-a1))))).(let H3 \def H2 in (ex2_ind A (\lambda (a1: A).(arity g d u a1))
-(\lambda (a1: A).(arity g d t (asucc g a1))) (ex2 A (\lambda (a1: A).(arity g
-c0 (TLRef n) a1)) (\lambda (a1: A).(arity g c0 (lift (S n) O t) (asucc g
-a1)))) (\lambda (x: A).(\lambda (H4: (arity g d u x)).(\lambda (H5: (arity g
-d t (asucc g x))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (TLRef n) a1))
-(\lambda (a1: A).(arity g c0 (lift (S n) O t) (asucc g a1))) x (arity_abbr g
-c0 d u n H0 x H4) (arity_lift g d t (asucc g x) H5 c0 (S n) O (getl_drop Abbr
-c0 d u n H0)))))) H3)))))))))) (\lambda (n: nat).(\lambda (c0: C).(\lambda
-(d: C).(\lambda (u: T).(\lambda (H0: (getl n c0 (CHead d (Bind Abst)
-u))).(\lambda (t: T).(\lambda (_: (ty3 g d u t)).(\lambda (H2: (ex2 A
-(\lambda (a1: A).(arity g d u a1)) (\lambda (a1: A).(arity g d t (asucc g
-a1))))).(let H3 \def H2 in (ex2_ind A (\lambda (a1: A).(arity g d u a1))
-(\lambda (a1: A).(arity g d t (asucc g a1))) (ex2 A (\lambda (a1: A).(arity g
-c0 (TLRef n) a1)) (\lambda (a1: A).(arity g c0 (lift (S n) O u) (asucc g
-a1)))) (\lambda (x: A).(\lambda (H4: (arity g d u x)).(\lambda (_: (arity g d
-t (asucc g x))).(let H_x \def (leq_asucc g x) in (let H6 \def H_x in (ex_ind
-A (\lambda (a0: A).(leq g x (asucc g a0))) (ex2 A (\lambda (a1: A).(arity g
-c0 (TLRef n) a1)) (\lambda (a1: A).(arity g c0 (lift (S n) O u) (asucc g
-a1)))) (\lambda (x0: A).(\lambda (H7: (leq g x (asucc g x0))).(ex_intro2 A
-(\lambda (a1: A).(arity g c0 (TLRef n) a1)) (\lambda (a1: A).(arity g c0
-(lift (S n) O u) (asucc g a1))) x0 (arity_abst g c0 d u n H0 x0 (arity_repl g
-d u x H4 (asucc g x0) H7)) (arity_repl g c0 (lift (S n) O u) x (arity_lift g
-d u x H4 c0 (S n) O (getl_drop Abst c0 d u n H0)) (asucc g x0) H7))))
-H6)))))) H3)))))))))) (\lambda (c0: C).(\lambda (u: T).(\lambda (t:
-T).(\lambda (_: (ty3 g c0 u t)).(\lambda (H1: (ex2 A (\lambda (a1: A).(arity
-g c0 u a1)) (\lambda (a1: A).(arity g c0 t (asucc g a1))))).(\lambda (b:
-B).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (ty3 g (CHead c0 (Bind b)
-u) t3 t4)).(\lambda (H3: (ex2 A (\lambda (a1: A).(arity g (CHead c0 (Bind b)
-u) t3 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t4 (asucc g
-a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 u a1))
-(\lambda (a1: A).(arity g c0 t (asucc g a1))) (ex2 A (\lambda (a1: A).(arity
-g c0 (THead (Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b)
-u t4) (asucc g a1)))) (\lambda (x: A).(\lambda (H5: (arity g c0 u
-x)).(\lambda (_: (arity g c0 t (asucc g x))).(let H7 \def H3 in (ex2_ind A
-(\lambda (a1: A).(arity g (CHead c0 (Bind b) u) t3 a1)) (\lambda (a1:
-A).(arity g (CHead c0 (Bind b) u) t4 (asucc g a1))) (ex2 A (\lambda (a1:
-A).(arity g c0 (THead (Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead
-(Bind b) u t4) (asucc g a1)))) (\lambda (x0: A).(\lambda (H8: (arity g (CHead
-c0 (Bind b) u) t3 x0)).(\lambda (H9: (arity g (CHead c0 (Bind b) u) t4 (asucc
