+x))).(let TMP_1 \def (Flat f) in (let H_x \def (lift_gen_head TMP_1 u t x h d
+H) in (let H0 \def H_x in (let TMP_4 \def (\lambda (y: T).(\lambda (z:
+T).(let TMP_2 \def (Flat f) in (let TMP_3 \def (THead TMP_2 y z) in (eq T x
+TMP_3))))) in (let TMP_6 \def (\lambda (y: T).(\lambda (_: T).(let TMP_5 \def
+(lift h d y) in (eq T u TMP_5)))) in (let TMP_8 \def (\lambda (_: T).(\lambda
+(z: T).(let TMP_7 \def (lift h d z) in (eq T t TMP_7)))) in (let TMP_11 \def
+(\lambda (y: T).(\lambda (z: T).(let TMP_9 \def (Flat f) in (let TMP_10 \def
+(THead TMP_9 y z) in (eq T x TMP_10))))) in (let TMP_13 \def (\lambda (y:
+T).(\lambda (_: T).(let TMP_12 \def (lift h d y) in (eq T u TMP_12)))) in
+(let TMP_15 \def (\lambda (_: T).(\lambda (z: T).(let TMP_14 \def (lift h d
+z) in (eq T t TMP_14)))) in (let TMP_16 \def (ex3_2 T T TMP_11 TMP_13 TMP_15)
+in (let TMP_71 \def (\lambda (x0: T).(\lambda (x1: T).(\lambda (H1: (eq T x
+(THead (Flat f) x0 x1))).(\lambda (H2: (eq T u (lift h d x0))).(\lambda (H3:
+(eq T t (lift h d x1))).(let TMP_17 \def (Flat f) in (let TMP_18 \def (THead
+TMP_17 x0 x1) in (let TMP_26 \def (\lambda (t0: T).(let TMP_21 \def (\lambda
+(y: T).(\lambda (z: T).(let TMP_19 \def (Flat f) in (let TMP_20 \def (THead
+TMP_19 y z) in (eq T t0 TMP_20))))) in (let TMP_23 \def (\lambda (y:
+T).(\lambda (_: T).(let TMP_22 \def (lift h d y) in (eq T u TMP_22)))) in
+(let TMP_25 \def (\lambda (_: T).(\lambda (z: T).(let TMP_24 \def (lift h d
+z) in (eq T t TMP_24)))) in (ex3_2 T T TMP_21 TMP_23 TMP_25))))) in (let
+TMP_27 \def (lift h d x1) in (let TMP_37 \def (\lambda (t0: T).(let TMP_32
+\def (\lambda (y: T).(\lambda (z: T).(let TMP_28 \def (Flat f) in (let TMP_29
+\def (THead TMP_28 x0 x1) in (let TMP_30 \def (Flat f) in (let TMP_31 \def
+(THead TMP_30 y z) in (eq T TMP_29 TMP_31))))))) in (let TMP_34 \def (\lambda
+(y: T).(\lambda (_: T).(let TMP_33 \def (lift h d y) in (eq T u TMP_33)))) in
+(let TMP_36 \def (\lambda (_: T).(\lambda (z: T).(let TMP_35 \def (lift h d
+z) in (eq T t0 TMP_35)))) in (ex3_2 T T TMP_32 TMP_34 TMP_36))))) in (let
+TMP_38 \def (lift h d x0) in (let TMP_49 \def (\lambda (t0: T).(let TMP_43
+\def (\lambda (y: T).(\lambda (z: T).(let TMP_39 \def (Flat f) in (let TMP_40
+\def (THead TMP_39 x0 x1) in (let TMP_41 \def (Flat f) in (let TMP_42 \def
+(THead TMP_41 y z) in (eq T TMP_40 TMP_42))))))) in (let TMP_45 \def (\lambda
+(y: T).(\lambda (_: T).(let TMP_44 \def (lift h d y) in (eq T t0 TMP_44))))
+in (let TMP_48 \def (\lambda (_: T).(\lambda (z: T).(let TMP_46 \def (lift h
+d x1) in (let TMP_47 \def (lift h d z) in (eq T TMP_46 TMP_47))))) in (ex3_2
+T T TMP_43 TMP_45 TMP_48))))) in (let TMP_54 \def (\lambda (y: T).(\lambda
+(z: T).(let TMP_50 \def (Flat f) in (let TMP_51 \def (THead TMP_50 x0 x1) in
+(let TMP_52 \def (Flat f) in (let TMP_53 \def (THead TMP_52 y z) in (eq T
+TMP_51 TMP_53))))))) in (let TMP_57 \def (\lambda (y: T).(\lambda (_: T).(let
+TMP_55 \def (lift h d x0) in (let TMP_56 \def (lift h d y) in (eq T TMP_55
+TMP_56))))) in (let TMP_60 \def (\lambda (_: T).(\lambda (z: T).(let TMP_58
+\def (lift h d x1) in (let TMP_59 \def (lift h d z) in (eq T TMP_58
+TMP_59))))) in (let TMP_61 \def (Flat f) in (let TMP_62 \def (THead TMP_61 x0
+x1) in (let TMP_63 \def (refl_equal T TMP_62) in (let TMP_64 \def (lift h d
+x0) in (let TMP_65 \def (refl_equal T TMP_64) in (let TMP_66 \def (lift h d
+x1) in (let TMP_67 \def (refl_equal T TMP_66) in (let TMP_68 \def
+(ex3_2_intro T T TMP_54 TMP_57 TMP_60 x0 x1 TMP_63 TMP_65 TMP_67) in (let
+TMP_69 \def (eq_ind_r T TMP_38 TMP_49 TMP_68 u H2) in (let TMP_70 \def
+(eq_ind_r T TMP_27 TMP_37 TMP_69 t H3) in (eq_ind_r T TMP_18 TMP_26 TMP_70 x
+H1)))))))))))))))))))))))))) in (ex3_2_ind T T TMP_4 TMP_6 TMP_8 TMP_16
+TMP_71 H0)))))))))))))))))).
