-u2)))))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H:
-(clear (CSort n) (CHead c2 (Bind b) u2))).(\lambda (k: K).(\lambda (u1:
-T).(K_ind (\lambda (k0: K).(clear (CHead (CSort n) k0 u1) (CHead (CTail k0 u1
-c2) (Bind b) u2))) (\lambda (b0: B).(clear_gen_sort (CHead c2 (Bind b) u2) n
-H (clear (CHead (CSort n) (Bind b0) u1) (CHead (CTail (Bind b0) u1 c2) (Bind
-b) u2)))) (\lambda (f: F).(clear_gen_sort (CHead c2 (Bind b) u2) n H (clear
-(CHead (CSort n) (Flat f) u1) (CHead (CTail (Flat f) u1 c2) (Bind b) u2))))
-k))))))) (\lambda (c: C).(\lambda (H: ((\forall (c2: C).(\forall (u2:
-T).((clear c (CHead c2 (Bind b) u2)) \to (\forall (k: K).(\forall (u1:
-T).(clear (CTail k u1 c) (CHead (CTail k u1 c2) (Bind b) u2))))))))).(\lambda
-(k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (u2: T).(\lambda (H0: (clear
-(CHead c k t) (CHead c2 (Bind b) u2))).(\lambda (k0: K).(\lambda (u1:
-T).(K_ind (\lambda (k1: K).((clear (CHead c k1 t) (CHead c2 (Bind b) u2)) \to
-(clear (CHead (CTail k0 u1 c) k1 t) (CHead (CTail k0 u1 c2) (Bind b) u2))))
-(\lambda (b0: B).(\lambda (H1: (clear (CHead c (Bind b0) t) (CHead c2 (Bind
-b) u2))).(let H2 \def (f_equal C C (\lambda (e: C).(match e in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow c2 | (CHead c0 _ _)
-\Rightarrow c0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t)
-(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in ((let H3 \def (f_equal
-C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
-\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 in K return (\lambda (_:
-K).B) with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])])) (CHead c2
-(Bind b) u2) (CHead c (Bind b0) t) (clear_gen_bind b0 c (CHead c2 (Bind b)
-u2) t H1)) in ((let H4 \def (f_equal C T (\lambda (e: C).(match e in C return
-(\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t0)
-\Rightarrow t0])) (CHead c2 (Bind b) u2) (CHead c (Bind b0) t)
-(clear_gen_bind b0 c (CHead c2 (Bind b) u2) t H1)) in (\lambda (H5: (eq B b
-b0)).(\lambda (H6: (eq C c2 c)).(eq_ind_r T t (\lambda (t0: T).(clear (CHead
-(CTail k0 u1 c) (Bind b0) t) (CHead (CTail k0 u1 c2) (Bind b) t0))) (eq_ind_r
-C c (\lambda (c0: C).(clear (CHead (CTail k0 u1 c) (Bind b0) t) (CHead (CTail
-k0 u1 c0) (Bind b) t))) (eq_ind B b (\lambda (b1: B).(clear (CHead (CTail k0
-u1 c) (Bind b1) t) (CHead (CTail k0 u1 c) (Bind b) t))) (clear_bind b (CTail
-k0 u1 c) t) b0 H5) c2 H6) u2 H4)))) H3)) H2)))) (\lambda (f: F).(\lambda (H1:
-(clear (CHead c (Flat f) t) (CHead c2 (Bind b) u2))).(clear_flat (CTail k0 u1
-c) (CHead (CTail k0 u1 c2) (Bind b) u2) (H c2 u2 (clear_gen_flat f c (CHead
-c2 (Bind b) u2) t H1) k0 u1) f t))) k H0)))))))))) c1)).
-(* COMMENTS
-Initial nodes: 819
-END *)
-
-theorem clear_cle:
- \forall (c1: C).(\forall (c2: C).((clear c1 c2) \to (cle c2 c1)))
-\def
- \lambda (c1: C).(C_ind (\lambda (c: C).(\forall (c2: C).((clear c c2) \to
-(le (cweight c2) (cweight c))))) (\lambda (n: nat).(\lambda (c2: C).(\lambda
-(H: (clear (CSort n) c2)).(clear_gen_sort c2 n H (le (cweight c2) O)))))
-(\lambda (c: C).(\lambda (H: ((\forall (c2: C).((clear c c2) \to (le (cweight
-c2) (cweight c)))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2:
-C).(\lambda (H0: (clear (CHead c k t) c2)).(K_ind (\lambda (k0: K).((clear
-(CHead c k0 t) c2) \to (le (cweight c2) (plus (cweight c) (tweight t)))))
-(\lambda (b: B).(\lambda (H1: (clear (CHead c (Bind b) t) c2)).(eq_ind_r C
-(CHead c (Bind b) t) (\lambda (c0: C).(le (cweight c0) (plus (cweight c)
-(tweight t)))) (le_n (plus (cweight c) (tweight t))) c2 (clear_gen_bind b c
-c2 t H1)))) (\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t)
-c2)).(le_plus_trans (cweight c2) (cweight c) (tweight t) (H c2
-(clear_gen_flat f c c2 t H1))))) k H0))))))) c1).