-g x0))).(let H_x \def (leq_asucc g x) in (let H10 \def H_x in (ex_ind A
-(\lambda (a0: A).(leq g x (asucc g a0))) (ex2 A (\lambda (a1: A).(arity g c0
-(THead (Bind b) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind b) u t4)
-(asucc g a1)))) (\lambda (x1: A).(\lambda (H11: (leq g x (asucc g
-x1))).(B_ind (\lambda (b0: B).((arity g (CHead c0 (Bind b0) u) t3 x0) \to
-((arity g (CHead c0 (Bind b0) u) t4 (asucc g x0)) \to (ex2 A (\lambda (a1:
-A).(arity g c0 (THead (Bind b0) u t3) a1)) (\lambda (a1: A).(arity g c0
-(THead (Bind b0) u t4) (asucc g a1))))))) (\lambda (H12: (arity g (CHead c0
-(Bind Abbr) u) t3 x0)).(\lambda (H13: (arity g (CHead c0 (Bind Abbr) u) t4
-(asucc g x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Bind Abbr) u
-t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abbr) u t4) (asucc g a1)))
-x0 (arity_bind g Abbr not_abbr_abst c0 u x H5 t3 x0 H12) (arity_bind g Abbr
-not_abbr_abst c0 u x H5 t4 (asucc g x0) H13)))) (\lambda (H12: (arity g
-(CHead c0 (Bind Abst) u) t3 x0)).(\lambda (H13: (arity g (CHead c0 (Bind
-Abst) u) t4 (asucc g x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead
-(Bind Abst) u t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t4)
-(asucc g a1))) (AHead x1 x0) (arity_head g c0 u x1 (arity_repl g c0 u x H5
-(asucc g x1) H11) t3 x0 H12) (arity_repl g c0 (THead (Bind Abst) u t4) (AHead
-x1 (asucc g x0)) (arity_head g c0 u x1 (arity_repl g c0 u x H5 (asucc g x1)
-H11) t4 (asucc g x0) H13) (asucc g (AHead x1 x0)) (leq_refl g (asucc g (AHead
-x1 x0))))))) (\lambda (H12: (arity g (CHead c0 (Bind Void) u) t3
-x0)).(\lambda (H13: (arity g (CHead c0 (Bind Void) u) t4 (asucc g
-x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Bind Void) u t3) a1))
-(\lambda (a1: A).(arity g c0 (THead (Bind Void) u t4) (asucc g a1))) x0
-(arity_bind g Void (sym_not_eq B Abst Void not_abst_void) c0 u x H5 t3 x0
-H12) (arity_bind g Void (sym_not_eq B Abst Void not_abst_void) c0 u x H5 t4
-(asucc g x0) H13)))) b H8 H9))) H10)))))) H7))))) H4)))))))))))) (\lambda
-(c0: C).(\lambda (w: T).(\lambda (u: T).(\lambda (_: (ty3 g c0 w u)).(\lambda
-(H1: (ex2 A (\lambda (a1: A).(arity g c0 w a1)) (\lambda (a1: A).(arity g c0
-u (asucc g a1))))).(\lambda (v: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 v
-(THead (Bind Abst) u t))).(\lambda (H3: (ex2 A (\lambda (a1: A).(arity g c0 v
-a1)) (\lambda (a1: A).(arity g c0 (THead (Bind Abst) u t) (asucc g
-a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 w a1))
-(\lambda (a1: A).(arity g c0 u (asucc g a1))) (ex2 A (\lambda (a1: A).(arity
-g c0 (THead (Flat Appl) w v) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat
-Appl) w (THead (Bind Abst) u t)) (asucc g a1)))) (\lambda (x: A).(\lambda
-(H5: (arity g c0 w x)).(\lambda (H6: (arity g c0 u (asucc g x))).(let H7 \def
-H3 in (ex2_ind A (\lambda (a1: A).(arity g c0 v a1)) (\lambda (a1: A).(arity
-g c0 (THead (Bind Abst) u t) (asucc g a1))) (ex2 A (\lambda (a1: A).(arity g
