+in F return (\lambda (_: F).Prop) with [Appl \Rightarrow False | Cast
+\Rightarrow True])])])) I (THead (Flat Appl) w v) H7) in (False_ind ((eq T t4
+t2) \to ((pr0 t3 t4) \to (ty3 g c2 t2 (THead (Flat Appl) w (THead (Bind Abst)
+u t0))))) H9)) H8 H6)))]) in (H6 (refl_equal T (THead (Flat Appl) w v))
+(refl_equal T t2)))))))))))))))) (\lambda (c: C).(\lambda (t2: T).(\lambda
+(t3: T).(\lambda (_: (ty3 g c t2 t3)).(\lambda (H1: ((\forall (c2: C).((wcpr0
+c c2) \to (\forall (t4: T).((pr0 t2 t4) \to (ty3 g c2 t4 t3))))))).(\lambda
+(t0: T).(\lambda (_: (ty3 g c t3 t0)).(\lambda (H3: ((\forall (c2: C).((wcpr0
+c c2) \to (\forall (t4: T).((pr0 t3 t4) \to (ty3 g c2 t4 t0))))))).(\lambda
+(c2: C).(\lambda (H4: (wcpr0 c c2)).(\lambda (t4: T).(\lambda (H5: (pr0
+(THead (Flat Cast) t3 t2) t4)).(let H6 \def (match H5 in pr0 return (\lambda
+(t5: T).(\lambda (t6: T).(\lambda (_: (pr0 t5 t6)).((eq T t5 (THead (Flat
+Cast) t3 t2)) \to ((eq T t6 t4) \to (ty3 g c2 t4 (THead (Flat Cast) t0
+t3))))))) with [(pr0_refl t5) \Rightarrow (\lambda (H6: (eq T t5 (THead (Flat
+Cast) t3 t2))).(\lambda (H7: (eq T t5 t4)).(eq_ind T (THead (Flat Cast) t3
+t2) (\lambda (t6: T).((eq T t6 t4) \to (ty3 g c2 t4 (THead (Flat Cast) t0
+t3)))) (\lambda (H8: (eq T (THead (Flat Cast) t3 t2) t4)).(eq_ind T (THead
+(Flat Cast) t3 t2) (\lambda (t6: T).(ty3 g c2 t6 (THead (Flat Cast) t0 t3)))
+(ty3_cast g c2 t2 t3 (H1 c2 H4 t2 (pr0_refl t2)) t0 (H3 c2 H4 t3 (pr0_refl
+t3))) t4 H8)) t5 (sym_eq T t5 (THead (Flat Cast) t3 t2) H6) H7))) | (pr0_comp
+u1 u2 H6 t5 t6 H7 k) \Rightarrow (\lambda (H8: (eq T (THead k u1 t5) (THead
+(Flat Cast) t3 t2))).(\lambda (H9: (eq T (THead k u2 t6) t4)).((let H10 \def
+(f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
+[(TSort _) \Rightarrow t5 | (TLRef _) \Rightarrow t5 | (THead _ _ t7)
+\Rightarrow t7])) (THead k u1 t5) (THead (Flat Cast) t3 t2) H8) in ((let H11
+\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T)
+with [(TSort _) \Rightarrow u1 | (TLRef _) \Rightarrow u1 | (THead _ t7 _)
+\Rightarrow t7])) (THead k u1 t5) (THead (Flat Cast) t3 t2) H8) in ((let H12
+\def (f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K)
+with [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k0 _ _)
+\Rightarrow k0])) (THead k u1 t5) (THead (Flat Cast) t3 t2) H8) in (eq_ind K
+(Flat Cast) (\lambda (k0: K).((eq T u1 t3) \to ((eq T t5 t2) \to ((eq T
+(THead k0 u2 t6) t4) \to ((pr0 u1 u2) \to ((pr0 t5 t6) \to (ty3 g c2 t4