+
+theorem lift_inj:
+ \forall (x: T).(\forall (t: T).(\forall (h: nat).(\forall (d: nat).((eq T
+(lift h d x) (lift h d t)) \to (eq T x t)))))
+\def
+ \lambda (x: T).(let TMP_1 \def (\lambda (t: T).(\forall (t0: T).(\forall (h:
+nat).(\forall (d: nat).((eq T (lift h d t) (lift h d t0)) \to (eq T t
+t0)))))) in (let TMP_10 \def (\lambda (n: nat).(\lambda (t: T).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (H: (eq T (lift h d (TSort n)) (lift h d
+t))).(let TMP_2 \def (TSort n) in (let TMP_3 \def (lift h d TMP_2) in (let
+TMP_5 \def (\lambda (t0: T).(let TMP_4 \def (lift h d t) in (eq T t0 TMP_4)))
+in (let TMP_6 \def (TSort n) in (let TMP_7 \def (lift_sort n h d) in (let H0
+\def (eq_ind T TMP_3 TMP_5 H TMP_6 TMP_7) in (let TMP_8 \def (TSort n) in
+(let TMP_9 \def (lift_gen_sort h d n t H0) in (sym_eq T t TMP_8
+TMP_9)))))))))))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda (t:
+T).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H: (eq T (lift h d (TLRef
+n)) (lift h d t))).(let TMP_11 \def (TLRef n) in (let TMP_12 \def (eq T
+TMP_11 t) in (let TMP_23 \def (\lambda (H0: (lt n d)).(let TMP_13 \def (TLRef
+n) in (let TMP_14 \def (lift h d TMP_13) in (let TMP_16 \def (\lambda (t0:
+T).(let TMP_15 \def (lift h d t) in (eq T t0 TMP_15))) in (let TMP_17 \def
+(TLRef n) in (let TMP_18 \def (lift_lref_lt n h d H0) in (let H1 \def (eq_ind
+T TMP_14 TMP_16 H TMP_17 TMP_18) in (let TMP_19 \def (TLRef n) in (let TMP_20
+\def (le_n d) in (let TMP_21 \def (lt_le_trans n d d H0 TMP_20) in (let
+TMP_22 \def (lift_gen_lref_lt h d n TMP_21 t H1) in (sym_eq T t TMP_19
+TMP_22)))))))))))) in (let TMP_33 \def (\lambda (H0: (le d n)).(let TMP_24
+\def (TLRef n) in (let TMP_25 \def (lift h d TMP_24) in (let TMP_27 \def
+(\lambda (t0: T).(let TMP_26 \def (lift h d t) in (eq T t0 TMP_26))) in (let
+TMP_28 \def (plus n h) in (let TMP_29 \def (TLRef TMP_28) in (let TMP_30 \def
+(lift_lref_ge n h d H0) in (let H1 \def (eq_ind T TMP_25 TMP_27 H TMP_29
+TMP_30) in (let TMP_31 \def (TLRef n) in (let TMP_32 \def (lift_gen_lref_ge h
+d n H0 t H1) in (sym_eq T t TMP_31 TMP_32))))))))))) in (lt_le_e n d TMP_12
+TMP_23 TMP_33)))))))))) in (let TMP_140 \def (\lambda (k: K).(let TMP_36 \def
+(\lambda (k0: K).(\forall (t: T).(((\forall (t0: T).(\forall (h:
+nat).(\forall (d: nat).((eq T (lift h d t) (lift h d t0)) \to (eq T t
+t0)))))) \to (\forall (t0: T).(((\forall (t1: T).(\forall (h: nat).(\forall
+(d: nat).((eq T (lift h d t0) (lift h d t1)) \to (eq T t0 t1)))))) \to
+(\forall (t1: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d (THead
+k0 t t0)) (lift h d t1)) \to (let TMP_35 \def (THead k0 t t0) in (eq T TMP_35
+t1))))))))))) in (let TMP_90 \def (\lambda (b: B).(\lambda (t: T).(\lambda
+(H: ((\forall (t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t)
+(lift h d t0)) \to (eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall
+(t1: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d
+t1)) \to (eq T t0 t1))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d:
+nat).(\lambda (H1: (eq T (lift h d (THead (Bind b) t t0)) (lift h d
+t1))).(let TMP_37 \def (Bind b) in (let TMP_38 \def (THead TMP_37 t t0) in
+(let TMP_39 \def (lift h d TMP_38) in (let TMP_41 \def (\lambda (t2: T).(let
+TMP_40 \def (lift h d t1) in (eq T t2 TMP_40))) in (let TMP_42 \def (Bind b)
+in (let TMP_43 \def (lift h d t) in (let TMP_44 \def (S d) in (let TMP_45
+\def (lift h TMP_44 t0) in (let TMP_46 \def (THead TMP_42 TMP_43 TMP_45) in
+(let TMP_47 \def (lift_bind b t t0 h d) in (let H2 \def (eq_ind T TMP_39
+TMP_41 H1 TMP_46 TMP_47) in (let TMP_50 \def (\lambda (y: T).(\lambda (z:
+T).(let TMP_48 \def (Bind b) in (let TMP_49 \def (THead TMP_48 y z) in (eq T
+t1 TMP_49))))) in (let TMP_53 \def (\lambda (y: T).(\lambda (_: T).(let
+TMP_51 \def (lift h d t) in (let TMP_52 \def (lift h d y) in (eq T TMP_51
+TMP_52))))) in (let TMP_58 \def (\lambda (_: T).(\lambda (z: T).(let TMP_54
+\def (S d) in (let TMP_55 \def (lift h TMP_54 t0) in (let TMP_56 \def (S d)
+in (let TMP_57 \def (lift h TMP_56 z) in (eq T TMP_55 TMP_57))))))) in (let
+TMP_59 \def (Bind b) in (let TMP_60 \def (THead TMP_59 t t0) in (let TMP_61
+\def (eq T TMP_60 t1) in (let TMP_85 \def (\lambda (x0: T).(\lambda (x1:
+T).(\lambda (H3: (eq T t1 (THead (Bind b) x0 x1))).(\lambda (H4: (eq T (lift
+h d t) (lift h d x0))).(\lambda (H5: (eq T (lift h (S d) t0) (lift h (S d)
+x1))).(let TMP_62 \def (Bind b) in (let TMP_63 \def (THead TMP_62 x0 x1) in
+(let TMP_66 \def (\lambda (t2: T).(let TMP_64 \def (Bind b) in (let TMP_65
+\def (THead TMP_64 t t0) in (eq T TMP_65 t2)))) in (let TMP_67 \def (Bind b)
+in (let TMP_68 \def (THead TMP_67 x0 x1) in (let TMP_69 \def (Bind b) in (let
+TMP_70 \def (THead TMP_69 t t0) in (let TMP_71 \def (Bind b) in (let TMP_72
+\def (THead TMP_71 t t0) in (let TMP_73 \def (Bind b) in (let TMP_74 \def
+(THead TMP_73 x0 x1) in (let TMP_75 \def (Bind b) in (let TMP_76 \def (Bind
+b) in (let TMP_77 \def (Bind b) in (let TMP_78 \def (refl_equal K TMP_77) in
+(let TMP_79 \def (H x0 h d H4) in (let TMP_80 \def (S d) in (let TMP_81 \def
+(H0 x1 h TMP_80 H5) in (let TMP_82 \def (f_equal3 K T T T THead TMP_75 TMP_76
+t x0 t0 x1 TMP_78 TMP_79 TMP_81) in (let TMP_83 \def (sym_eq T TMP_72 TMP_74
+TMP_82) in (let TMP_84 \def (sym_eq T TMP_68 TMP_70 TMP_83) in (eq_ind_r T
+TMP_63 TMP_66 TMP_84 t1 H3))))))))))))))))))))))))))) in (let TMP_86 \def
+(lift h d t) in (let TMP_87 \def (S d) in (let TMP_88 \def (lift h TMP_87 t0)
+in (let TMP_89 \def (lift_gen_bind b TMP_86 TMP_88 t1 h d H2) in (ex3_2_ind T
+T TMP_50 TMP_53 TMP_58 TMP_61 TMP_85 TMP_89))))))))))))))))))))))))))))))))
+in (let TMP_139 \def (\lambda (f: F).(\lambda (t: T).(\lambda (H: ((\forall