-c0 (THead (Flat Appl) w v) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat
-Appl) w (THead (Bind Abst) u t)) (asucc g a1)))) (\lambda (x0: A).(\lambda
-(H8: (arity g c0 v x0)).(\lambda (H9: (arity g c0 (THead (Bind Abst) u t)
-(asucc g x0))).(let H10 \def (arity_gen_abst g c0 u t (asucc g x0) H9) in
-(ex3_2_ind A A (\lambda (a1: A).(\lambda (a2: A).(eq A (asucc g x0) (AHead a1
-a2)))) (\lambda (a1: A).(\lambda (_: A).(arity g c0 u (asucc g a1))))
-(\lambda (_: A).(\lambda (a2: A).(arity g (CHead c0 (Bind Abst) u) t a2)))
-(ex2 A (\lambda (a1: A).(arity g c0 (THead (Flat Appl) w v) a1)) (\lambda
-(a1: A).(arity g c0 (THead (Flat Appl) w (THead (Bind Abst) u t)) (asucc g
-a1)))) (\lambda (x1: A).(\lambda (x2: A).(\lambda (H11: (eq A (asucc g x0)
+a1))))).(let H3 \def H2 in (let TMP_75 \def (\lambda (a1: A).(arity g d u
+a1)) in (let TMP_77 \def (\lambda (a1: A).(let TMP_76 \def (asucc g a1) in
+(arity g d t TMP_76))) in (let TMP_79 \def (\lambda (a1: A).(let TMP_78 \def
+(TLRef n) in (arity g c0 TMP_78 a1))) in (let TMP_83 \def (\lambda (a1:
+A).(let TMP_80 \def (S n) in (let TMP_81 \def (lift TMP_80 O u) in (let
+TMP_82 \def (asucc g a1) in (arity g c0 TMP_81 TMP_82))))) in (let TMP_84
+\def (ex2 A TMP_79 TMP_83) in (let TMP_111 \def (\lambda (x: A).(\lambda (H4:
+(arity g d u x)).(\lambda (_: (arity g d t (asucc g x))).(let H_x \def
+(leq_asucc g x) in (let H6 \def H_x in (let TMP_86 \def (\lambda (a0: A).(let
+TMP_85 \def (asucc g a0) in (leq g x TMP_85))) in (let TMP_88 \def (\lambda
+(a1: A).(let TMP_87 \def (TLRef n) in (arity g c0 TMP_87 a1))) in (let TMP_92
+\def (\lambda (a1: A).(let TMP_89 \def (S n) in (let TMP_90 \def (lift TMP_89
+O u) in (let TMP_91 \def (asucc g a1) in (arity g c0 TMP_90 TMP_91))))) in
+(let TMP_93 \def (ex2 A TMP_88 TMP_92) in (let TMP_110 \def (\lambda (x0:
+A).(\lambda (H7: (leq g x (asucc g x0))).(let TMP_95 \def (\lambda (a1:
+A).(let TMP_94 \def (TLRef n) in (arity g c0 TMP_94 a1))) in (let TMP_99 \def
+(\lambda (a1: A).(let TMP_96 \def (S n) in (let TMP_97 \def (lift TMP_96 O u)
+in (let TMP_98 \def (asucc g a1) in (arity g c0 TMP_97 TMP_98))))) in (let
+TMP_100 \def (asucc g x0) in (let TMP_101 \def (arity_repl g d u x H4 TMP_100
+H7) in (let TMP_102 \def (arity_abst g c0 d u n H0 x0 TMP_101) in (let
+TMP_103 \def (S n) in (let TMP_104 \def (lift TMP_103 O u) in (let TMP_105
+\def (S n) in (let TMP_106 \def (getl_drop Abst c0 d u n H0) in (let TMP_107
+\def (arity_lift g d u x H4 c0 TMP_105 O TMP_106) in (let TMP_108 \def (asucc
+g x0) in (let TMP_109 \def (arity_repl g c0 TMP_104 x TMP_107 TMP_108 H7) in
+(ex_intro2 A TMP_95 TMP_99 x0 TMP_102 TMP_109))))))))))))))) in (ex_ind A
+TMP_86 TMP_93 TMP_110 H6))))))))))) in (ex2_ind A TMP_75 TMP_77 TMP_84
+TMP_111 H3)))))))))))))))) in (let TMP_208 \def (\lambda (c0: C).(\lambda (u:
+T).(\lambda (t: T).(\lambda (_: (ty3 g c0 u t)).(\lambda (H1: (ex2 A (\lambda
+(a1: A).(arity g c0 u a1)) (\lambda (a1: A).(arity g c0 t (asucc g
