-(t2: T).(\lambda (H: (pr2 (CTail k u c) t1 t2)).(insert_eq C (CTail k u c)
-(\lambda (c0: C).(pr2 c0 t1 t2)) (\lambda (_: C).(or (pr2 c t1 t2) (ex3 T
-(\lambda (_: T).(eq K k (Bind Abbr))) (\lambda (t: T).(pr0 t1 t)) (\lambda
-(t: T).(subst0 (clen c) u t t2))))) (\lambda (y: C).(\lambda (H0: (pr2 y t1
-t2)).(pr2_ind (\lambda (c0: C).(\lambda (t: T).(\lambda (t0: T).((eq C c0
-(CTail k u c)) \to (or (pr2 c t t0) (ex3 T (\lambda (_: T).(eq K k (Bind
-Abbr))) (\lambda (t3: T).(pr0 t t3)) (\lambda (t3: T).(subst0 (clen c) u t3
-t0)))))))) (\lambda (c0: C).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H1:
-(pr0 t3 t4)).(\lambda (_: (eq C c0 (CTail k u c))).(or_introl (pr2 c t3 t4)
-(ex3 T (\lambda (_: T).(eq K k (Bind Abbr))) (\lambda (t: T).(pr0 t3 t))
-(\lambda (t: T).(subst0 (clen c) u t t4))) (pr2_free c t3 t4 H1)))))))
-(\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (i: nat).(\lambda
-(H1: (getl i c0 (CHead d (Bind Abbr) u0))).(\lambda (t3: T).(\lambda (t4:
-T).(\lambda (H2: (pr0 t3 t4)).(\lambda (t: T).(\lambda (H3: (subst0 i u0 t4
-t)).(\lambda (H4: (eq C c0 (CTail k u c))).(let H5 \def (eq_ind C c0 (\lambda
-(c1: C).(getl i c1 (CHead d (Bind Abbr) u0))) H1 (CTail k u c) H4) in (let
-H_x \def (getl_gen_tail k Abbr u u0 d c i H5) in (let H6 \def H_x in (or_ind
-(ex2 C (\lambda (e: C).(eq C d (CTail k u e))) (\lambda (e: C).(getl i c
-(CHead e (Bind Abbr) u0)))) (ex4 nat (\lambda (_: nat).(eq nat i (clen c)))
-(\lambda (_: nat).(eq K k (Bind Abbr))) (\lambda (_: nat).(eq T u u0))
-(\lambda (n: nat).(eq C d (CSort n)))) (or (pr2 c t3 t) (ex3 T (\lambda (_:
-T).(eq K k (Bind Abbr))) (\lambda (t0: T).(pr0 t3 t0)) (\lambda (t0:
-T).(subst0 (clen c) u t0 t)))) (\lambda (H7: (ex2 C (\lambda (e: C).(eq C d
-(CTail k u e))) (\lambda (e: C).(getl i c (CHead e (Bind Abbr)
-u0))))).(ex2_ind C (\lambda (e: C).(eq C d (CTail k u e))) (\lambda (e:
-C).(getl i c (CHead e (Bind Abbr) u0))) (or (pr2 c t3 t) (ex3 T (\lambda (_:
-T).(eq K k (Bind Abbr))) (\lambda (t0: T).(pr0 t3 t0)) (\lambda (t0:
-T).(subst0 (clen c) u t0 t)))) (\lambda (x: C).(\lambda (_: (eq C d (CTail k
-u x))).(\lambda (H9: (getl i c (CHead x (Bind Abbr) u0))).(or_introl (pr2 c
-t3 t) (ex3 T (\lambda (_: T).(eq K k (Bind Abbr))) (\lambda (t0: T).(pr0 t3
-t0)) (\lambda (t0: T).(subst0 (clen c) u t0 t))) (pr2_delta c x u0 i H9 t3 t4
-H2 t H3))))) H7)) (\lambda (H7: (ex4 nat (\lambda (_: nat).(eq nat i (clen
-c))) (\lambda (_: nat).(eq K k (Bind Abbr))) (\lambda (_: nat).(eq T u u0))
-(\lambda (n: nat).(eq C d (CSort n))))).(ex4_ind nat (\lambda (_: nat).(eq
-nat i (clen c))) (\lambda (_: nat).(eq K k (Bind Abbr))) (\lambda (_:
-nat).(eq T u u0)) (\lambda (n: nat).(eq C d (CSort n))) (or (pr2 c t3 t) (ex3
-T (\lambda (_: T).(eq K k (Bind Abbr))) (\lambda (t0: T).(pr0 t3 t0))
