C).(\lambda (H0: (csub3 g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c3
e1) \to (ex2 C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2: C).(clear c4
e2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (e1: C).(\lambda (H2:
-(clear (CHead c3 k u) e1)).((match k in K return (\lambda (k0: K).((clear
-(CHead c3 k0 u) e1) \to (ex2 C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda
-(e2: C).(clear (CHead c4 k0 u) e2))))) with [(Bind b) \Rightarrow (\lambda
-(H3: (clear (CHead c3 (Bind b) u) e1)).(eq_ind_r C (CHead c3 (Bind b) u)
+(clear (CHead c3 k u) e1)).(K_ind (\lambda (k0: K).((clear (CHead c3 k0 u)
+e1) \to (ex2 C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2: C).(clear
+(CHead c4 k0 u) e2))))) (\lambda (b: B).(\lambda (H3: (clear (CHead c3 (Bind
+b) u) e1)).(eq_ind_r C (CHead c3 (Bind b) u) (\lambda (c: C).(ex2 C (\lambda
+(e2: C).(csub3 g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b) u) e2))))
+(ex_intro2 C (\lambda (e2: C).(csub3 g (CHead c3 (Bind b) u) e2)) (\lambda
+(e2: C).(clear (CHead c4 (Bind b) u) e2)) (CHead c4 (Bind b) u) (csub3_head g
+c3 c4 H0 (Bind b) u) (clear_bind b c4 u)) e1 (clear_gen_bind b c3 e1 u H3))))
+(\lambda (f: F).(\lambda (H3: (clear (CHead c3 (Flat f) u) e1)).(let H4 \def
+(H1 e1 (clear_gen_flat f c3 e1 u H3)) in (ex2_ind C (\lambda (e2: C).(csub3 g
+e1 e2)) (\lambda (e2: C).(clear c4 e2)) (ex2 C (\lambda (e2: C).(csub3 g e1
+e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f) u) e2))) (\lambda (x:
+C).(\lambda (H5: (csub3 g e1 x)).(\lambda (H6: (clear c4 x)).(ex_intro2 C
+(\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f)
+u) e2)) x H5 (clear_flat c4 x H6 f u))))) H4)))) k H2))))))))) (\lambda (c3:
+C).(\lambda (c4: C).(\lambda (H0: (csub3 g c3 c4)).(\lambda (_: ((\forall
+(e1: C).((clear c3 e1) \to (ex2 C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda
+(e2: C).(clear c4 e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b
+Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3:
+(clear (CHead c3 (Bind Void) u1) e1)).(eq_ind_r C (CHead c3 (Bind Void) u1)
(\lambda (c: C).(ex2 C (\lambda (e2: C).(csub3 g c e2)) (\lambda (e2:
-C).(clear (CHead c4 (Bind b) u) e2)))) (ex_intro2 C (\lambda (e2: C).(csub3 g
-(CHead c3 (Bind b) u) e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b) u) e2))
-(CHead c4 (Bind b) u) (csub3_head g c3 c4 H0 (Bind b) u) (clear_bind b c4 u))
-e1 (clear_gen_bind b c3 e1 u H3))) | (Flat f) \Rightarrow (\lambda (H3:
-(clear (CHead c3 (Flat f) u) e1)).(let H4 \def (H1 e1 (clear_gen_flat f c3 e1
-u H3)) in (ex2_ind C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2:
-C).(clear c4 e2)) (ex2 C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2:
-C).(clear (CHead c4 (Flat f) u) e2))) (\lambda (x: C).(\lambda (H5: (csub3 g
-e1 x)).(\lambda (H6: (clear c4 x)).(ex_intro2 C (\lambda (e2: C).(csub3 g e1
-e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f) u) e2)) x H5 (clear_flat c4 x
-H6 f u))))) H4)))]) H2))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda
-(H0: (csub3 g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear c3 e1) \to (ex2
-C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2: C).(clear c4
-e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1:
-T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: (clear (CHead c3 (Bind
-Void) u1) e1)).(eq_ind_r C (CHead c3 (Bind Void) u1) (\lambda (c: C).(ex2 C
-(\lambda (e2: C).(csub3 g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b)
-u2) e2)))) (ex_intro2 C (\lambda (e2: C).(csub3 g (CHead c3 (Bind Void) u1)
-e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b) u2) e2)) (CHead c4 (Bind b)
-u2) (csub3_void g c3 c4 H0 b H2 u1 u2) (clear_bind b c4 u2)) e1
-(clear_gen_bind Void c3 e1 u1 H3)))))))))))) (\lambda (c3: C).(\lambda (c4:
-C).(\lambda (H0: (csub3 g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear c3
-e1) \to (ex2 C (\lambda (e2: C).(csub3 g e1 e2)) (\lambda (e2: C).(clear c4
-e2))))))).(\lambda (u: T).(\lambda (t: T).(\lambda (H2: (ty3 g c4 u
-t)).(\lambda (e1: C).(\lambda (H3: (clear (CHead c3 (Bind Abst) t)
-e1)).(eq_ind_r C (CHead c3 (Bind Abst) t) (\lambda (c: C).(ex2 C (\lambda
-(e2: C).(csub3 g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u)
-e2)))) (ex_intro2 C (\lambda (e2: C).(csub3 g (CHead c3 (Bind Abst) t) e2))
-(\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u) e2)) (CHead c4 (Bind Abbr)
-u) (csub3_abst g c3 c4 H0 u t H2) (clear_bind Abbr c4 u)) e1 (clear_gen_bind
-Abst c3 e1 t H3))))))))))) c1 c2 H)))).
+C).(clear (CHead c4 (Bind b) u2) e2)))) (ex_intro2 C (\lambda (e2: C).(csub3
+g (CHead c3 (Bind Void) u1) e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b)
+u2) e2)) (CHead c4 (Bind b) u2) (csub3_void g c3 c4 H0 b H2 u1 u2)
+(clear_bind b c4 u2)) e1 (clear_gen_bind Void c3 e1 u1 H3))))))))))))
+(\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csub3 g c3 c4)).(\lambda (_:
+((\forall (e1: C).((clear c3 e1) \to (ex2 C (\lambda (e2: C).(csub3 g e1 e2))
+(\lambda (e2: C).(clear c4 e2))))))).(\lambda (u: T).(\lambda (t: T).(\lambda
+(H2: (ty3 g c4 u t)).(\lambda (e1: C).(\lambda (H3: (clear (CHead c3 (Bind
+Abst) t) e1)).(eq_ind_r C (CHead c3 (Bind Abst) t) (\lambda (c: C).(ex2 C
+(\lambda (e2: C).(csub3 g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind
+Abbr) u) e2)))) (ex_intro2 C (\lambda (e2: C).(csub3 g (CHead c3 (Bind Abst)
+t) e2)) (\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u) e2)) (CHead c4 (Bind
+Abbr) u) (csub3_abst g c3 c4 H0 u t H2) (clear_bind Abbr c4 u)) e1
+(clear_gen_bind Abst c3 e1 t H3))))))))))) c1 c2 H)))).