+a1))))).(\lambda (b: B).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (ty3 g
+(CHead c0 (Bind b) u) t3 t4)).(\lambda (H3: (ex2 A (\lambda (a1: A).(arity g
+(CHead c0 (Bind b) u) t3 a1)) (\lambda (a1: A).(arity g (CHead c0 (Bind b) u)
+t4 (asucc g a1))))).(let H4 \def H1 in (let TMP_113 \def (\lambda (a1:
+A).(arity g c0 u a1)) in (let TMP_115 \def (\lambda (a1: A).(let TMP_114 \def
+(asucc g a1) in (arity g c0 t TMP_114))) in (let TMP_118 \def (\lambda (a1:
+A).(let TMP_116 \def (Bind b) in (let TMP_117 \def (THead TMP_116 u t3) in
+(arity g c0 TMP_117 a1)))) in (let TMP_122 \def (\lambda (a1: A).(let TMP_119
+\def (Bind b) in (let TMP_120 \def (THead TMP_119 u t4) in (let TMP_121 \def
+(asucc g a1) in (arity g c0 TMP_120 TMP_121))))) in (let TMP_123 \def (ex2 A
+TMP_118 TMP_122) in (let TMP_207 \def (\lambda (x: A).(\lambda (H5: (arity g
+c0 u x)).(\lambda (_: (arity g c0 t (asucc g x))).(let H7 \def H3 in (let
+TMP_126 \def (\lambda (a1: A).(let TMP_124 \def (Bind b) in (let TMP_125 \def
+(CHead c0 TMP_124 u) in (arity g TMP_125 t3 a1)))) in (let TMP_130 \def
+(\lambda (a1: A).(let TMP_127 \def (Bind b) in (let TMP_128 \def (CHead c0
+TMP_127 u) in (let TMP_129 \def (asucc g a1) in (arity g TMP_128 t4
+TMP_129))))) in (let TMP_133 \def (\lambda (a1: A).(let TMP_131 \def (Bind b)
+in (let TMP_132 \def (THead TMP_131 u t3) in (arity g c0 TMP_132 a1)))) in
+(let TMP_137 \def (\lambda (a1: A).(let TMP_134 \def (Bind b) in (let TMP_135
+\def (THead TMP_134 u t4) in (let TMP_136 \def (asucc g a1) in (arity g c0
+TMP_135 TMP_136))))) in (let TMP_138 \def (ex2 A TMP_133 TMP_137) in (let
+TMP_206 \def (\lambda (x0: A).(\lambda (H8: (arity g (CHead c0 (Bind b) u) t3
+x0)).(\lambda (H9: (arity g (CHead c0 (Bind b) u) t4 (asucc g x0))).(let H_x
+\def (leq_asucc g x) in (let H10 \def H_x in (let TMP_140 \def (\lambda (a0:
+A).(let TMP_139 \def (asucc g a0) in (leq g x TMP_139))) in (let TMP_143 \def
+(\lambda (a1: A).(let TMP_141 \def (Bind b) in (let TMP_142 \def (THead
+TMP_141 u t3) in (arity g c0 TMP_142 a1)))) in (let TMP_147 \def (\lambda
+(a1: A).(let TMP_144 \def (Bind b) in (let TMP_145 \def (THead TMP_144 u t4)
+in (let TMP_146 \def (asucc g a1) in (arity g c0 TMP_145 TMP_146))))) in (let
+TMP_148 \def (ex2 A TMP_143 TMP_147) in (let TMP_205 \def (\lambda (x1:
+A).(\lambda (H11: (leq g x (asucc g x1))).(let TMP_156 \def (\lambda (b0:
+B).((arity g (CHead c0 (Bind b0) u) t3 x0) \to ((arity g (CHead c0 (Bind b0)
+u) t4 (asucc g x0)) \to (let TMP_151 \def (\lambda (a1: A).(let TMP_149 \def
+(Bind b0) in (let TMP_150 \def (THead TMP_149 u t3) in (arity g c0 TMP_150
+a1)))) in (let TMP_155 \def (\lambda (a1: A).(let TMP_152 \def (Bind b0) in
+(let TMP_153 \def (THead TMP_152 u t4) in (let TMP_154 \def (asucc g a1) in
+(arity g c0 TMP_153 TMP_154))))) in (ex2 A TMP_151 TMP_155)))))) in (let
+TMP_167 \def (\lambda (H12: (arity g (CHead c0 (Bind Abbr) u) t3
+x0)).(\lambda (H13: (arity g (CHead c0 (Bind Abbr) u) t4 (asucc g x0))).(let
