Some more painful work.

[helm.git] / helm / software / matita / contribs / LAMBDA-TYPES / LambdaDelta-1 / csubc / clear.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubc/clear.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubc/clear.ma
index f266b8bc8372974b47ffbfb44ed1f87c1d87f33d..69f700b8bdcc6a6663d37f1116dc625b696ed3ff 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubc/clear.ma
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/csubc/clear.ma
@@ -26,93 +26,142 @@ e1)).(clear_ind (\lambda (c: C).(\lambda (c0: C).(\forall (c2: C).((csubc g c
 c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c0 
 e2))))))) (\lambda (b: B).(\lambda (e: C).(\lambda (u: T).(\lambda (c2: 
 C).(\lambda (H0: (csubc g (CHead e (Bind b) u) c2)).(let H_x \def 
-(csubc_gen_head_l g e c2 u (Bind b) H0) in (let H1 \def H_x in (or_ind (ex2 C 
-(\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g e 
-c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K 
+(csubc_gen_head_l g e c2 u (Bind b) H0) in (let H1 \def H_x in (or3_ind (ex2 
+C (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g 
+e c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K 
 (Bind b) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq 
 C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda 
 (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 
 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g 
-a c3 w))))) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g 
-(CHead e (Bind b) u) e2))) (\lambda (H2: (ex2 C (\lambda (c3: C).(eq C c2 
-(CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g e c3)))).(ex2_ind C 
+a c3 w))))) (ex4_3 B C T (\lambda (b0: B).(\lambda (c3: C).(\lambda (v2: 
+T).(eq C c2 (CHead c3 (Bind b0) v2))))) (\lambda (_: B).(\lambda (_: 
+C).(\lambda (_: T).(eq K (Bind b) (Bind Void))))) (\lambda (b0: B).(\lambda 
+(_: C).(\lambda (_: T).(not (eq B b0 Void))))) (\lambda (_: B).(\lambda (c3: 
+C).(\lambda (_: T).(csubc g e c3))))) (ex2 C (\lambda (e2: C).(clear c2 e2)) 
+(\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (H2: (ex2 C 
 (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda (c3: C).(csubc g e 
-c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g (CHead 
-e (Bind b) u) e2))) (\lambda (x: C).(\lambda (H3: (eq C c2 (CHead x (Bind b) 
-u))).(\lambda (H4: (csubc g e x)).(eq_ind_r C (CHead x (Bind b) u) (\lambda 
-(c: C).(ex2 C (\lambda (e2: C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead 
-e (Bind b) u) e2)))) (ex_intro2 C (\lambda (e2: C).(clear (CHead x (Bind b) 
-u) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2)) (CHead x (Bind b) 
-u) (clear_bind b x u) (csubc_head g e x H4 (Bind b) u)) c2 H3)))) H2)) 
-(\lambda (H2: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: 
-A).(eq K (Bind b) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
-(_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: 
-T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda 
-(a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
-(a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_: 
+c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 (Bind b) u))) (\lambda 
+(c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: 
+C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (x: C).(\lambda (H3: (eq C c2 
+(CHead x (Bind b) u))).(\lambda (H4: (csubc g e x)).(eq_ind_r C (CHead x 
+(Bind b) u) (\lambda (c: C).(ex2 C (\lambda (e2: C).(clear c e2)) (\lambda 
+(e2: C).(csubc g (CHead e (Bind b) u) e2)))) (ex_intro2 C (\lambda (e2: 
+C).(clear (CHead x (Bind b) u) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind 
+b) u) e2)) (CHead x (Bind b) u) (clear_bind b x u) (csubc_head g e x H4 (Bind 
+b) u)) c2 H3)))) H2)) (\lambda (H2: (ex5_3 C T A (\lambda (_: C).(\lambda (_: 
 T).(\lambda (_: A).(eq K (Bind b) (Bind Abst))))) (\lambda (c3: C).(\lambda 
 (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: 