-(\lambda (t0: T).(subst0 (clen c) u t0 t)))) (\lambda (x0: nat).(\lambda (H8:
-(eq nat i (clen c))).(\lambda (H9: (eq K k (Bind Abbr))).(\lambda (H10: (eq T
-u u0)).(\lambda (_: (eq C d (CSort x0))).(let H12 \def (eq_ind nat i (\lambda
-(n: nat).(subst0 n u0 t4 t)) H3 (clen c) H8) in (let H13 \def (eq_ind_r T u0
-(\lambda (t0: T).(subst0 (clen c) t0 t4 t)) H12 u H10) in (eq_ind_r K (Bind
-Abbr) (\lambda (k0: K).(or (pr2 c t3 t) (ex3 T (\lambda (_: T).(eq K k0 (Bind
-Abbr))) (\lambda (t0: T).(pr0 t3 t0)) (\lambda (t0: T).(subst0 (clen c) u t0
-t))))) (or_intror (pr2 c t3 t) (ex3 T (\lambda (_: T).(eq K (Bind Abbr) (Bind
-Abbr))) (\lambda (t0: T).(pr0 t3 t0)) (\lambda (t0: T).(subst0 (clen c) u t0
-t))) (ex3_intro T (\lambda (_: T).(eq K (Bind Abbr) (Bind Abbr))) (\lambda
-(t0: T).(pr0 t3 t0)) (\lambda (t0: T).(subst0 (clen c) u t0 t)) t4
-(refl_equal K (Bind Abbr)) H2 H13)) k H9)))))))) H7)) H6))))))))))))))) y t1
-t2 H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1161
-END *)
+(t2: T).(\lambda (H: (pr2 (CTail k u c) t1 t2)).(let TMP_1 \def (CTail k u c)
+in (let TMP_2 \def (\lambda (c0: C).(pr2 c0 t1 t2)) in (let TMP_10 \def
+(\lambda (_: C).(let TMP_3 \def (pr2 c t1 t2) in (let TMP_5 \def (\lambda (_:
+T).(let TMP_4 \def (Bind Abbr) in (eq K k TMP_4))) in (let TMP_6 \def
+(\lambda (t: T).(pr0 t1 t)) in (let TMP_8 \def (\lambda (t: T).(let TMP_7
+\def (clen c) in (subst0 TMP_7 u t t2))) in (let TMP_9 \def (ex3 T TMP_5
+TMP_6 TMP_8) in (or TMP_3 TMP_9))))))) in (let TMP_126 \def (\lambda (y:
+C).(\lambda (H0: (pr2 y t1 t2)).(let TMP_18 \def (\lambda (c0: C).(\lambda
+(t: T).(\lambda (t0: T).((eq C c0 (CTail k u c)) \to (let TMP_11 \def (pr2 c
+t t0) in (let TMP_13 \def (\lambda (_: T).(let TMP_12 \def (Bind Abbr) in (eq
+K k TMP_12))) in (let TMP_14 \def (\lambda (t3: T).(pr0 t t3)) in (let TMP_16
+\def (\lambda (t3: T).(let TMP_15 \def (clen c) in (subst0 TMP_15 u t3 t0)))
+in (let TMP_17 \def (ex3 T TMP_13 TMP_14 TMP_16) in (or TMP_11
+TMP_17)))))))))) in (let TMP_27 \def (\lambda (c0: C).(\lambda (t3:
+T).(\lambda (t4: T).(\lambda (H1: (pr0 t3 t4)).(\lambda (_: (eq C c0 (CTail k
+u c))).(let TMP_19 \def (pr2 c t3 t4) in (let TMP_21 \def (\lambda (_:
+T).(let TMP_20 \def (Bind Abbr) in (eq K k TMP_20))) in (let TMP_22 \def
+(\lambda (t: T).(pr0 t3 t)) in (let TMP_24 \def (\lambda (t: T).(let TMP_23
+\def (clen c) in (subst0 TMP_23 u t t4))) in (let TMP_25 \def (ex3 T TMP_21
+TMP_22 TMP_24) in (let TMP_26 \def (pr2_free c t3 t4 H1) in (or_introl TMP_19
+TMP_25 TMP_26)))))))))))) in (let TMP_125 \def (\lambda (c0: C).(\lambda (d:
+C).(\lambda (u0: T).(\lambda (i: nat).(\lambda (H1: (getl i c0 (CHead d (Bind
+Abbr) u0))).(\lambda (t3: T).(\lambda (t4: T).(\lambda (H2: (pr0 t3
+t4)).(\lambda (t: T).(\lambda (H3: (subst0 i u0 t4 t)).(\lambda (H4: (eq C c0