+(THead (Flat Cast) t0 t3)))))))) (\lambda (H13: (eq T u1 t3)).(eq_ind T t3
+(\lambda (t7: T).((eq T t5 t2) \to ((eq T (THead (Flat Cast) u2 t6) t4) \to
+((pr0 t7 u2) \to ((pr0 t5 t6) \to (ty3 g c2 t4 (THead (Flat Cast) t0
+t3))))))) (\lambda (H14: (eq T t5 t2)).(eq_ind T t2 (\lambda (t7: T).((eq T
+(THead (Flat Cast) u2 t6) t4) \to ((pr0 t3 u2) \to ((pr0 t7 t6) \to (ty3 g c2
+t4 (THead (Flat Cast) t0 t3)))))) (\lambda (H15: (eq T (THead (Flat Cast) u2
+t6) t4)).(eq_ind T (THead (Flat Cast) u2 t6) (\lambda (t7: T).((pr0 t3 u2)
+\to ((pr0 t2 t6) \to (ty3 g c2 t7 (THead (Flat Cast) t0 t3))))) (\lambda
+(H16: (pr0 t3 u2)).(\lambda (H17: (pr0 t2 t6)).(ex_ind T (\lambda (t7:
+T).(ty3 g c2 t0 t7)) (ty3 g c2 (THead (Flat Cast) u2 t6) (THead (Flat Cast)
+t0 t3)) (\lambda (x: T).(\lambda (H18: (ty3 g c2 t0 x)).(ty3_conv g c2 (THead
+(Flat Cast) t0 t3) (THead (Flat Cast) x t0) (ty3_cast g c2 t3 t0 (H3 c2 H4 t3
+(pr0_refl t3)) x H18) (THead (Flat Cast) u2 t6) (THead (Flat Cast) t0 u2)
+(ty3_cast g c2 t6 u2 (ty3_conv g c2 u2 t0 (H3 c2 H4 u2 H16) t6 t3 (H1 c2 H4
+t6 H17) (pc3_pr2_r c2 t3 u2 (pr2_free c2 t3 u2 H16))) t0 (H3 c2 H4 u2 H16))
+(pc3_s c2 (THead (Flat Cast) t0 u2) (THead (Flat Cast) t0 t3) (pc3_pr2_r c2
+(THead (Flat Cast) t0 t3) (THead (Flat Cast) t0 u2) (pr2_thin_dx c2 t3 u2
+(pr2_free c2 t3 u2 H16) t0 Cast)))))) (ty3_correct g c2 t3 t0 (H3 c2 H4 t3
+(pr0_refl t3)))))) t4 H15)) t5 (sym_eq T t5 t2 H14))) u1 (sym_eq T u1 t3
+H13))) k (sym_eq K k (Flat Cast) H12))) H11)) H10)) H9 H6 H7))) | (pr0_beta u
+v1 v2 H6 t5 t6 H7) \Rightarrow (\lambda (H8: (eq T (THead (Flat Appl) v1
+(THead (Bind Abst) u t5)) (THead (Flat Cast) t3 t2))).(\lambda (H9: (eq T
+(THead (Bind Abbr) v2 t6) t4)).((let H10 \def (eq_ind T (THead (Flat Appl) v1
+(THead (Bind Abst) u t5)) (\lambda (e: T).(match e in T return (\lambda (_:
+T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
+(THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
+[(Bind _) \Rightarrow False | (Flat f) \Rightarrow (match f in F return
+(\lambda (_: F).Prop) with [Appl \Rightarrow True | Cast \Rightarrow
+False])])])) I (THead (Flat Cast) t3 t2) H8) in (False_ind ((eq T (THead
+(Bind Abbr) v2 t6) t4) \to ((pr0 v1 v2) \to ((pr0 t5 t6) \to (ty3 g c2 t4
+(THead (Flat Cast) t0 t3))))) H10)) H9 H6 H7))) | (pr0_upsilon b H6 v1 v2 H7
+u1 u2 H8 t5 t6 H9) \Rightarrow (\lambda (H10: (eq T (THead (Flat Appl) v1