+(t0: T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t) (lift h d
+t0)) \to (eq T t t0))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (t1:
+T).(\forall (h: nat).(\forall (d: nat).((eq T (lift h d t0) (lift h d t1))
+\to (eq T t0 t1))))))).(\lambda (t1: T).(\lambda (h: nat).(\lambda (d:
+nat).(\lambda (H1: (eq T (lift h d (THead (Flat f) t t0)) (lift h d
+t1))).(let TMP_91 \def (Flat f) in (let TMP_92 \def (THead TMP_91 t t0) in
+(let TMP_93 \def (lift h d TMP_92) in (let TMP_95 \def (\lambda (t2: T).(let
+TMP_94 \def (lift h d t1) in (eq T t2 TMP_94))) in (let TMP_96 \def (Flat f)
+in (let TMP_97 \def (lift h d t) in (let TMP_98 \def (lift h d t0) in (let
+TMP_99 \def (THead TMP_96 TMP_97 TMP_98) in (let TMP_100 \def (lift_flat f t
+t0 h d) in (let H2 \def (eq_ind T TMP_93 TMP_95 H1 TMP_99 TMP_100) in (let
+TMP_103 \def (\lambda (y: T).(\lambda (z: T).(let TMP_101 \def (Flat f) in
+(let TMP_102 \def (THead TMP_101 y z) in (eq T t1 TMP_102))))) in (let
+TMP_106 \def (\lambda (y: T).(\lambda (_: T).(let TMP_104 \def (lift h d t)
+in (let TMP_105 \def (lift h d y) in (eq T TMP_104 TMP_105))))) in (let
+TMP_109 \def (\lambda (_: T).(\lambda (z: T).(let TMP_107 \def (lift h d t0)
+in (let TMP_108 \def (lift h d z) in (eq T TMP_107 TMP_108))))) in (let
+TMP_110 \def (Flat f) in (let TMP_111 \def (THead TMP_110 t t0) in (let
+TMP_112 \def (eq T TMP_111 t1) in (let TMP_135 \def (\lambda (x0: T).(\lambda
+(x1: T).(\lambda (H3: (eq T t1 (THead (Flat f) x0 x1))).(\lambda (H4: (eq T
+(lift h d t) (lift h d x0))).(\lambda (H5: (eq T (lift h d t0) (lift h d
+x1))).(let TMP_113 \def (Flat f) in (let TMP_114 \def (THead TMP_113 x0 x1)
+in (let TMP_117 \def (\lambda (t2: T).(let TMP_115 \def (Flat f) in (let
+TMP_116 \def (THead TMP_115 t t0) in (eq T TMP_116 t2)))) in (let TMP_118
+\def (Flat f) in (let TMP_119 \def (THead TMP_118 x0 x1) in (let TMP_120 \def
+(Flat f) in (let TMP_121 \def (THead TMP_120 t t0) in (let TMP_122 \def (Flat
+f) in (let TMP_123 \def (THead TMP_122 t t0) in (let TMP_124 \def (Flat f) in
+(let TMP_125 \def (THead TMP_124 x0 x1) in (let TMP_126 \def (Flat f) in (let
+TMP_127 \def (Flat f) in (let TMP_128 \def (Flat f) in (let TMP_129 \def
+(refl_equal K TMP_128) in (let TMP_130 \def (H x0 h d H4) in (let TMP_131
+\def (H0 x1 h d H5) in (let TMP_132 \def (f_equal3 K T T T THead TMP_126
+TMP_127 t x0 t0 x1 TMP_129 TMP_130 TMP_131) in (let TMP_133 \def (sym_eq T
+TMP_123 TMP_125 TMP_132) in (let TMP_134 \def (sym_eq T TMP_119 TMP_121
+TMP_133) in (eq_ind_r T TMP_114 TMP_117 TMP_134 t1
+H3)))))))))))))))))))))))))) in (let TMP_136 \def (lift h d t) in (let
+TMP_137 \def (lift h d t0) in (let TMP_138 \def (lift_gen_flat f TMP_136
+TMP_137 t1 h d H2) in (ex3_2_ind T T TMP_103 TMP_106 TMP_109 TMP_112 TMP_135
+TMP_138)))))))))))))))))))))))))))))) in (K_ind TMP_36 TMP_90 TMP_139 k)))))
+in (T_ind TMP_1 TMP_10 TMP_34 TMP_140 x))))).