+(CTail k u c))).(let TMP_30 \def (\lambda (c1: C).(let TMP_28 \def (Bind
+Abbr) in (let TMP_29 \def (CHead d TMP_28 u0) in (getl i c1 TMP_29)))) in
+(let TMP_31 \def (CTail k u c) in (let H5 \def (eq_ind C c0 TMP_30 H1 TMP_31
+H4) in (let H_x \def (getl_gen_tail k Abbr u u0 d c i H5) in (let H6 \def H_x
+in (let TMP_33 \def (\lambda (e: C).(let TMP_32 \def (CTail k u e) in (eq C d
+TMP_32))) in (let TMP_36 \def (\lambda (e: C).(let TMP_34 \def (Bind Abbr) in
+(let TMP_35 \def (CHead e TMP_34 u0) in (getl i c TMP_35)))) in (let TMP_37
+\def (ex2 C TMP_33 TMP_36) in (let TMP_39 \def (\lambda (_: nat).(let TMP_38
+\def (clen c) in (eq nat i TMP_38))) in (let TMP_41 \def (\lambda (_:
+nat).(let TMP_40 \def (Bind Abbr) in (eq K k TMP_40))) in (let TMP_42 \def
+(\lambda (_: nat).(eq T u u0)) in (let TMP_44 \def (\lambda (n: nat).(let
+TMP_43 \def (CSort n) in (eq C d TMP_43))) in (let TMP_45 \def (ex4 nat
+TMP_39 TMP_41 TMP_42 TMP_44) in (let TMP_46 \def (pr2 c t3 t) in (let TMP_48
+\def (\lambda (_: T).(let TMP_47 \def (Bind Abbr) in (eq K k TMP_47))) in
+(let TMP_49 \def (\lambda (t0: T).(pr0 t3 t0)) in (let TMP_51 \def (\lambda
+(t0: T).(let TMP_50 \def (clen c) in (subst0 TMP_50 u t0 t))) in (let TMP_52
+\def (ex3 T TMP_48 TMP_49 TMP_51) in (let TMP_53 \def (or TMP_46 TMP_52) in
+(let TMP_76 \def (\lambda (H7: (ex2 C (\lambda (e: C).(eq C d (CTail k u e)))
+(\lambda (e: C).(getl i c (CHead e (Bind Abbr) u0))))).(let TMP_55 \def
+(\lambda (e: C).(let TMP_54 \def (CTail k u e) in (eq C d TMP_54))) in (let
+TMP_58 \def (\lambda (e: C).(let TMP_56 \def (Bind Abbr) in (let TMP_57 \def
+(CHead e TMP_56 u0) in (getl i c TMP_57)))) in (let TMP_59 \def (pr2 c t3 t)
+in (let TMP_61 \def (\lambda (_: T).(let TMP_60 \def (Bind Abbr) in (eq K k
+TMP_60))) in (let TMP_62 \def (\lambda (t0: T).(pr0 t3 t0)) in (let TMP_64
+\def (\lambda (t0: T).(let TMP_63 \def (clen c) in (subst0 TMP_63 u t0 t)))
+in (let TMP_65 \def (ex3 T TMP_61 TMP_62 TMP_64) in (let TMP_66 \def (or
+TMP_59 TMP_65) in (let TMP_75 \def (\lambda (x: C).(\lambda (_: (eq C d
+(CTail k u x))).(\lambda (H9: (getl i c (CHead x (Bind Abbr) u0))).(let
+TMP_67 \def (pr2 c t3 t) in (let TMP_69 \def (\lambda (_: T).(let TMP_68 \def
+(Bind Abbr) in (eq K k TMP_68))) in (let TMP_70 \def (\lambda (t0: T).(pr0 t3
+t0)) in (let TMP_72 \def (\lambda (t0: T).(let TMP_71 \def (clen c) in
+(subst0 TMP_71 u t0 t))) in (let TMP_73 \def (ex3 T TMP_69 TMP_70 TMP_72) in
+(let TMP_74 \def (pr2_delta c x u0 i H9 t3 t4 H2 t H3) in (or_introl TMP_67
+TMP_73 TMP_74)))))))))) in (ex2_ind C TMP_55 TMP_58 TMP_66 TMP_75
+H7))))))))))) in (let TMP_124 \def (\lambda (H7: (ex4 nat (\lambda (_:
+nat).(eq nat i (clen c))) (\lambda (_: nat).(eq K k (Bind Abbr))) (\lambda