-(* COMMENTS
-Initial nodes: 247
-END *)
+u2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (c2: C).(\lambda (u2:
+T).(\lambda (H0: (clear (CHead c k t) (CHead c2 (Bind b) u2))).(\lambda (k0:
+K).(\lambda (u1: T).(let TMP_40 \def (\lambda (k1: K).((clear (CHead c k1 t)
+(CHead c2 (Bind b) u2)) \to (let TMP_35 \def (CTail k0 u1 c) in (let TMP_36
+\def (CHead TMP_35 k1 t) in (let TMP_37 \def (CTail k0 u1 c2) in (let TMP_38
+\def (Bind b) in (let TMP_39 \def (CHead TMP_37 TMP_38 u2) in (clear TMP_36
+TMP_39)))))))) in (let TMP_92 \def (\lambda (b0: B).(\lambda (H1: (clear
+(CHead c (Bind b0) t) (CHead c2 (Bind b) u2))).(let TMP_41 \def (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow c0]))
+in (let TMP_42 \def (Bind b) in (let TMP_43 \def (CHead c2 TMP_42 u2) in (let
+TMP_44 \def (Bind b0) in (let TMP_45 \def (CHead c TMP_44 t) in (let TMP_46
+\def (Bind b) in (let TMP_47 \def (CHead c2 TMP_46 u2) in (let TMP_48 \def
+(clear_gen_bind b0 c TMP_47 t H1) in (let H2 \def (f_equal C C TMP_41 TMP_43
+TMP_45 TMP_48) in (let TMP_49 \def (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow b | (CHead _ k1 _) \Rightarrow (match k1 with [(Bind b1)
+\Rightarrow b1 | (Flat _) \Rightarrow b])])) in (let TMP_50 \def (Bind b) in
+(let TMP_51 \def (CHead c2 TMP_50 u2) in (let TMP_52 \def (Bind b0) in (let
+TMP_53 \def (CHead c TMP_52 t) in (let TMP_54 \def (Bind b) in (let TMP_55
+\def (CHead c2 TMP_54 u2) in (let TMP_56 \def (clear_gen_bind b0 c TMP_55 t
+H1) in (let H3 \def (f_equal C B TMP_49 TMP_51 TMP_53 TMP_56) in (let TMP_57
+\def (\lambda (e: C).(match e with [(CSort _) \Rightarrow u2 | (CHead _ _ t0)
+\Rightarrow t0])) in (let TMP_58 \def (Bind b) in (let TMP_59 \def (CHead c2
+TMP_58 u2) in (let TMP_60 \def (Bind b0) in (let TMP_61 \def (CHead c TMP_60
+t) in (let TMP_62 \def (Bind b) in (let TMP_63 \def (CHead c2 TMP_62 u2) in
+(let TMP_64 \def (clear_gen_bind b0 c TMP_63 t H1) in (let H4 \def (f_equal C
+T TMP_57 TMP_59 TMP_61 TMP_64) in (let TMP_90 \def (\lambda (H5: (eq B b
+b0)).(\lambda (H6: (eq C c2 c)).(let TMP_71 \def (\lambda (t0: T).(let TMP_65
+\def (CTail k0 u1 c) in (let TMP_66 \def (Bind b0) in (let TMP_67 \def (CHead
+TMP_65 TMP_66 t) in (let TMP_68 \def (CTail k0 u1 c2) in (let TMP_69 \def
+(Bind b) in (let TMP_70 \def (CHead TMP_68 TMP_69 t0) in (clear TMP_67
+TMP_70)))))))) in (let TMP_78 \def (\lambda (c0: C).(let TMP_72 \def (CTail
+k0 u1 c) in (let TMP_73 \def (Bind b0) in (let TMP_74 \def (CHead TMP_72
+TMP_73 t) in (let TMP_75 \def (CTail k0 u1 c0) in (let TMP_76 \def (Bind b)
+in (let TMP_77 \def (CHead TMP_75 TMP_76 t) in (clear TMP_74 TMP_77))))))))
+in (let TMP_85 \def (\lambda (b1: B).(let TMP_79 \def (CTail k0 u1 c) in (let
+TMP_80 \def (Bind b1) in (let TMP_81 \def (CHead TMP_79 TMP_80 t) in (let
+TMP_82 \def (CTail k0 u1 c) in (let TMP_83 \def (Bind b) in (let TMP_84 \def
+(CHead TMP_82 TMP_83 t) in (clear TMP_81 TMP_84)))))))) in (let TMP_86 \def
+(CTail k0 u1 c) in (let TMP_87 \def (clear_bind b TMP_86 t) in (let TMP_88
+\def (eq_ind B b TMP_85 TMP_87 b0 H5) in (let TMP_89 \def (eq_ind_r C c
+TMP_78 TMP_88 c2 H6) in (eq_ind_r T t TMP_71 TMP_89 u2 H4)))))))))) in (let
+TMP_91 \def (TMP_90 H3) in (TMP_91 H2)))))))))))))))))))))))))))))))) in (let
+TMP_101 \def (\lambda (f: F).(\lambda (H1: (clear (CHead c (Flat f) t) (CHead
+c2 (Bind b) u2))).(let TMP_93 \def (CTail k0 u1 c) in (let TMP_94 \def (CTail
+k0 u1 c2) in (let TMP_95 \def (Bind b) in (let TMP_96 \def (CHead TMP_94
+TMP_95 u2) in (let TMP_97 \def (Bind b) in (let TMP_98 \def (CHead c2 TMP_97
+u2) in (let TMP_99 \def (clear_gen_flat f c TMP_98 t H1) in (let TMP_100 \def
+(H c2 u2 TMP_99 k0 u1) in (clear_flat TMP_93 TMP_96 TMP_100 f t))))))))))) in
+(K_ind TMP_40 TMP_92 TMP_101 k H0))))))))))))) in (C_ind TMP_5 TMP_34 TMP_102
+c1))))).