update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csubv / clear.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubv/clear.ma b/matita/matita/contribs/lambdadelta/basic_1/csubv/clear.ma
index 5c54f5b9ab552b93674cd755f001271bda44bb4b..4f4a012727acf4b2a72e238463f3335565fbfba2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csubv/clear.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csubv/clear.ma
@@ -14,11 +14,11 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/csubv/defs.ma".
+include "basic_1/csubv/fwd.ma".
 
-include "Basic-1/clear/fwd.ma".
+include "basic_1/clear/fwd.ma".
 
-theorem csubv_clear_conf:
+lemma csubv_clear_conf:
  \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (b1: 
 B).(\forall (d1: C).(\forall (v1: T).((clear c1 (CHead d1 (Bind b1) v1)) \to 
 (ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 
@@ -42,76 +42,70 @@ C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2:
 C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind b2) v2)))))))))))).(\lambda 
 (v1: T).(\lambda (v2: T).(\lambda (b1: B).(\lambda (d1: C).(\lambda (v0: 
 T).(\lambda (H2: (clear (CHead c3 (Bind Void) v1) (CHead d1 (Bind b1) 
-v0))).(let H3 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda 
-(_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c])) 
-(CHead d1 (Bind b1) v0) (CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 
-(CHead d1 (Bind b1) v0) v1 H2)) in ((let H4 \def (f_equal C B (\lambda (e: 
-C).(match e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow b1 | 
-(CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind 
-b) \Rightarrow b | (Flat _) \Rightarrow b1])])) (CHead d1 (Bind b1) v0) 
+v0))).(let H3 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind b1) v0) 
 (CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind b1) v0) v1 
-H2)) in ((let H5 \def (f_equal C T (\lambda (e: C).(match e in C return 
-(\lambda (_: C).T) with [(CSort _) \Rightarrow v0 | (CHead _ _ t) \Rightarrow 
-t])) (CHead d1 (Bind b1) v0) (CHead c3 (Bind Void) v1) (clear_gen_bind Void 
-c3 (CHead d1 (Bind b1) v0) v1 H2)) in (\lambda (_: (eq B b1 Void)).(\lambda 
-(H7: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c: C).(ex2_3 B C T (\lambda (_: 
-B).(\lambda (d2: C).(\lambda (_: T).(csubv c d2)))) (\lambda (b2: B).(\lambda 
-(d2: C).(\lambda (v3: T).(clear (CHead c4 (Bind Void) v2) (CHead d2 (Bind b2) 
-v3))))))) (ex2_3_intro B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: 
-T).(csubv c3 d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear 
-(CHead c4 (Bind Void) v2) (CHead d2 (Bind b2) v3))))) Void c4 v2 H0 
-(clear_bind Void c4 v2)) d1 H7)))) H4)) H3)))))))))))) (\lambda (c3: 
-C).(\lambda (c4: C).(\lambda (H0: (csubv c3 c4)).(\lambda (_: ((\forall (b1: 
-B).(\forall (d1: C).(\forall (v1: T).((clear c3 (CHead d1 (Bind b1) v1)) \to 
-(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 
-d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2 
-(Bind b2) v2)))))))))))).(\lambda (b1: B).(\lambda (_: (not (eq B b1 
-Void))).(\lambda (b2: B).(\lambda (v1: T).(\lambda (v2: T).(\lambda (b0: 
-B).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H3: (clear (CHead c3 (Bind b1) 
-v1) (CHead d1 (Bind b0) v0))).(let H4 \def (f_equal C C (\lambda (e: 
-C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | 