+
+theorem lift_gen_lift:
+ \forall (t1: T).(\forall (x: T).(\forall (h1: nat).(\forall (h2:
+nat).(\forall (d1: nat).(\forall (d2: nat).((le d1 d2) \to ((eq T (lift h1 d1
+t1) (lift h2 (plus d2 h1) x)) \to (ex2 T (\lambda (t2: T).(eq T x (lift h1 d1
+t2))) (\lambda (t2: T).(eq T t1 (lift h2 d2 t2)))))))))))
+\def
+ \lambda (t1: T).(let TMP_5 \def (\lambda (t: T).(\forall (x: T).(\forall
+(h1: nat).(\forall (h2: nat).(\forall (d1: nat).(\forall (d2: nat).((le d1
+d2) \to ((eq T (lift h1 d1 t) (lift h2 (plus d2 h1) x)) \to (let TMP_2 \def
+(\lambda (t2: T).(let TMP_1 \def (lift h1 d1 t2) in (eq T x TMP_1))) in (let
+TMP_4 \def (\lambda (t2: T).(let TMP_3 \def (lift h2 d2 t2) in (eq T t
+TMP_3))) in (ex2 T TMP_2 TMP_4))))))))))) in (let TMP_48 \def (\lambda (n:
+nat).(\lambda (x: T).(\lambda (h1: nat).(\lambda (h2: nat).(\lambda (d1:
+nat).(\lambda (d2: nat).(\lambda (_: (le d1 d2)).(\lambda (H0: (eq T (lift h1
+d1 (TSort n)) (lift h2 (plus d2 h1) x))).(let TMP_6 \def (TSort n) in (let
+TMP_7 \def (lift h1 d1 TMP_6) in (let TMP_10 \def (\lambda (t: T).(let TMP_8
+\def (plus d2 h1) in (let TMP_9 \def (lift h2 TMP_8 x) in (eq T t TMP_9))))
+in (let TMP_11 \def (TSort n) in (let TMP_12 \def (lift_sort n h1 d1) in (let
+H1 \def (eq_ind T TMP_7 TMP_10 H0 TMP_11 TMP_12) in (let TMP_13 \def (TSort
+n) in (let TMP_19 \def (\lambda (t: T).(let TMP_15 \def (\lambda (t2: T).(let
+TMP_14 \def (lift h1 d1 t2) in (eq T t TMP_14))) in (let TMP_18 \def (\lambda
+(t2: T).(let TMP_16 \def (TSort n) in (let TMP_17 \def (lift h2 d2 t2) in (eq
+T TMP_16 TMP_17)))) in (ex2 T TMP_15 TMP_18)))) in (let TMP_22 \def (\lambda
+(t2: T).(let TMP_20 \def (TSort n) in (let TMP_21 \def (lift h1 d1 t2) in (eq
+T TMP_20 TMP_21)))) in (let TMP_25 \def (\lambda (t2: T).(let TMP_23 \def
+(TSort n) in (let TMP_24 \def (lift h2 d2 t2) in (eq T TMP_23 TMP_24)))) in
+(let TMP_26 \def (TSort n) in (let TMP_27 \def (TSort n) in (let TMP_29 \def
+(\lambda (t: T).(let TMP_28 \def (TSort n) in (eq T TMP_28 t))) in (let
+TMP_30 \def (TSort n) in (let TMP_31 \def (refl_equal T TMP_30) in (let
+TMP_32 \def (TSort n) in (let TMP_33 \def (lift h1 d1 TMP_32) in (let TMP_34
+\def (lift_sort n h1 d1) in (let TMP_35 \def (eq_ind_r T TMP_27 TMP_29 TMP_31
+TMP_33 TMP_34) in (let TMP_36 \def (TSort n) in (let TMP_38 \def (\lambda (t:
+T).(let TMP_37 \def (TSort n) in (eq T TMP_37 t))) in (let TMP_39 \def (TSort
+n) in (let TMP_40 \def (refl_equal T TMP_39) in (let TMP_41 \def (TSort n) in
+(let TMP_42 \def (lift h2 d2 TMP_41) in (let TMP_43 \def (lift_sort n h2 d2)
+in (let TMP_44 \def (eq_ind_r T TMP_36 TMP_38 TMP_40 TMP_42 TMP_43) in (let
+TMP_45 \def (ex_intro2 T TMP_22 TMP_25 TMP_26 TMP_35 TMP_44) in (let TMP_46
+\def (plus d2 h1) in (let TMP_47 \def (lift_gen_sort h2 TMP_46 n x H1) in
+(eq_ind_r T TMP_13 TMP_19 TMP_45 x
+TMP_47))))))))))))))))))))))))))))))))))))))) in (let TMP_325 \def (\lambda
+(n: nat).(\lambda (x: T).(\lambda (h1: nat).(\lambda (h2: nat).(\lambda (d1:
+nat).(\lambda (d2: nat).(\lambda (H: (le d1 d2)).(\lambda (H0: (eq T (lift h1
+d1 (TLRef n)) (lift h2 (plus d2 h1) x))).(let TMP_50 \def (\lambda (t2:
+T).(let TMP_49 \def (lift h1 d1 t2) in (eq T x TMP_49))) in (let TMP_53 \def
+(\lambda (t2: T).(let TMP_51 \def (TLRef n) in (let TMP_52 \def (lift h2 d2
+t2) in (eq T TMP_51 TMP_52)))) in (let TMP_54 \def (ex2 T TMP_50 TMP_53) in
+(let TMP_101 \def (\lambda (H1: (lt n d1)).(let TMP_55 \def (TLRef n) in (let