+TMP_159 \def (\lambda (a1: A).(let TMP_157 \def (Bind Abbr) in (let TMP_158
+\def (THead TMP_157 u t3) in (arity g c0 TMP_158 a1)))) in (let TMP_163 \def
+(\lambda (a1: A).(let TMP_160 \def (Bind Abbr) in (let TMP_161 \def (THead
+TMP_160 u t4) in (let TMP_162 \def (asucc g a1) in (arity g c0 TMP_161
+TMP_162))))) in (let TMP_164 \def (arity_bind g Abbr not_abbr_abst c0 u x H5
+t3 x0 H12) in (let TMP_165 \def (asucc g x0) in (let TMP_166 \def (arity_bind
+g Abbr not_abbr_abst c0 u x H5 t4 TMP_165 H13) in (ex_intro2 A TMP_159
+TMP_163 x0 TMP_164 TMP_166)))))))) in (let TMP_193 \def (\lambda (H12: (arity
+g (CHead c0 (Bind Abst) u) t3 x0)).(\lambda (H13: (arity g (CHead c0 (Bind
+Abst) u) t4 (asucc g x0))).(let TMP_170 \def (\lambda (a1: A).(let TMP_168
+\def (Bind Abst) in (let TMP_169 \def (THead TMP_168 u t3) in (arity g c0
+TMP_169 a1)))) in (let TMP_174 \def (\lambda (a1: A).(let TMP_171 \def (Bind
+Abst) in (let TMP_172 \def (THead TMP_171 u t4) in (let TMP_173 \def (asucc g
+a1) in (arity g c0 TMP_172 TMP_173))))) in (let TMP_175 \def (AHead x1 x0) in
+(let TMP_176 \def (asucc g x1) in (let TMP_177 \def (arity_repl g c0 u x H5
+TMP_176 H11) in (let TMP_178 \def (arity_head g c0 u x1 TMP_177 t3 x0 H12) in
+(let TMP_179 \def (Bind Abst) in (let TMP_180 \def (THead TMP_179 u t4) in
+(let TMP_181 \def (asucc g x0) in (let TMP_182 \def (AHead x1 TMP_181) in
+(let TMP_183 \def (asucc g x1) in (let TMP_184 \def (arity_repl g c0 u x H5
+TMP_183 H11) in (let TMP_185 \def (asucc g x0) in (let TMP_186 \def
+(arity_head g c0 u x1 TMP_184 t4 TMP_185 H13) in (let TMP_187 \def (AHead x1
+x0) in (let TMP_188 \def (asucc g TMP_187) in (let TMP_189 \def (AHead x1 x0)
+in (let TMP_190 \def (asucc g TMP_189) in (let TMP_191 \def (leq_refl g
+TMP_190) in (let TMP_192 \def (arity_repl g c0 TMP_180 TMP_182 TMP_186
+TMP_188 TMP_191) in (ex_intro2 A TMP_170 TMP_174 TMP_175 TMP_178
+TMP_192))))))))))))))))))))))) in (let TMP_204 \def (\lambda (H12: (arity g
+(CHead c0 (Bind Void) u) t3 x0)).(\lambda (H13: (arity g (CHead c0 (Bind
+Void) u) t4 (asucc g x0))).(let TMP_196 \def (\lambda (a1: A).(let TMP_194
+\def (Bind Void) in (let TMP_195 \def (THead TMP_194 u t3) in (arity g c0
+TMP_195 a1)))) in (let TMP_200 \def (\lambda (a1: A).(let TMP_197 \def (Bind
+Void) in (let TMP_198 \def (THead TMP_197 u t4) in (let TMP_199 \def (asucc g
+a1) in (arity g c0 TMP_198 TMP_199))))) in (let TMP_201 \def (arity_bind g
+Void not_void_abst c0 u x H5 t3 x0 H12) in (let TMP_202 \def (asucc g x0) in
+(let TMP_203 \def (arity_bind g Void not_void_abst c0 u x H5 t4 TMP_202 H13)
+in (ex_intro2 A TMP_196 TMP_200 x0 TMP_201 TMP_203)))))))) in (B_ind TMP_156
+TMP_167 TMP_193 TMP_204 b H8 H9))))))) in (ex_ind A TMP_140 TMP_148 TMP_205
+H10))))))))))) in (ex2_ind A TMP_126 TMP_130 TMP_138 TMP_206 H7))))))))))) in
+(ex2_ind A TMP_113 TMP_115 TMP_123 TMP_207 H4)))))))))))))))))) in (let
+TMP_304 \def (\lambda (c0: C).(\lambda (w: T).(\lambda (u: T).(\lambda (_:
+(ty3 g c0 w u)).(\lambda (H1: (ex2 A (\lambda (a1: A).(arity g c0 w a1))
+(\lambda (a1: A).(arity g c0 u (asucc g a1))))).(\lambda (v: T).(\lambda (t:
+T).(\lambda (_: (ty3 g c0 v (THead (Bind Abst) u t))).(\lambda (H3: (ex2 A
+(\lambda (a1: A).(arity g c0 v a1)) (\lambda (a1: A).(arity g c0 (THead (Bind
+Abst) u t) (asucc g a1))))).(let H4 \def H1 in (let TMP_209 \def (\lambda
+(a1: A).(arity g c0 w a1)) in (let TMP_211 \def (\lambda (a1: A).(let TMP_210
+\def (asucc g a1) in (arity g c0 u TMP_210))) in (let TMP_214 \def (\lambda
+(a1: A).(let TMP_212 \def (Flat Appl) in (let TMP_213 \def (THead TMP_212 w
+v) in (arity g c0 TMP_213 a1)))) in (let TMP_220 \def (\lambda (a1: A).(let
+TMP_215 \def (Flat Appl) in (let TMP_216 \def (Bind Abst) in (let TMP_217
+\def (THead TMP_216 u t) in (let TMP_218 \def (THead TMP_215 w TMP_217) in
+(let TMP_219 \def (asucc g a1) in (arity g c0 TMP_218 TMP_219))))))) in (let
+TMP_221 \def (ex2 A TMP_214 TMP_220) in (let TMP_303 \def (\lambda (x:
+A).(\lambda (H5: (arity g c0 w x)).(\lambda (H6: (arity g c0 u (asucc g
+x))).(let H7 \def H3 in (let TMP_222 \def (\lambda (a1: A).(arity g c0 v a1))
+in (let TMP_226 \def (\lambda (a1: A).(let TMP_223 \def (Bind Abst) in (let
+TMP_224 \def (THead TMP_223 u t) in (let TMP_225 \def (asucc g a1) in (arity
+g c0 TMP_224 TMP_225))))) in (let TMP_229 \def (\lambda (a1: A).(let TMP_227
+\def (Flat Appl) in (let TMP_228 \def (THead TMP_227 w v) in (arity g c0
+TMP_228 a1)))) in (let TMP_235 \def (\lambda (a1: A).(let TMP_230 \def (Flat
+Appl) in (let TMP_231 \def (Bind Abst) in (let TMP_232 \def (THead TMP_231 u
+t) in (let TMP_233 \def (THead TMP_230 w TMP_232) in (let TMP_234 \def (asucc
+g a1) in (arity g c0 TMP_233 TMP_234))))))) in (let TMP_236 \def (ex2 A
+TMP_229 TMP_235) in (let TMP_302 \def (\lambda (x0: A).(\lambda (H8: (arity g
+c0 v x0)).(\lambda (H9: (arity g c0 (THead (Bind Abst) u t) (asucc g
+x0))).(let TMP_237 \def (asucc g x0) in (let H10 \def (arity_gen_abst g c0 u
+t TMP_237 H9) in (let TMP_240 \def (\lambda (a1: A).(\lambda (a2: A).(let
+TMP_238 \def (asucc g x0) in (let TMP_239 \def (AHead a1 a2) in (eq A TMP_238
+TMP_239))))) in (let TMP_242 \def (\lambda (a1: A).(\lambda (_: A).(let
+TMP_241 \def (asucc g a1) in (arity g c0 u TMP_241)))) in (let TMP_245 \def
+(\lambda (_: A).(\lambda (a2: A).(let TMP_243 \def (Bind Abst) in (let
+TMP_244 \def (CHead c0 TMP_243 u) in (arity g TMP_244 t a2))))) in (let
+TMP_248 \def (\lambda (a1: A).(let TMP_246 \def (Flat Appl) in (let TMP_247
+\def (THead TMP_246 w v) in (arity g c0 TMP_247 a1)))) in (let TMP_254 \def
+(\lambda (a1: A).(let TMP_249 \def (Flat Appl) in (let TMP_250 \def (Bind
+Abst) in (let TMP_251 \def (THead TMP_250 u t) in (let TMP_252 \def (THead
+TMP_249 w TMP_251) in (let TMP_253 \def (asucc g a1) in (arity g c0 TMP_252
+TMP_253))))))) in (let TMP_255 \def (ex2 A TMP_248 TMP_254) in (let TMP_301
+\def (\lambda (x1: A).(\lambda (x2: A).(\lambda (H11: (eq A (asucc g x0)