 C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda 
 (_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda 
-(w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda (e2: C).(clear c2 
-e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (x0: 
-C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H3: (eq K (Bind b) (Bind 
-Abst))).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda (H5: 
-(csubc g e x0)).(\lambda (H6: (sc3 g (asucc g x2) e u)).(\lambda (H7: (sc3 g 
-x2 x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c: C).(ex2 C 
-(\lambda (e2: C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) 
-e2)))) (let H8 \def (f_equal K B (\lambda (e0: K).(match e0 in K return 
+(w: T).(\lambda (a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: 
+C).(\lambda (_: T).(\lambda (_: A).(eq K (Bind b) (Bind Abst))))) (\lambda 
+(c3: C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) 
+(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda 
+(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda 
+(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda 
+(e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) 
+(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H3: (eq K (Bind 
+b) (Bind Abst))).(\lambda (H4: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda 
+(H5: (csubc g e x0)).(\lambda (H6: (sc3 g (asucc g x2) e u)).(\lambda (H7: 
+(sc3 g x2 x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c: C).(ex2 
+C (\lambda (e2: C).(clear c e2)) (\lambda (e2: C).(csubc g (CHead e (Bind b) 
+u) e2)))) (let H8 \def (f_equal K B (\lambda (e0: K).(match e0 in K return 
 (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow b])) 
 (Bind b) (Bind Abst) H3) in (eq_ind_r B Abst (\lambda (b0: B).(ex2 C (\lambda 
 (e2: C).(clear (CHead x0 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g 
 (CHead e (Bind b0) u) e2)))) (ex_intro2 C (\lambda (e2: C).(clear (CHead x0 
 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g (CHead e (Bind Abst) u) e2)) 
 (CHead x0 (Bind Abbr) x1) (clear_bind Abbr x0 x1) (csubc_abst g e x0 H5 u x2 
-H6 x1 H7)) b H8)) c2 H4))))))))) H2)) H1)))))))) (\lambda (e: C).(\lambda (c: 
-C).(\lambda (_: (clear e c)).(\lambda (H1: ((\forall (c2: C).((csubc g e c2) 
-\to (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c 
-e2))))))).(\lambda (f: F).(\lambda (u: T).(\lambda (c2: C).(\lambda (H2: 
-(csubc g (CHead e (Flat f) u) c2)).(let H_x \def (csubc_gen_head_l g e c2 u 
-(Flat f) H2) in (let H3 \def H_x in (or_ind (ex2 C (\lambda (c3: C).(eq C c2 
-(CHead c3 (Flat f) u))) (\lambda (c3: C).(csubc g e c3))) (ex5_3 C T A 
-(\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K (Flat f) (Bind 
-Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 
-(Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g 
-e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) e 
-u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w))))) 
-(ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) 
-(\lambda (H4: (ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) 
-(\lambda (c3: C).(csubc g e c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 
-(CHead c3 (Flat f) u))) (\lambda (c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: 
-C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (x: C).(\lambda 
-(H5: (eq C c2 (CHead x (Flat f) u))).(\lambda (H6: (csubc g e x)).(eq_ind_r C 
-(CHead x (Flat f) u) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2)) 
-(\lambda (e2: C).(csubc g c e2)))) (let H_x0 \def (H1 x H6) in (let H7 \def 
-H_x0 in (ex2_ind C (\lambda (e2: C).(clear x e2)) (\lambda (e2: C).(csubc g c 
-e2)) (ex2 C (\lambda (e2: C).(clear (CHead x (Flat f) u) e2)) (\lambda (e2: 
-C).(csubc g c e2))) (\lambda (x0: C).(\lambda (H8: (clear x x0)).(\lambda 
-(H9: (csubc g c x0)).(ex_intro2 C (\lambda (e2: C).(clear (CHead x (Flat f) 
-u) e2)) (\lambda (e2: C).(csubc g c e2)) x0 (clear_flat x x0 H8 f u) H9)))) 
