-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)
-(AHead x1 x2))).(\lambda (H12: (arity g c0 u (asucc g x1))).(\lambda (H13:
-(arity g (CHead c0 (Bind Abst) u) t x2)).(let TMP_256 \def (asucc g x0) in
-(let TMP_257 \def (AHead x1 x2) in (let H14 \def (sym_eq A TMP_256 TMP_257
-H11) in (let H15 \def (asucc_gen_head g x1 x2 x0 H14) in (let TMP_259 \def
-(\lambda (a0: A).(let TMP_258 \def (AHead x1 a0) in (eq A x0 TMP_258))) in
-(let TMP_261 \def (\lambda (a0: A).(let TMP_260 \def (asucc g a0) in (eq A x2
-TMP_260))) in (let TMP_264 \def (\lambda (a1: A).(let TMP_262 \def (Flat
-Appl) in (let TMP_263 \def (THead TMP_262 w v) in (arity g c0 TMP_263 a1))))
-in (let TMP_270 \def (\lambda (a1: A).(let TMP_265 \def (Flat Appl) in (let
-TMP_266 \def (Bind Abst) in (let TMP_267 \def (THead TMP_266 u t) in (let
-TMP_268 \def (THead TMP_265 w TMP_267) in (let TMP_269 \def (asucc g a1) in
-(arity g c0 TMP_268 TMP_269))))))) in (let TMP_271 \def (ex2 A TMP_264
-TMP_270) in (let TMP_300 \def (\lambda (x3: A).(\lambda (H16: (eq A x0 (AHead
-x1 x3))).(\lambda (H17: (eq A x2 (asucc g x3))).(let TMP_274 \def (\lambda
-(a: A).(let TMP_272 \def (Bind Abst) in (let TMP_273 \def (CHead c0 TMP_272
-u) in (arity g TMP_273 t a)))) in (let TMP_275 \def (asucc g x3) in (let H18
-\def (eq_ind A x2 TMP_274 H13 TMP_275 H17) in (let TMP_276 \def (\lambda (a:
-A).(arity g c0 v a)) in (let TMP_277 \def (AHead x1 x3) in (let H19 \def
-(eq_ind A x0 TMP_276 H8 TMP_277 H16) in (let TMP_280 \def (\lambda (a1:
-A).(let TMP_278 \def (Flat Appl) in (let TMP_279 \def (THead TMP_278 w v) in
-(arity g c0 TMP_279 a1)))) in (let TMP_286 \def (\lambda (a1: A).(let TMP_281
-\def (Flat Appl) in (let TMP_282 \def (Bind Abst) in (let TMP_283 \def (THead
-TMP_282 u t) in (let TMP_284 \def (THead TMP_281 w TMP_283) in (let TMP_285
-\def (asucc g a1) in (arity g c0 TMP_284 TMP_285))))))) in (let TMP_287 \def
-(asucc g x1) in (let TMP_288 \def (asucc g x) in (let TMP_289 \def
-(arity_mono g c0 u TMP_287 H12 TMP_288 H6) in (let TMP_290 \def (asucc_inj g
-x1 x TMP_289) in (let TMP_291 \def (leq_sym g x1 x TMP_290) in (let TMP_292
-\def (arity_repl g c0 w x H5 x1 TMP_291) in (let TMP_293 \def (arity_appl g
-c0 w x1 TMP_292 v x3 H19) in (let TMP_294 \def (Bind Abst) in (let TMP_295
-\def (THead TMP_294 u t) in (let TMP_296 \def (asucc g x3) in (let TMP_297
-\def (asucc g x3) in (let TMP_298 \def (arity_head g c0 u x H6 t TMP_297 H18)
-in (let TMP_299 \def (arity_appl g c0 w x H5 TMP_295 TMP_296 TMP_298) in
-(ex_intro2 A TMP_280 TMP_286 x3 TMP_293 TMP_299))))))))))))))))))))))))) in
-(ex2_ind A TMP_259 TMP_261 TMP_271 TMP_300 H15)))))))))))))))) in (ex3_2_ind
-A A TMP_240 TMP_242 TMP_245 TMP_255 TMP_301 H10))))))))))))) in (ex2_ind A
-TMP_222 TMP_226 TMP_236 TMP_302 H7))))))))))) in (ex2_ind A TMP_209 TMP_211
