-(let TMP_219 \def (lift1 TMP_218 u) in (let TMP_220 \def (Bind Abst) in (let
-H_x1 \def (csubc_gen_head_l g x x0 TMP_219 TMP_220 H11) in (let H12 \def H_x1
-in (let TMP_225 \def (\lambda (c3: C).(let TMP_221 \def (Bind Abst) in (let
-TMP_222 \def (ptrans is i) in (let TMP_223 \def (lift1 TMP_222 u) in (let
-TMP_224 \def (CHead c3 TMP_221 TMP_223) in (eq C x0 TMP_224)))))) in (let
-TMP_226 \def (\lambda (c3: C).(csubc g x c3)) in (let TMP_227 \def (ex2 C
-TMP_225 TMP_226) in (let TMP_230 \def (\lambda (_: C).(\lambda (_:
-T).(\lambda (_: A).(let TMP_228 \def (Bind Abst) in (let TMP_229 \def (Bind
-Abst) in (eq K TMP_228 TMP_229)))))) in (let TMP_233 \def (\lambda (c3:
-C).(\lambda (w: T).(\lambda (_: A).(let TMP_231 \def (Bind Abbr) in (let
-TMP_232 \def (CHead c3 TMP_231 w) in (eq C x0 TMP_232)))))) in (let TMP_234
-\def (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) in
-(let TMP_238 \def (\lambda (_: C).(\lambda (_: T).(\lambda (a1: A).(let
-TMP_235 \def (asucc g a1) in (let TMP_236 \def (ptrans is i) in (let TMP_237
-\def (lift1 TMP_236 u) in (sc3 g TMP_235 x TMP_237))))))) in (let TMP_239
-\def (\lambda (c3: C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w)))) in
-(let TMP_240 \def (ex5_3 C T A TMP_230 TMP_233 TMP_234 TMP_238 TMP_239) in
-(let TMP_243 \def (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(let
-TMP_241 \def (Bind b) in (let TMP_242 \def (CHead c3 TMP_241 v2) in (eq C x0
-TMP_242)))))) in (let TMP_246 \def (\lambda (_: B).(\lambda (_: C).(\lambda
-(_: T).(let TMP_244 \def (Bind Abst) in (let TMP_245 \def (Bind Void) in (eq
-K TMP_244 TMP_245)))))) in (let TMP_248 \def (\lambda (b: B).(\lambda (_:
-C).(\lambda (_: T).(let TMP_247 \def (eq B b Void) in (not TMP_247))))) in
-(let TMP_249 \def (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x
-c3)))) in (let TMP_250 \def (ex4_3 B C T TMP_243 TMP_246 TMP_248 TMP_249) in
-(let TMP_251 \def (TLRef i) in (let TMP_252 \def (lift1 is TMP_251) in (let
-TMP_253 \def (sc3 g a0 c2 TMP_252) in (let TMP_295 \def (\lambda (H13: (ex2 C
+(arity g c1 t a)).(arity_ind g (\lambda (c: C).(\lambda (t0: T).(\lambda (a0:
+A).(\forall (d1: C).(\forall (is: PList).((drop1 is d1 c) \to (\forall (c2:
+C).((csubc g d1 c2) \to (sc3 g a0 c2 (lift1 is t0)))))))))) (\lambda (c:
+C).(\lambda (n: nat).(\lambda (d1: C).(\lambda (is: PList).(\lambda (_:
+(drop1 is d1 c)).(\lambda (c2: C).(\lambda (_: (csubc g d1 c2)).(eq_ind_r T
+(TSort n) (\lambda (t0: T).(land (arity g c2 t0 (ASort O n)) (sn3 c2 t0)))
+(conj (arity g c2 (TSort n) (ASort O n)) (sn3 c2 (TSort n)) (arity_sort g c2
+n) (sn3_nf2 c2 (TSort n) (nf2_sort c2 n))) (lift1 is (TSort n)) (lift1_sort n
+is))))))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
+nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0:
+A).(\lambda (_: (arity g d u a0)).(\lambda (H2: ((\forall (d1: C).(\forall
+(is: PList).((drop1 is d1 d) \to (\forall (c2: C).((csubc g d1 c2) \to (sc3 g
+a0 c2 (lift1 is u))))))))).(\lambda (d1: C).(\lambda (is: PList).(\lambda
+(H3: (drop1 is d1 c)).(\lambda (c2: C).(\lambda (H4: (csubc g d1 c2)).(let
+H_x \def (drop1_getl_trans is c d1 H3 Abbr d u i H0) in (let H5 \def H_x in
+(ex2_ind C (\lambda (e2: C).(drop1 (ptrans is i) e2 d)) (\lambda (e2:
+C).(getl (trans is i) d1 (CHead e2 (Bind Abbr) (lift1 (ptrans is i) u))))
+(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x: C).(\lambda (_: (drop1
+(ptrans is i) x d)).(\lambda (H7: (getl (trans is i) d1 (CHead x (Bind Abbr)