+TMP_56 \def (lift h1 d1 TMP_55) in (let TMP_59 \def (\lambda (t: T).(let
+TMP_57 \def (plus d2 h1) in (let TMP_58 \def (lift h2 TMP_57 x) in (eq T t
+TMP_58)))) in (let TMP_60 \def (TLRef n) in (let TMP_61 \def (lift_lref_lt n
+h1 d1 H1) in (let H2 \def (eq_ind T TMP_56 TMP_59 H0 TMP_60 TMP_61) in (let
+TMP_62 \def (TLRef n) in (let TMP_68 \def (\lambda (t: T).(let TMP_64 \def
+(\lambda (t2: T).(let TMP_63 \def (lift h1 d1 t2) in (eq T t TMP_63))) in
+(let TMP_67 \def (\lambda (t2: T).(let TMP_65 \def (TLRef n) in (let TMP_66
+\def (lift h2 d2 t2) in (eq T TMP_65 TMP_66)))) in (ex2 T TMP_64 TMP_67))))
+in (let TMP_71 \def (\lambda (t2: T).(let TMP_69 \def (TLRef n) in (let
+TMP_70 \def (lift h1 d1 t2) in (eq T TMP_69 TMP_70)))) in (let TMP_74 \def
+(\lambda (t2: T).(let TMP_72 \def (TLRef n) in (let TMP_73 \def (lift h2 d2
+t2) in (eq T TMP_72 TMP_73)))) in (let TMP_75 \def (TLRef n) in (let TMP_76
+\def (TLRef n) in (let TMP_78 \def (\lambda (t: T).(let TMP_77 \def (TLRef n)
+in (eq T TMP_77 t))) in (let TMP_79 \def (TLRef n) in (let TMP_80 \def
+(refl_equal T TMP_79) in (let TMP_81 \def (TLRef n) in (let TMP_82 \def (lift
+h1 d1 TMP_81) in (let TMP_83 \def (lift_lref_lt n h1 d1 H1) in (let TMP_84
+\def (eq_ind_r T TMP_76 TMP_78 TMP_80 TMP_82 TMP_83) in (let TMP_85 \def
+(TLRef n) in (let TMP_87 \def (\lambda (t: T).(let TMP_86 \def (TLRef n) in
+(eq T TMP_86 t))) in (let TMP_88 \def (TLRef n) in (let TMP_89 \def
+(refl_equal T TMP_88) in (let TMP_90 \def (TLRef n) in (let TMP_91 \def (lift
+h2 d2 TMP_90) in (let TMP_92 \def (lt_le_trans n d1 d2 H1 H) in (let TMP_93
+\def (lift_lref_lt n h2 d2 TMP_92) in (let TMP_94 \def (eq_ind_r T TMP_85
+TMP_87 TMP_89 TMP_91 TMP_93) in (let TMP_95 \def (ex_intro2 T TMP_71 TMP_74
+TMP_75 TMP_84 TMP_94) in (let TMP_96 \def (plus d2 h1) in (let TMP_97 \def
+(plus d2 h1) in (let TMP_98 \def (le_plus_trans d1 d2 h1 H) in (let TMP_99
+\def (lt_le_trans n d1 TMP_97 H1 TMP_98) in (let TMP_100 \def
+(lift_gen_lref_lt h2 TMP_96 n TMP_99 x H2) in (eq_ind_r T TMP_62 TMP_68
+TMP_95 x TMP_100)))))))))))))))))))))))))))))))))))) in (let TMP_324 \def
+(\lambda (H1: (le d1 n)).(let TMP_102 \def (TLRef n) in (let TMP_103 \def
+(lift h1 d1 TMP_102) in (let TMP_106 \def (\lambda (t: T).(let TMP_104 \def
+(plus d2 h1) in (let TMP_105 \def (lift h2 TMP_104 x) in (eq T t TMP_105))))
+in (let TMP_107 \def (plus n h1) in (let TMP_108 \def (TLRef TMP_107) in (let
+TMP_109 \def (lift_lref_ge n h1 d1 H1) in (let H2 \def (eq_ind T TMP_103
+TMP_106 H0 TMP_108 TMP_109) in (let TMP_111 \def (\lambda (t2: T).(let
+TMP_110 \def (lift h1 d1 t2) in (eq T x TMP_110))) in (let TMP_114 \def
+(\lambda (t2: T).(let TMP_112 \def (TLRef n) in (let TMP_113 \def (lift h2 d2
+t2) in (eq T TMP_112 TMP_113)))) in (let TMP_115 \def (ex2 T TMP_111 TMP_114)
+in (let TMP_158 \def (\lambda (H3: (lt n d2)).(let TMP_116 \def (plus n h1)
+in (let TMP_117 \def (TLRef TMP_116) in (let TMP_123 \def (\lambda (t:
+T).(let TMP_119 \def (\lambda (t2: T).(let TMP_118 \def (lift h1 d1 t2) in
+(eq T t TMP_118))) in (let TMP_122 \def (\lambda (t2: T).(let TMP_120 \def
+(TLRef n) in (let TMP_121 \def (lift h2 d2 t2) in (eq T TMP_120 TMP_121))))
+in (ex2 T TMP_119 TMP_122)))) in (let TMP_127 \def (\lambda (t2: T).(let
+TMP_124 \def (plus n h1) in (let TMP_125 \def (TLRef TMP_124) in (let TMP_126
+\def (lift h1 d1 t2) in (eq T TMP_125 TMP_126))))) in (let TMP_130 \def