-(CHead c _ _) \Rightarrow c])) (CHead d1 (Bind b0) v0) (CHead c3 (Bind b1) 
-v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3)) in ((let H5 \def 
-(f_equal C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with 
-[(CSort _) \Rightarrow b0 | (CHead _ k _) \Rightarrow (match k in K return 
-(\lambda (_: K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow 
-b0])])) (CHead d1 (Bind b0) v0) (CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 
-(CHead d1 (Bind b0) v0) v1 H3)) in ((let H6 \def (f_equal C T (\lambda (e: 
-C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow v0 | 
-(CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind b0) v0) (CHead c3 (Bind b1) 
-v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3)) in (\lambda (_: (eq 
-B b0 b1)).(\lambda (H8: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c: C).(ex2_3 B 
-C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv c d2)))) (\lambda 
+H2)) in ((let H4 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow b1 | (CHead _ k _) \Rightarrow (match k with [(Bind b) 
+\Rightarrow b | (Flat _) \Rightarrow b1])])) (CHead d1 (Bind b1) v0) (CHead 
+c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind b1) v0) v1 H2)) in 
+((let H5 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow v0 | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind b1) v0) 
+(CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind b1) v0) v1 
+H2)) in (\lambda (_: (eq B b1 Void)).(\lambda (H7: (eq C d1 c3)).(eq_ind_r C 
+c3 (\lambda (c: C).(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: 
+T).(csubv c d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear 
+(CHead c4 (Bind Void) v2) (CHead d2 (Bind b2) v3))))))) (ex2_3_intro B C T 
+(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv c3 d2)))) (\lambda 
+(b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Bind Void) v2) 
+(CHead d2 (Bind b2) v3))))) Void c4 v2 H0 (clear_bind Void c4 v2)) d1 H7)))) 
+H4)) H3)))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csubv c3 
+c4)).(\lambda (_: ((\forall (b1: B).(\forall (d1: C).(\forall (v1: T).((clear 
+c3 (CHead d1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_: B).(\lambda (d2: 
+C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2: 
+C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind b2) v2)))))))))))).(\lambda 
+(b1: B).(\lambda (_: (not (eq B b1 Void))).(\lambda (b2: B).(\lambda (v1: 
+T).(\lambda (v2: T).(\lambda (b0: B).(\lambda (d1: C).(\lambda (v0: 
+T).(\lambda (H3: (clear (CHead c3 (Bind b1) v1) (CHead d1 (Bind b0) 
+v0))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind b0) v0) 
+(CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3)) 
+in ((let H5 \def (f_equal C B (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow b0 | (CHead _ k _) \Rightarrow (match k with [(Bind b) 
+\Rightarrow b | (Flat _) \Rightarrow b0])])) (CHead d1 (Bind b0) v0) (CHead 
+c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3)) in 
+((let H6 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow v0 | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind b0) v0) 
+(CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind b0) v0) v1 H3)) 
+in (\lambda (_: (eq B b0 b1)).(\lambda (H8: (eq C d1 c3)).(eq_ind_r C c3 
+(\lambda (c: C).(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: 