+(lift1 (ptrans is i) u)))).(let H_x0 \def (csubc_getl_conf g d1 (CHead x
+(Bind Abbr) (lift1 (ptrans is i) u)) (trans is i) H7 c2 H4) in (let H8 \def
+H_x0 in (ex2_ind C (\lambda (e2: C).(getl (trans is i) c2 e2)) (\lambda (e2:
+C).(csubc g (CHead x (Bind Abbr) (lift1 (ptrans is i) u)) e2)) (sc3 g a0 c2
+(lift1 is (TLRef i))) (\lambda (x0: C).(\lambda (H9: (getl (trans is i) c2
+x0)).(\lambda (H10: (csubc g (CHead x (Bind Abbr) (lift1 (ptrans is i) u))
+x0)).(let H_x1 \def (csubc_gen_head_l g x x0 (lift1 (ptrans is i) u) (Bind
+Abbr) H10) in (let H11 \def H_x1 in (or3_ind (ex2 C (\lambda (c3: C).(eq C x0
+(CHead c3 (Bind Abbr) (lift1 (ptrans is i) u)))) (\lambda (c3: C).(csubc g x
+c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K
+(Bind Abbr) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
+A).(eq C x0 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
+T).(\lambda (_: A).(csubc g x c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans is i) u))))) (\lambda (c3:
+C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w))))) (ex4_3 B C T (\lambda
+(b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C x0 (CHead c3 (Bind b) v2)))))
+(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind Abbr) (Bind
+Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
+Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3)))))
+(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (H12: (ex2 C (\lambda (c3: C).(eq
+C x0 (CHead c3 (Bind Abbr) (lift1 (ptrans is i) u)))) (\lambda (c3: C).(csubc
+g x c3)))).(ex2_ind C (\lambda (c3: C).(eq C x0 (CHead c3 (Bind Abbr) (lift1
+(ptrans is i) u)))) (\lambda (c3: C).(csubc g x c3)) (sc3 g a0 c2 (lift1 is
+(TLRef i))) (\lambda (x1: C).(\lambda (H13: (eq C x0 (CHead x1 (Bind Abbr)
+(lift1 (ptrans is i) u)))).(\lambda (_: (csubc g x x1)).(let H15 \def (eq_ind
+C x0 (\lambda (c0: C).(getl (trans is i) c2 c0)) H9 (CHead x1 (Bind Abbr)
+(lift1 (ptrans is i) u)) H13) in (let H_y \def (sc3_abbr g a0 TNil) in
+(eq_ind_r T (TLRef (trans is i)) (\lambda (t0: T).(sc3 g a0 c2 t0)) (H_y
+(trans is i) x1 (lift1 (ptrans is i) u) c2 (eq_ind T (lift1 is (lift (S i) O
+u)) (\lambda (t0: T).(sc3 g a0 c2 t0)) (eq_ind T (lift1 (PConsTail is (S i)
+O) u) (\lambda (t0: T).(sc3 g a0 c2 t0)) (H2 d1 (PConsTail is (S i) O)
+(drop1_cons_tail c d (S i) O (getl_drop Abbr c d u i H0) is d1 H3) c2 H4)
+(lift1 is (lift (S i) O u)) (lift1_cons_tail u (S i) O is)) (lift (S (trans
+is i)) O (lift1 (ptrans is i) u)) (lift1_free is i u)) H15) (lift1 is (TLRef
+i)) (lift1_lref is i))))))) H12)) (\lambda (H12: (ex5_3 C T A (\lambda (_:
+C).(\lambda (_: T).(\lambda (_: A).(eq K (Bind Abbr) (Bind Abst))))) (\lambda
+(c3: C).(\lambda (w: T).(\lambda (_: A).(eq C x0 (CHead c3 (Bind Abbr) w)))))
+(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x c3)))) (\lambda
+(_: C).(\lambda (_: T).(\lambda (a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans
+is i) u))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3
+w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq
+K (Bind Abbr) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_:
+A).(eq C x0 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_:
+T).(\lambda (_: A).(csubc g x c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda
+(a1: A).(sc3 g (asucc g a1) x (lift1 (ptrans is i) u))))) (\lambda (c3:
+C).(\lambda (w: T).(\lambda (a1: A).(sc3 g a1 c3 w)))) (sc3 g a0 c2 (lift1 is