+(\lambda (t2: T).(let TMP_128 \def (TLRef n) in (let TMP_129 \def (lift h2 d2
+t2) in (eq T TMP_128 TMP_129)))) in (let TMP_131 \def (TLRef n) in (let
+TMP_132 \def (plus n h1) in (let TMP_133 \def (TLRef TMP_132) in (let TMP_136
+\def (\lambda (t: T).(let TMP_134 \def (plus n h1) in (let TMP_135 \def
+(TLRef TMP_134) in (eq T TMP_135 t)))) in (let TMP_137 \def (plus n h1) in
+(let TMP_138 \def (TLRef TMP_137) in (let TMP_139 \def (refl_equal T TMP_138)
+in (let TMP_140 \def (TLRef n) in (let TMP_141 \def (lift h1 d1 TMP_140) in
+(let TMP_142 \def (lift_lref_ge n h1 d1 H1) in (let TMP_143 \def (eq_ind_r T
+TMP_133 TMP_136 TMP_139 TMP_141 TMP_142) in (let TMP_144 \def (TLRef n) in
+(let TMP_146 \def (\lambda (t: T).(let TMP_145 \def (TLRef n) in (eq T
+TMP_145 t))) in (let TMP_147 \def (TLRef n) in (let TMP_148 \def (refl_equal
+T TMP_147) in (let TMP_149 \def (TLRef n) in (let TMP_150 \def (lift h2 d2
+TMP_149) in (let TMP_151 \def (lift_lref_lt n h2 d2 H3) in (let TMP_152 \def
+(eq_ind_r T TMP_144 TMP_146 TMP_148 TMP_150 TMP_151) in (let TMP_153 \def
+(ex_intro2 T TMP_127 TMP_130 TMP_131 TMP_143 TMP_152) in (let TMP_154 \def
+(plus d2 h1) in (let TMP_155 \def (plus n h1) in (let TMP_156 \def (lt_reg_r
+n d2 h1 H3) in (let TMP_157 \def (lift_gen_lref_lt h2 TMP_154 TMP_155 TMP_156
+x H2) in (eq_ind_r T TMP_117 TMP_123 TMP_153 x
+TMP_157))))))))))))))))))))))))))))))) in (let TMP_323 \def (\lambda (H3: (le
+d2 n)).(let TMP_159 \def (plus d2 h2) in (let TMP_161 \def (\lambda (t2:
+T).(let TMP_160 \def (lift h1 d1 t2) in (eq T x TMP_160))) in (let TMP_164
+\def (\lambda (t2: T).(let TMP_162 \def (TLRef n) in (let TMP_163 \def (lift
+h2 d2 t2) in (eq T TMP_162 TMP_163)))) in (let TMP_165 \def (ex2 T TMP_161
+TMP_164) in (let TMP_186 \def (\lambda (H4: (lt n (plus d2 h2))).(let TMP_166
+\def (plus d2 h1) in (let TMP_167 \def (plus n h1) in (let TMP_168 \def (le_n
+h1) in (let TMP_169 \def (le_plus_plus d2 n h1 h1 H3 TMP_168) in (let TMP_170
+\def (plus d2 h2) in (let TMP_171 \def (plus TMP_170 h1) in (let TMP_173 \def
+(\lambda (n0: nat).(let TMP_172 \def (plus n h1) in (lt TMP_172 n0))) in (let
+TMP_174 \def (plus d2 h2) in (let TMP_175 \def (lt_reg_r n TMP_174 h1 H4) in
+(let TMP_176 \def (plus d2 h1) in (let TMP_177 \def (plus TMP_176 h2) in (let
+TMP_178 \def (plus_permute_2_in_3 d2 h1 h2) in (let TMP_179 \def (eq_ind_r
+nat TMP_171 TMP_173 TMP_175 TMP_177 TMP_178) in (let TMP_181 \def (\lambda
+(t2: T).(let TMP_180 \def (lift h1 d1 t2) in (eq T x TMP_180))) in (let
+TMP_184 \def (\lambda (t2: T).(let TMP_182 \def (TLRef n) in (let TMP_183
+\def (lift h2 d2 t2) in (eq T TMP_182 TMP_183)))) in (let TMP_185 \def (ex2 T
+TMP_181 TMP_184) in (lift_gen_lref_false h2 TMP_166 TMP_167 TMP_169 TMP_179 x
+H2 TMP_185)))))))))))))))))) in (let TMP_322 \def (\lambda (H4: (le (plus d2
+h2) n)).(let TMP_187 \def (plus n h1) in (let TMP_191 \def (\lambda (n0:
+nat).(let TMP_188 \def (TLRef n0) in (let TMP_189 \def (plus d2 h1) in (let
+TMP_190 \def (lift h2 TMP_189 x) in (eq T TMP_188 TMP_190))))) in (let
+TMP_192 \def (plus n h1) in (let TMP_193 \def (minus TMP_192 h2) in (let
+TMP_194 \def (plus TMP_193 h2) in (let TMP_195 \def (plus n h1) in (let
+TMP_196 \def (plus d2 h2) in (let TMP_197 \def (le_plus_r d2 h2) in (let
+TMP_198 \def (le_trans h2 TMP_196 n TMP_197 H4) in (let TMP_199 \def
+(le_plus_trans h2 n h1 TMP_198) in (let TMP_200 \def (le_plus_minus_sym h2