+T).(csubv c d2)))) (\lambda (b3: B).(\lambda (d2: C).(\lambda (v3: T).(clear 
+(CHead c4 (Bind b2) v2) (CHead d2 (Bind b3) v3))))))) (ex2_3_intro B C T 
+(\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv c3 d2)))) (\lambda 
 (b3: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Bind b2) v2) 
-(CHead d2 (Bind b3) v3))))))) (ex2_3_intro B C T (\lambda (_: B).(\lambda 
-(d2: C).(\lambda (_: T).(csubv c3 d2)))) (\lambda (b3: B).(\lambda (d2: 
-C).(\lambda (v3: T).(clear (CHead c4 (Bind b2) v2) (CHead d2 (Bind b3) 
-v3))))) b2 c4 v2 H0 (clear_bind b2 c4 v2)) d1 H8)))) H5)) H4))))))))))))))) 
-(\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubv c3 c4)).(\lambda (H1: 
-((\forall (b1: B).(\forall (d1: C).(\forall (v1: T).((clear c3 (CHead d1 
-(Bind b1) v1)) \to (ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: 
-T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v2: T).(clear 
-c4 (CHead d2 (Bind b2) v2)))))))))))).(\lambda (f1: F).(\lambda (f2: 
-F).(\lambda (v1: T).(\lambda (v2: T).(\lambda (b1: B).(\lambda (d1: 
-C).(\lambda (v0: T).(\lambda (H2: (clear (CHead c3 (Flat f1) v1) (CHead d1 
-(Bind b1) v0))).(let H_x \def (H1 b1 d1 v0 (clear_gen_flat f1 c3 (CHead d1 
-(Bind b1) v0) v1 H2)) in (let H3 \def H_x in (ex2_3_ind B C T (\lambda (_: 
+(CHead d2 (Bind b3) v3))))) b2 c4 v2 H0 (clear_bind b2 c4 v2)) d1 H8)))) H5)) 
+H4))))))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubv c3 
+c4)).(\lambda (H1: ((\forall (b1: B).(\forall (d1: C).(\forall (v1: 
+T).((clear c3 (CHead d1 (Bind b1) v1)) \to (ex2_3 B C T (\lambda (_: 
 B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: 
-B).(\lambda (d2: C).(\lambda (v3: T).(clear c4 (CHead d2 (Bind b2) v3))))) 
-(ex2_3 B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 
-d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 
-(Flat f2) v2) (CHead d2 (Bind b2) v3)))))) (\lambda (x0: B).(\lambda (x1: 
-C).(\lambda (x2: T).(\lambda (H4: (csubv d1 x1)).(\lambda (H5: (clear c4 
-(CHead x1 (Bind x0) x2))).(ex2_3_intro B C T (\lambda (_: B).(\lambda (d2: 
+B).(\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind b2) 
+v2)))))))))))).(\lambda (f1: F).(\lambda (f2: F).(\lambda (v1: T).(\lambda 
+(v2: T).(\lambda (b1: B).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H2: 
+(clear (CHead c3 (Flat f1) v1) (CHead d1 (Bind b1) v0))).(let H_x \def (H1 b1 
+d1 v0 (clear_gen_flat f1 c3 (CHead d1 (Bind b1) v0) v1 H2)) in (let H3 \def 
+H_x in (ex2_3_ind B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: 
+T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear 
+c4 (CHead d2 (Bind b2) v3))))) (ex2_3 B C T (\lambda (_: B).(\lambda (d2: 
 C).(\lambda (_: T).(csubv d1 d2)))) (\lambda (b2: B).(\lambda (d2: 
 C).(\lambda (v3: T).(clear (CHead c4 (Flat f2) v2) (CHead d2 (Bind b2) 
-v3))))) x0 x1 x2 H4 (clear_flat c4 (CHead x1 (Bind x0) x2) H5 f2 v2))))))) 
-H3))))))))))))))) c1 c2 H))).
-(* COMMENTS
-Initial nodes: 1357
-END *)
+v3)))))) (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H4: 
+(csubv d1 x1)).(\lambda (H5: (clear c4 (CHead x1 (Bind x0) x2))).(ex2_3_intro 
+B C T (\lambda (_: B).(\lambda (d2: C).(\lambda (_: T).(csubv d1 d2)))) 
+(\lambda (b2: B).(\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Flat f2) 
+v2) (CHead d2 (Bind b2) v3))))) x0 x1 x2 H4 (clear_flat c4 (CHead x1 (Bind 
+x0) x2) H5 f2 v2))))))) H3))))))))))))))) c1 c2 H))).