-TMP_221 TMP_303 H4))))))))))))))))) in (let TMP_347 \def (\lambda (c0:
-C).(\lambda (t3: T).(\lambda (t4: T).(\lambda (_: (ty3 g c0 t3 t4)).(\lambda
-(H1: (ex2 A (\lambda (a1: A).(arity g c0 t3 a1)) (\lambda (a1: A).(arity g c0
-t4 (asucc g a1))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t4 t0)).(\lambda
-(H3: (ex2 A (\lambda (a1: A).(arity g c0 t4 a1)) (\lambda (a1: A).(arity g c0
-t0 (asucc g a1))))).(let H4 \def H1 in (let TMP_305 \def (\lambda (a1:
-A).(arity g c0 t3 a1)) in (let TMP_307 \def (\lambda (a1: A).(let TMP_306
-\def (asucc g a1) in (arity g c0 t4 TMP_306))) in (let TMP_310 \def (\lambda
-(a1: A).(let TMP_308 \def (Flat Cast) in (let TMP_309 \def (THead TMP_308 t4
-t3) in (arity g c0 TMP_309 a1)))) in (let TMP_314 \def (\lambda (a1: A).(let
-TMP_311 \def (Flat Cast) in (let TMP_312 \def (THead TMP_311 t0 t4) in (let
-TMP_313 \def (asucc g a1) in (arity g c0 TMP_312 TMP_313))))) in (let TMP_315
-\def (ex2 A TMP_310 TMP_314) in (let TMP_346 \def (\lambda (x: A).(\lambda
-(H5: (arity g c0 t3 x)).(\lambda (H6: (arity g c0 t4 (asucc g x))).(let H7
-\def H3 in (let TMP_316 \def (\lambda (a1: A).(arity g c0 t4 a1)) in (let
-TMP_318 \def (\lambda (a1: A).(let TMP_317 \def (asucc g a1) in (arity g c0
-t0 TMP_317))) in (let TMP_321 \def (\lambda (a1: A).(let TMP_319 \def (Flat
-Cast) in (let TMP_320 \def (THead TMP_319 t4 t3) in (arity g c0 TMP_320
-a1)))) in (let TMP_325 \def (\lambda (a1: A).(let TMP_322 \def (Flat Cast) in
-(let TMP_323 \def (THead TMP_322 t0 t4) in (let TMP_324 \def (asucc g a1) in
-(arity g c0 TMP_323 TMP_324))))) in (let TMP_326 \def (ex2 A TMP_321 TMP_325)
-in (let TMP_345 \def (\lambda (x0: A).(\lambda (H8: (arity g c0 t4
-x0)).(\lambda (H9: (arity g c0 t0 (asucc g x0))).(let TMP_329 \def (\lambda
-(a1: A).(let TMP_327 \def (Flat Cast) in (let TMP_328 \def (THead TMP_327 t4
-t3) in (arity g c0 TMP_328 a1)))) in (let TMP_333 \def (\lambda (a1: A).(let
-TMP_330 \def (Flat Cast) in (let TMP_331 \def (THead TMP_330 t0 t4) in (let
-TMP_332 \def (asucc g a1) in (arity g c0 TMP_331 TMP_332))))) in (let TMP_334
-\def (arity_cast g c0 t4 x H6 t3 H5) in (let TMP_335 \def (asucc g x) in (let
-TMP_336 \def (asucc g x0) in (let TMP_337 \def (asucc g x) in (let TMP_338
-\def (asucc g TMP_337) in (let TMP_339 \def (asucc g x) in (let TMP_340 \def
-(asucc g x) in (let TMP_341 \def (arity_mono g c0 t4 x0 H8 TMP_340 H6) in
-(let TMP_342 \def (asucc_repl g x0 TMP_339 TMP_341) in (let TMP_343 \def
-(arity_repl g c0 t0 TMP_336 H9 TMP_338 TMP_342) in (let TMP_344 \def
-(arity_cast g c0 t0 TMP_335 TMP_343 t4 H6) in (ex_intro2 A TMP_329 TMP_333 x
-TMP_334 TMP_344))))))))))))))))) in (ex2_ind A TMP_316 TMP_318 TMP_326
-TMP_345 H7))))))))))) in (ex2_ind A TMP_305 TMP_307 TMP_315 TMP_346
-H4)))))))))))))))) in (ty3_ind g TMP_4 TMP_40 TMP_51 TMP_74 TMP_112 TMP_208
-TMP_304 TMP_347 c t1 t2 H))))))))))))).