-H7))) c2 H5)))) H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: 
+H6 x1 H7)) b H8)) c2 H4))))))))) H2)) (\lambda (H2: (ex4_3 B C T (\lambda 
+(b0: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b0) 
+v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K (Bind b) (Bind 
+Void))))) (\lambda (b0: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b0 
+Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g e 
+c3)))))).(ex4_3_ind B C T (\lambda (b0: B).(\lambda (c3: C).(\lambda (v2: 
+T).(eq C c2 (CHead c3 (Bind b0) v2))))) (\lambda (_: B).(\lambda (_: 
+C).(\lambda (_: T).(eq K (Bind b) (Bind Void))))) (\lambda (b0: B).(\lambda 
+(_: C).(\lambda (_: T).(not (eq B b0 Void))))) (\lambda (_: B).(\lambda (c3: 
+C).(\lambda (_: T).(csubc g e c3)))) (ex2 C (\lambda (e2: C).(clear c2 e2)) 
+(\lambda (e2: C).(csubc g (CHead e (Bind b) u) e2))) (\lambda (x0: 
+B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H3: (eq C c2 (CHead x1 (Bind 
+x0) x2))).(\lambda (H4: (eq K (Bind b) (Bind Void))).(\lambda (H5: (not (eq B 
+x0 Void))).(\lambda (H6: (csubc g e x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) 
+(\lambda (c: C).(ex2 C (\lambda (e2: C).(clear c e2)) (\lambda (e2: C).(csubc 
+g (CHead e (Bind b) u) e2)))) (let H7 \def (f_equal K B (\lambda (e0: 
+K).(match e0 in K return (\lambda (_: K).B) with [(Bind b0) \Rightarrow b0 | 
+(Flat _) \Rightarrow b])) (Bind b) (Bind Void) H4) in (eq_ind_r B Void 
+(\lambda (b0: B).(ex2 C (\lambda (e2: C).(clear (CHead x1 (Bind x0) x2) e2)) 
+(\lambda (e2: C).(csubc g (CHead e (Bind b0) u) e2)))) (ex_intro2 C (\lambda 
+(e2: C).(clear (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g (CHead 
+e (Bind Void) u) e2)) (CHead x1 (Bind x0) x2) (clear_bind x0 x1 x2) 
+(csubc_void g e x1 H6 x0 H5 u x2)) b H7)) c2 H3)))))))) H2)) H1)))))))) 
+(\lambda (e: C).(\lambda (c: C).(\lambda (_: (clear e c)).(\lambda (H1: 
+((\forall (c2: C).((csubc g e c2) \to (ex2 C (\lambda (e2: C).(clear c2 e2)) 
+(\lambda (e2: C).(csubc g c e2))))))).(\lambda (f: F).(\lambda (u: 
+T).(\lambda (c2: C).(\lambda (H2: (csubc g (CHead e (Flat f) u) c2)).(let H_x 
+\def (csubc_gen_head_l g e c2 u (Flat f) H2) in (let H3 \def H_x in (or3_ind 
+(ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda (c3: 
+C).(csubc g e c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: 
+A).(eq K (Flat f) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: 
+T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda 
+(a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(a: A).(sc3 g a c3 w))))) (ex4_3 B C T (\lambda (b: B).(\lambda (c3: 
+C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: 
+B).(\lambda (_: C).(\lambda (_: T).(eq K (Flat f) (Bind Void))))) (\lambda 
+(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: 
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3))))) (ex2 C (\lambda (e2: 
+C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (H4: (ex2 C 
+(\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda (c3: C).(csubc g e 
+c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 (CHead c3 (Flat f) u))) (\lambda 
+(c3: C).(csubc g e c3)) (ex2 C (\lambda (e2: C).(clear c2 e2)) (\lambda (e2: 
+C).(csubc g c e2))) (\lambda (x: C).(\lambda (H5: (eq C c2 (CHead x (Flat f) 
+u))).(\lambda (H6: (csubc g e x)).(eq_ind_r C (CHead x (Flat f) u) (\lambda 
+(c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2)) (\lambda (e2: C).(csubc g c 
+e2)))) (let H_x0 \def (H1 x H6) in (let H7 \def H_x0 in (ex2_ind C (\lambda 
+(e2: C).(clear x e2)) (\lambda (e2: C).(csubc g c e2)) (ex2 C (\lambda (e2: 
+C).(clear (CHead x (Flat f) u) e2)) (\lambda (e2: C).(csubc g c e2))) 
+(\lambda (x0: C).(\lambda (H8: (clear x x0)).(\lambda (H9: (csubc g c 
+x0)).(ex_intro2 C (\lambda (e2: C).(clear (CHead x (Flat f) u) e2)) (\lambda 
+(e2: C).(csubc g c e2)) x0 (clear_flat x x0 H8 f u) H9)))) H7))) c2 H5)))) 
+H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: 