 
-theorem csubv_clear_conf_void:
+lemma csubv_clear_conf_void:
  \forall (c1: C).(\forall (c2: C).((csubv c1 c2) \to (\forall (d1: 
 C).(\forall (v1: T).((clear c1 (CHead d1 (Bind Void) v1)) \to (ex2_2 C T 
 (\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda 
@@ -131,11 +125,10 @@ d2 (Bind Void) v2)))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0:
 T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2 
 (Bind Void) v2)))))))))).(\lambda (v1: T).(\lambda (v2: T).(\lambda (d1: 
 C).(\lambda (v0: T).(\lambda (H2: (clear (CHead c3 (Bind Void) v1) (CHead d1 
-(Bind Void) v0))).(let H3 \def (f_equal C C (\lambda (e: C).(match e in C 
-return (\lambda (_: C).C) with [(CSort _) \Rightarrow d1 | (CHead c _ _) 
-\Rightarrow c])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind Void) v1) 
-(clear_gen_bind Void c3 (CHead d1 (Bind Void) v0) v1 H2)) in ((let H4 \def 
-(f_equal C T (\lambda (e: C).(match e in C return (\lambda (_: C).T) with 
+(Bind Void) v0))).(let H3 \def (f_equal C C (\lambda (e: C).(match e with 
+[(CSort _) \Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind 
+Void) v0) (CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind 
+Void) v0) v1 H2)) in ((let H4 \def (f_equal C T (\lambda (e: C).(match e with 
 [(CSort _) \Rightarrow v0 | (CHead _ _ t) \Rightarrow t])) (CHead d1 (Bind 
 Void) v0) (CHead c3 (Bind Void) v1) (clear_gen_bind Void c3 (CHead d1 (Bind 
 Void) v0) v1 H2)) in (\lambda (H5: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c: 
@@ -151,44 +144,36 @@ C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind Void) v2)))))))))).(\lambda
 (b1: B).(\lambda (H2: (not (eq B b1 Void))).(\lambda (b2: B).(\lambda (v1: 
 T).(\lambda (v2: T).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H3: (clear 
 (CHead c3 (Bind b1) v1) (CHead d1 (Bind Void) v0))).(let H4 \def (f_equal C C 
-(\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) 
-\Rightarrow d1 | (CHead c _ _) \Rightarrow c])) (CHead d1 (Bind Void) v0) 
-(CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 
-H3)) in ((let H5 \def (f_equal C B (\lambda (e: C).(match e in C return 
-(\lambda (_: C).B) with [(CSort _) \Rightarrow Void | (CHead _ k _) 
-\Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b) 
-\Rightarrow b | (Flat _) \Rightarrow Void])])) (CHead d1 (Bind Void) v0) 
-(CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 
-H3)) in ((let H6 \def (f_equal C T (\lambda (e: C).(match e in C return 
-(\lambda (_: C).T) with [(CSort _) \Rightarrow v0 | (CHead _ _ t) \Rightarrow 
-t])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1) (clear_gen_bind b1 c3 
-(CHead d1 (Bind Void) v0) v1 H3)) in (\lambda (H7: (eq B Void b1)).(\lambda 
-(H8: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c: C).(ex2_2 C T (\lambda (d2: 
-C).(\lambda (_: T).(csubv c d2))) (\lambda (d2: C).(\lambda (v3: T).(clear 
-(CHead c4 (Bind b2) v2) (CHead d2 (Bind Void) v3)))))) (let H9 \def (eq_ind_r 
-B b1 (\lambda (b: B).(not (eq B b Void))) H2 Void H7) in (let H10 \def (match 
-(H9 (refl_equal B Void)) in False return (\lambda (_: False).(ex2_2 C T 
-(\lambda (d2: C).(\lambda (_: T).(csubv c3 d2))) (\lambda (d2: C).(\lambda 
-(v3: T).(clear (CHead c4 (Bind b2) v2) (CHead d2 (Bind Void) v3)))))) with 
-[]) in H10)) d1 H8)))) H5)) H4)))))))))))))) (\lambda (c3: C).(\lambda (c4: 
-C).(\lambda (_: (csubv c3 c4)).(\lambda (H1: ((\forall (d1: C).(\forall (v1: 
-T).((clear c3 (CHead d1 (Bind Void) v1)) \to (ex2_2 C T (\lambda (d2: 