+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) (AHead x1 x2))).(\lambda (H12: (arity g c0 u (asucc g
+x1))).(\lambda (H13: (arity g (CHead c0 (Bind Abst) u) t x2)).(let H14 \def
+(sym_eq A (asucc g x0) (AHead x1 x2) H11) in (let H15 \def (asucc_gen_head g
+x1 x2 x0 H14) in (ex2_ind A (\lambda (a0: A).(eq A x0 (AHead x1 a0)))
+(\lambda (a0: A).(eq A x2 (asucc g a0))) (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 (x3: A).(\lambda (H16:
+(eq A x0 (AHead x1 x3))).(\lambda (H17: (eq A x2 (asucc g x3))).(let H18 \def
+(eq_ind A x2 (\lambda (a: A).(arity g (CHead c0 (Bind Abst) u) t a)) H13
+(asucc g x3) H17) in (let H19 \def (eq_ind A x0 (\lambda (a: A).(arity g c0 v
+a)) H8 (AHead x1 x3) H16) in (ex_intro2 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))) x3 (arity_appl g c0 w x1 (arity_repl
+g c0 w x H5 x1 (leq_sym g x1 x (asucc_inj g x1 x (arity_mono g c0 u (asucc g
+x1) H12 (asucc g x) H6)))) v x3 H19) (arity_appl g c0 w x H5 (THead (Bind
+Abst) u t) (asucc g x3) (arity_head g c0 u x H6 t (asucc g x3) H18))))))))
+H15)))))))) H10))))) H7))))) H4))))))))))) (\lambda (c0: C).(\lambda (t3:
+T).(\lambda (t4: T).(\lambda (_: (ty3 g c0 t3 t4)).(\lambda (H1: (ex2 A
+(\lambda (a1: A).(arity g c0 t3 a1)) (\lambda (a1: A).(arity g c0 t4 (asucc g
+a1))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t4 t0)).(\lambda (H3: (ex2 A
+(\lambda (a1: A).(arity g c0 t4 a1)) (\lambda (a1: A).(arity g c0 t0 (asucc g
+a1))))).(let H4 \def H1 in (ex2_ind A (\lambda (a1: A).(arity g c0 t3 a1))
+(\lambda (a1: A).(arity g c0 t4 (asucc g a1))) (ex2 A (\lambda (a1: A).(arity
+g c0 (THead (Flat Cast) t4 t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat
+Cast) t0 t4) (asucc g a1)))) (\lambda (x: A).(\lambda (H5: (arity g c0 t3
+x)).(\lambda (H6: (arity g c0 t4 (asucc g x))).(let H7 \def H3 in (ex2_ind A
+(\lambda (a1: A).(arity g c0 t4 a1)) (\lambda (a1: A).(arity g c0 t0 (asucc g
+a1))) (ex2 A (\lambda (a1: A).(arity g c0 (THead (Flat Cast) t4 t3) a1))
+(\lambda (a1: A).(arity g c0 (THead (Flat Cast) t0 t4) (asucc g a1))))
+(\lambda (x0: A).(\lambda (H8: (arity g c0 t4 x0)).(\lambda (H9: (arity g c0
+t0 (asucc g x0))).(ex_intro2 A (\lambda (a1: A).(arity g c0 (THead (Flat
+Cast) t4 t3) a1)) (\lambda (a1: A).(arity g c0 (THead (Flat Cast) t0 t4)
+(asucc g a1))) x (arity_cast g c0 t4 x H6 t3 H5) (arity_cast g c0 t0 (asucc g
+x) (arity_repl g c0 t0 (asucc g x0) H9 (asucc g (asucc g x)) (asucc_repl g x0
+(asucc g x) (arity_mono g c0 t4 x0 H8 (asucc g x) H6))) t4 H6))))) H7)))))
+H4)))))))))) c t1 t2 H))))).