+A).(eq K (Flat f) (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: 
+T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda 
+(a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda (w: T).(\lambda 
+(a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: C).(\lambda (_: 
 T).(\lambda (_: A).(eq K (Flat f) (Bind Abst))))) (\lambda (c3: C).(\lambda 
 (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: 
 C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda (_: C).(\lambda 
 (_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda (c3: C).(\lambda 
-(w: T).(\lambda (a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A (\lambda (_: 
-C).(\lambda (_: T).(\lambda (_: A).(eq K (Flat f) (Bind Abst))))) (\lambda 
-(c3: C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) 
-(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g e c3)))) (\lambda 
-(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) e u)))) (\lambda 
-(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda 
-(e2: C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (x0: 
-C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H5: (eq K (Flat f) (Bind 
-Abst))).(\lambda (H6: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda (_: 
-(csubc g e x0)).(\lambda (_: (sc3 g (asucc g x2) e u)).(\lambda (_: (sc3 g x2 
-x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C 
-(\lambda (e2: C).(clear c0 e2)) (\lambda (e2: C).(csubc g c e2)))) (let H10 
-\def (eq_ind K (Flat f) (\lambda (ee: K).(match ee in K return (\lambda (_: 
-K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])) I 
-(Bind Abst) H5) in (False_ind (ex2 C (\lambda (e2: C).(clear (CHead x0 (Bind 
-Abbr) x1) e2)) (\lambda (e2: C).(csubc g c e2))) H10)) c2 H6))))))))) H4)) 
-H3))))))))))) c1 e1 H)))).
+(w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 C (\lambda (e2: C).(clear c2 
+e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (x0: C).(\lambda (x1: 
+T).(\lambda (x2: A).(\lambda (H5: (eq K (Flat f) (Bind Abst))).(\lambda (H6: 
+(eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda (_: (csubc g e x0)).(\lambda 
+(_: (sc3 g (asucc g x2) e u)).(\lambda (_: (sc3 g x2 x0 x1)).(eq_ind_r C 
+(CHead x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0 
+e2)) (\lambda (e2: C).(csubc g c e2)))) (let H10 \def (eq_ind K (Flat f) 
+(\lambda (ee: K).(match ee in K return (\lambda (_: K).Prop) with [(Bind _) 
+\Rightarrow False | (Flat _) \Rightarrow True])) I (Bind Abst) H5) in 
+(False_ind (ex2 C (\lambda (e2: C).(clear (CHead x0 (Bind Abbr) x1) e2)) 
+(\lambda (e2: C).(csubc g c e2))) H10)) c2 H6))))))))) H4)) (\lambda (H4: 
+(ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 
+(CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: 
+T).(eq K (Flat f) (Bind Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda 
+(_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: 
+T).(csubc g e c3)))))).(ex4_3_ind B C T (\lambda (b: B).(\lambda (c3: 
+C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: 
+B).(\lambda (_: C).(\lambda (_: T).(eq K (Flat f) (Bind Void))))) (\lambda 
+(b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: 
+B).(\lambda (c3: C).(\lambda (_: T).(csubc g e c3)))) (ex2 C (\lambda (e2: 
+C).(clear c2 e2)) (\lambda (e2: C).(csubc g c e2))) (\lambda (x0: B).(\lambda 
+(x1: C).(\lambda (x2: T).(\lambda (H5: (eq C c2 (CHead x1 (Bind x0) 
+x2))).(\lambda (H6: (eq K (Flat f) (Bind Void))).(\lambda (_: (not (eq B x0 
+Void))).(\lambda (_: (csubc g e x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) 
+(\lambda (c0: C).(ex2 C (\lambda (e2: C).(clear c0 e2)) (\lambda (e2: 
+C).(csubc g c e2)))) (let H9 \def (eq_ind K (Flat f) (\lambda (ee: K).(match 
+ee in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat 
+_) \Rightarrow True])) I (Bind Void) H6) in (False_ind (ex2 C (\lambda (e2: 
+C).(clear (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g c e2))) H9)) 
+c2 H5)))))))) H4)) H3))))))))))) c1 e1 H)))).