-C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v2: T).(clear 
-c4 (CHead d2 (Bind Void) v2)))))))))).(\lambda (f1: F).(\lambda (f2: 
-F).(\lambda (v1: T).(\lambda (v2: T).(\lambda (d1: C).(\lambda (v0: 
-T).(\lambda (H2: (clear (CHead c3 (Flat f1) v1) (CHead d1 (Bind Void) 
-v0))).(let H_x \def (H1 d1 v0 (clear_gen_flat f1 c3 (CHead d1 (Bind Void) v0) 
-v1 H2)) in (let H3 \def H_x in (ex2_2_ind C T (\lambda (d2: C).(\lambda (_: 
-T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v3: T).(clear c4 (CHead d2 
-(Bind Void) v3)))) (ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv d1 
-d2))) (\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Flat f2) v2) (CHead 
-d2 (Bind Void) v3))))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H4: (csubv 
-d1 x0)).(\lambda (H5: (clear c4 (CHead x0 (Bind Void) x1))).(ex2_2_intro C T 
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow d1 | (CHead c _ _) 
+\Rightarrow c])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1) 
+(clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 H3)) in ((let H5 \def 
+(f_equal C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow Void | 
+(CHead _ k _) \Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) 
+\Rightarrow Void])])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1) 
+(clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 H3)) in ((let H6 \def 
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow v0 | (CHead 
+_ _ t) \Rightarrow t])) (CHead d1 (Bind Void) v0) (CHead c3 (Bind b1) v1) 
+(clear_gen_bind b1 c3 (CHead d1 (Bind Void) v0) v1 H3)) in (\lambda (H7: (eq 
+B Void b1)).(\lambda (H8: (eq C d1 c3)).(eq_ind_r C c3 (\lambda (c: C).(ex2_2 
+C T (\lambda (d2: C).(\lambda (_: T).(csubv c d2))) (\lambda (d2: C).(\lambda 
+(v3: T).(clear (CHead c4 (Bind b2) v2) (CHead d2 (Bind Void) v3)))))) (let H9 
+\def (eq_ind_r B b1 (\lambda (b: B).(not (eq B b Void))) H2 Void H7) in (let 
+H10 \def (match (H9 (refl_equal B Void)) in False with []) in H10)) d1 H8)))) 
+H5)) H4)))))))))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (_: (csubv 
+c3 c4)).(\lambda (H1: ((\forall (d1: C).(\forall (v1: T).((clear c3 (CHead d1 
+(Bind Void) v1)) \to (ex2_2 C T (\lambda (d2: C).(\lambda (_: T).(csubv d1 
+d2))) (\lambda (d2: C).(\lambda (v2: T).(clear c4 (CHead d2 (Bind Void) 
+v2)))))))))).(\lambda (f1: F).(\lambda (f2: F).(\lambda (v1: T).(\lambda (v2: 
+T).(\lambda (d1: C).(\lambda (v0: T).(\lambda (H2: (clear (CHead c3 (Flat f1) 
+v1) (CHead d1 (Bind Void) v0))).(let H_x \def (H1 d1 v0 (clear_gen_flat f1 c3 
+(CHead d1 (Bind Void) v0) v1 H2)) in (let H3 \def H_x in (ex2_2_ind C T 
 (\lambda (d2: C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda 
-(v3: T).(clear (CHead c4 (Flat f2) v2) (CHead d2 (Bind Void) v3)))) x0 x1 H4 
-(clear_flat c4 (CHead x0 (Bind Void) x1) H5 f2 v2)))))) H3)))))))))))))) c1 
-c2 H))).
-(* COMMENTS
-Initial nodes: 1205
-END *)
+(v3: T).(clear c4 (CHead d2 (Bind Void) v3)))) (ex2_2 C T (\lambda (d2: 
+C).(\lambda (_: T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v3: T).(clear 
+(CHead c4 (Flat f2) v2) (CHead d2 (Bind Void) v3))))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H4: (csubv d1 x0)).(\lambda (H5: (clear c4 
+(CHead x0 (Bind Void) x1))).(ex2_2_intro C T (\lambda (d2: C).(\lambda (_: 
+T).(csubv d1 d2))) (\lambda (d2: C).(\lambda (v3: T).(clear (CHead c4 (Flat 
+f2) v2) (CHead d2 (Bind Void) v3)))) x0 x1 H4 (clear_flat c4 (CHead x0 (Bind 
+Void) x1) H5 f2 v2)))))) H3)))))))))))))) c1 c2 H))).