+(TLRef i))) (\lambda (x1: C).(\lambda (x2: T).(\lambda (x3: A).(\lambda (H13:
+(eq K (Bind Abbr) (Bind Abst))).(\lambda (H14: (eq C x0 (CHead x1 (Bind Abbr)
+x2))).(\lambda (_: (csubc g x x1)).(\lambda (_: (sc3 g (asucc g x3) x (lift1
+(ptrans is i) u))).(\lambda (_: (sc3 g x3 x1 x2)).(let H18 \def (eq_ind C x0
+(\lambda (c0: C).(getl (trans is i) c2 c0)) H9 (CHead x1 (Bind Abbr) x2) H14)
+in (let H19 \def (eq_ind K (Bind Abbr) (\lambda (ee: K).(match ee with [(Bind
+b) \Rightarrow (match b with [Abbr \Rightarrow True | Abst \Rightarrow False
+| Void \Rightarrow False]) | (Flat _) \Rightarrow False])) I (Bind Abst) H13)
+in (False_ind (sc3 g a0 c2 (lift1 is (TLRef i))) H19))))))))))) H12))
+(\lambda (H12: (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2:
+T).(eq C x0 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_:
+C).(\lambda (_: T).(eq K (Bind Abbr) (Bind Void))))) (\lambda (b: B).(\lambda
+(_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3:
+C).(\lambda (_: T).(csubc g x c3)))))).(ex4_3_ind B C T (\lambda (b:
+B).(\lambda (c3: C).(\lambda (v2: T).(eq C x0 (CHead c3 (Bind b) v2)))))
+(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind Abbr) (Bind
+Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b
+Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g x c3))))
+(sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x1: B).(\lambda (x2: C).(\lambda
+(x3: T).(\lambda (H13: (eq C x0 (CHead x2 (Bind x1) x3))).(\lambda (H14: (eq
+K (Bind Abbr) (Bind Void))).(\lambda (_: (not (eq B x1 Void))).(\lambda (_:
+(csubc g x x2)).(let H17 \def (eq_ind C x0 (\lambda (c0: C).(getl (trans is
+i) c2 c0)) H9 (CHead x2 (Bind x1) x3) H13) in (let H18 \def (eq_ind K (Bind
+Abbr) (\lambda (ee: K).(match ee with [(Bind b) \Rightarrow (match b with
+[Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) |
+(Flat _) \Rightarrow False])) I (Bind Void) H14) in (False_ind (sc3 g a0 c2
+(lift1 is (TLRef i))) H18)))))))))) H12)) H11)))))) H8))))))
+H5)))))))))))))))) (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda
+(i: nat).(\lambda (H0: (getl i c (CHead d (Bind Abst) u))).(\lambda (a0:
+A).(\lambda (H1: (arity g d u (asucc g a0))).(\lambda (_: ((\forall (d1:
+C).(\forall (is: PList).((drop1 is d1 d) \to (\forall (c2: C).((csubc g d1
+c2) \to (sc3 g (asucc g a0) c2 (lift1 is u))))))))).(\lambda (d1: C).(\lambda
+(is: PList).(\lambda (H3: (drop1 is d1 c)).(\lambda (c2: C).(\lambda (H4:
+(csubc g d1 c2)).(let H5 \def H0 in (let H_x \def (drop1_getl_trans is c d1
+H3 Abst d u i H5) in (let H6 \def H_x in (ex2_ind C (\lambda (e2: C).(drop1
+(ptrans is i) e2 d)) (\lambda (e2: C).(getl (trans is i) d1 (CHead e2 (Bind
+Abst) (lift1 (ptrans is i) u)))) (sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda
+(x: C).(\lambda (H7: (drop1 (ptrans is i) x d)).(\lambda (H8: (getl (trans is
+i) d1 (CHead x (Bind Abst) (lift1 (ptrans is i) u)))).(let H_x0 \def
+(csubc_getl_conf g d1 (CHead x (Bind Abst) (lift1 (ptrans is i) u)) (trans is
+i) H8 c2 H4) in (let H9 \def H_x0 in (ex2_ind C (\lambda (e2: C).(getl (trans
+is i) c2 e2)) (\lambda (e2: C).(csubc g (CHead x (Bind Abst) (lift1 (ptrans
+is i) u)) e2)) (sc3 g a0 c2 (lift1 is (TLRef i))) (\lambda (x0: C).(\lambda
+(H10: (getl (trans is i) c2 x0)).(\lambda (H11: (csubc g (CHead x (Bind Abst)
+(lift1 (ptrans is i) u)) x0)).(let H_x1 \def (csubc_gen_head_l g x x0 (lift1
+(ptrans is i) u) (Bind Abst) H11) in (let H12 \def H_x1 in (or3_ind (ex2 C