t)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0)
t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall
(P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
-t0) t3)) t (ty3_cast g c2 t0 t (ty3_conv g c2 t x H6 t0 x0 H9 H12) x H6))))
-(\lambda (H12: (((pc3 c2 x0 t) \to (\forall (P: Prop).P)))).(or_intror (ex T
-(\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
-T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))
-(\lambda (t3: T).(\lambda (H13: (ty3 g c2 (THead (Flat Cast) t t0)
-t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0 t) P (\lambda (_:
-(pc3 c2 t t3)).(\lambda (H15: (ty3 g c2 t0 t)).(let H_y \def (ty3_unique g c2
-t0 t H15 x0 H9) in (H12 (pc3_s c2 x0 t H_y) P)))) (ty3_gen_cast g c2 t0 t t3
-H13))))))) H11))))) (ty3_correct g c2 t0 x0 H9)))) H8)) (\lambda (H8:
-((\forall (t3: T).((ty3 g c2 t0 t3) \to (\forall (P: Prop).P))))).(or_intror
-(ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
-T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))
-(\lambda (t3: T).(\lambda (H9: (ty3 g c2 (THead (Flat Cast) t t0)
-t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0 t) P (\lambda (_:
-(pc3 c2 t t3)).(\lambda (H11: (ty3 g c2 t0 t)).(H8 t H11 P))) (ty3_gen_cast g
-c2 t0 t t3 H9))))))) H7)))) H5)) (\lambda (H5: ((\forall (t3: T).((ty3 g c2 t
-t3) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2
-(THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast)
-t t0) t3) \to (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H6: (ty3 g
-c2 (THead (Flat Cast) t t0) t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3)
-(ty3 g c2 t0 t) P (\lambda (_: (pc3 c2 t t3)).(\lambda (H8: (ty3 g c2 t0
-t)).(ex_ind T (\lambda (t4: T).(ty3 g c2 t t4)) P (\lambda (x: T).(\lambda
-(H9: (ty3 g c2 t x)).(H5 x H9 P))) (ty3_correct g c2 t0 t H8))))
+t0) t3)) (THead (Flat Cast) x t) (ty3_cast g c2 t0 t (ty3_conv g c2 t x H6 t0
+x0 H9 H12) x H6)))) (\lambda (H12: (((pc3 c2 x0 t) \to (\forall (P:
+Prop).P)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
+(\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H13: (ty3 g c2 (THead
+(Flat Cast) t t0) t3)).(\lambda (P: Prop).(ex3_ind T (\lambda (t4: T).(pc3 c2
+(THead (Flat Cast) t4 t) t3)) (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4:
+T).(ty3 g c2 t t4)) P (\lambda (x2: T).(\lambda (_: (pc3 c2 (THead (Flat
+Cast) x2 t) t3)).(\lambda (H15: (ty3 g c2 t0 t)).(\lambda (H16: (ty3 g c2 t
+x2)).(let H_y \def (ty3_unique g c2 t x2 H16 x H6) in (let H_y0 \def
+(ty3_unique g c2 t0 t H15 x0 H9) in (H12 (pc3_s c2 x0 t H_y0) P)))))))
+(ty3_gen_cast g c2 t0 t t3 H13))))))) H11))))) (ty3_correct g c2 t0 x0 H9))))
+H8)) (\lambda (H8: ((\forall (t3: T).((ty3 g c2 t0 t3) \to (\forall (P:
+Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
+(\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H9: (ty3 g c2 (THead (Flat
+Cast) t t0) t3)).(\lambda (P: Prop).(ex3_ind T (\lambda (t4: T).(pc3 c2
+(THead (Flat Cast) t4 t) t3)) (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4:
+T).(ty3 g c2 t t4)) P (\lambda (x0: T).(\lambda (_: (pc3 c2 (THead (Flat
+Cast) x0 t) t3)).(\lambda (H11: (ty3 g c2 t0 t)).(\lambda (_: (ty3 g c2 t
+x0)).(H8 t H11 P))))) (ty3_gen_cast g c2 t0 t t3 H9))))))) H7)))) H5))
+(\lambda (H5: ((\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P:
+Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
+t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
+(\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H6: (ty3 g c2 (THead (Flat
+Cast) t t0) t3)).(\lambda (P: Prop).(ex3_ind T (\lambda (t4: T).(pc3 c2
+(THead (Flat Cast) t4 t) t3)) (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4:
+T).(ty3 g c2 t t4)) P (\lambda (x0: T).(\lambda (_: (pc3 c2 (THead (Flat
+Cast) x0 t) t3)).(\lambda (_: (ty3 g c2 t0 t)).(\lambda (H9: (ty3 g c2 t
+x0)).(ex_ind T (\lambda (t4: T).(ty3 g c2 x0 t4)) P (\lambda (x: T).(\lambda
+(_: (ty3 g c2 x0 x)).(H5 x0 H9 P))) (ty3_correct g c2 t x0 H9))))))
(ty3_gen_cast g c2 t0 t t3 H6))))))) H4))) f H2))) k H1))))))) t2))) c t1))).