+(_: nat).(eq T u u0)) (\lambda (n: nat).(eq C d (CSort n))))).(let TMP_78
+\def (\lambda (_: nat).(let TMP_77 \def (clen c) in (eq nat i TMP_77))) in
+(let TMP_80 \def (\lambda (_: nat).(let TMP_79 \def (Bind Abbr) in (eq K k
+TMP_79))) in (let TMP_81 \def (\lambda (_: nat).(eq T u u0)) in (let TMP_83
+\def (\lambda (n: nat).(let TMP_82 \def (CSort n) in (eq C d TMP_82))) in
+(let TMP_84 \def (pr2 c t3 t) in (let TMP_86 \def (\lambda (_: T).(let TMP_85
+\def (Bind Abbr) in (eq K k TMP_85))) in (let TMP_87 \def (\lambda (t0:
+T).(pr0 t3 t0)) in (let TMP_89 \def (\lambda (t0: T).(let TMP_88 \def (clen
+c) in (subst0 TMP_88 u t0 t))) in (let TMP_90 \def (ex3 T TMP_86 TMP_87
+TMP_89) in (let TMP_91 \def (or TMP_84 TMP_90) in (let TMP_123 \def (\lambda
+(x0: nat).(\lambda (H8: (eq nat i (clen c))).(\lambda (H9: (eq K k (Bind
+Abbr))).(\lambda (H10: (eq T u u0)).(\lambda (_: (eq C d (CSort x0))).(let
+TMP_92 \def (\lambda (n: nat).(subst0 n u0 t4 t)) in (let TMP_93 \def (clen
+c) in (let H12 \def (eq_ind nat i TMP_92 H3 TMP_93 H8) in (let TMP_95 \def
+(\lambda (t0: T).(let TMP_94 \def (clen c) in (subst0 TMP_94 t0 t4 t))) in
+(let H13 \def (eq_ind_r T u0 TMP_95 H12 u H10) in (let TMP_96 \def (Bind
+Abbr) in (let TMP_104 \def (\lambda (k0: K).(let TMP_97 \def (pr2 c t3 t) in
+(let TMP_99 \def (\lambda (_: T).(let TMP_98 \def (Bind Abbr) in (eq K k0
+TMP_98))) in (let TMP_100 \def (\lambda (t0: T).(pr0 t3 t0)) in (let TMP_102
+\def (\lambda (t0: T).(let TMP_101 \def (clen c) in (subst0 TMP_101 u t0 t)))
+in (let TMP_103 \def (ex3 T TMP_99 TMP_100 TMP_102) in (or TMP_97
+TMP_103))))))) in (let TMP_105 \def (pr2 c t3 t) in (let TMP_108 \def
+(\lambda (_: T).(let TMP_106 \def (Bind Abbr) in (let TMP_107 \def (Bind
+Abbr) in (eq K TMP_106 TMP_107)))) in (let TMP_109 \def (\lambda (t0: T).(pr0
+t3 t0)) in (let TMP_111 \def (\lambda (t0: T).(let TMP_110 \def (clen c) in
+(subst0 TMP_110 u t0 t))) in (let TMP_112 \def (ex3 T TMP_108 TMP_109
+TMP_111) in (let TMP_115 \def (\lambda (_: T).(let TMP_113 \def (Bind Abbr)
+in (let TMP_114 \def (Bind Abbr) in (eq K TMP_113 TMP_114)))) in (let TMP_116
+\def (\lambda (t0: T).(pr0 t3 t0)) in (let TMP_118 \def (\lambda (t0: T).(let
+TMP_117 \def (clen c) in (subst0 TMP_117 u t0 t))) in (let TMP_119 \def (Bind
+Abbr) in (let TMP_120 \def (refl_equal K TMP_119) in (let TMP_121 \def
+(ex3_intro T TMP_115 TMP_116 TMP_118 t4 TMP_120 H2 H13) in (let TMP_122 \def
+(or_intror TMP_105 TMP_112 TMP_121) in (eq_ind_r K TMP_96 TMP_104 TMP_122 k
+H9))))))))))))))))))))))))) in (ex4_ind nat TMP_78 TMP_80 TMP_81 TMP_83
+TMP_91 TMP_123 H7))))))))))))) in (or_ind TMP_37 TMP_45 TMP_53 TMP_76 TMP_124
+H6))))))))))))))))))))))))))))))))) in (pr2_ind TMP_18 TMP_27 TMP_125 y t1 t2
+H0)))))) in (insert_eq C TMP_1 TMP_2 TMP_10 TMP_126 H)))))))))).