+TMP_195 TMP_199) in (let H5 \def (eq_ind nat TMP_187 TMP_191 H2 TMP_194
+TMP_200) in (let TMP_201 \def (plus n h1) in (let TMP_202 \def (minus TMP_201
+h2) in (let TMP_203 \def (TLRef TMP_202) in (let TMP_209 \def (\lambda (t:
+T).(let TMP_205 \def (\lambda (t2: T).(let TMP_204 \def (lift h1 d1 t2) in
+(eq T t TMP_204))) in (let TMP_208 \def (\lambda (t2: T).(let TMP_206 \def
+(TLRef n) in (let TMP_207 \def (lift h2 d2 t2) in (eq T TMP_206 TMP_207))))
+in (ex2 T TMP_205 TMP_208)))) in (let TMP_214 \def (\lambda (t2: T).(let
+TMP_210 \def (plus n h1) in (let TMP_211 \def (minus TMP_210 h2) in (let
+TMP_212 \def (TLRef TMP_211) in (let TMP_213 \def (lift h1 d1 t2) in (eq T
+TMP_212 TMP_213)))))) in (let TMP_217 \def (\lambda (t2: T).(let TMP_215 \def
+(TLRef n) in (let TMP_216 \def (lift h2 d2 t2) in (eq T TMP_215 TMP_216))))
+in (let TMP_218 \def (minus n h2) in (let TMP_219 \def (TLRef TMP_218) in
+(let TMP_220 \def (minus n h2) in (let TMP_221 \def (plus TMP_220 h1) in (let
+TMP_226 \def (\lambda (n0: nat).(let TMP_222 \def (TLRef n0) in (let TMP_223
+\def (minus n h2) in (let TMP_224 \def (TLRef TMP_223) in (let TMP_225 \def
+(lift h1 d1 TMP_224) in (eq T TMP_222 TMP_225)))))) in (let TMP_227 \def
+(minus n h2) in (let TMP_228 \def (plus TMP_227 h1) in (let TMP_229 \def
+(TLRef TMP_228) in (let TMP_233 \def (\lambda (t: T).(let TMP_230 \def (minus
+n h2) in (let TMP_231 \def (plus TMP_230 h1) in (let TMP_232 \def (TLRef
+TMP_231) in (eq T TMP_232 t))))) in (let TMP_234 \def (minus n h2) in (let
+TMP_235 \def (plus TMP_234 h1) in (let TMP_236 \def (TLRef TMP_235) in (let
+TMP_237 \def (refl_equal T TMP_236) in (let TMP_238 \def (minus n h2) in (let
+TMP_239 \def (TLRef TMP_238) in (let TMP_240 \def (lift h1 d1 TMP_239) in
+(let TMP_241 \def (minus n h2) in (let TMP_242 \def (minus n h2) in (let
+TMP_243 \def (le_minus d2 n h2 H4) in (let TMP_244 \def (le_trans d1 d2
+TMP_242 H TMP_243) in (let TMP_245 \def (lift_lref_ge TMP_241 h1 d1 TMP_244)
+in (let TMP_246 \def (eq_ind_r T TMP_229 TMP_233 TMP_237 TMP_240 TMP_245) in
+(let TMP_247 \def (plus n h1) in (let TMP_248 \def (minus TMP_247 h2) in (let
+TMP_249 \def (plus d2 h2) in (let TMP_250 \def (le_plus_r d2 h2) in (let
+TMP_251 \def (le_trans h2 TMP_249 n TMP_250 H4) in (let TMP_252 \def
+(le_minus_plus h2 n TMP_251 h1) in (let TMP_253 \def (eq_ind_r nat TMP_221
+TMP_226 TMP_246 TMP_248 TMP_252) in (let TMP_254 \def (minus n h2) in (let
+TMP_255 \def (plus TMP_254 h2) in (let TMP_260 \def (\lambda (n0: nat).(let
+TMP_256 \def (TLRef n0) in (let TMP_257 \def (minus n0 h2) in (let TMP_258
+\def (TLRef TMP_257) in (let TMP_259 \def (lift h2 d2 TMP_258) in (eq T
+TMP_256 TMP_259)))))) in (let TMP_261 \def (minus n h2) in (let TMP_262 \def
+(plus TMP_261 h2) in (let TMP_263 \def (minus TMP_262 h2) in (let TMP_264
+\def (plus TMP_263 h2) in (let TMP_265 \def (TLRef TMP_264) in (let TMP_269
+\def (\lambda (t: T).(let TMP_266 \def (minus n h2) in (let TMP_267 \def
+(plus TMP_266 h2) in (let TMP_268 \def (TLRef TMP_267) in (eq T TMP_268
+t))))) in (let TMP_270 \def (minus n h2) in (let TMP_271 \def (plus TMP_270
+h2) in (let TMP_272 \def (minus TMP_271 h2) in (let TMP_273 \def (plus
+TMP_272 h2) in (let TMP_274 \def (TLRef TMP_273) in (let TMP_275 \def (minus
+n h2) in (let TMP_276 \def (plus TMP_275 h2) in (let TMP_277 \def (TLRef
+TMP_276) in (let TMP_278 \def (minus n h2) in (let TMP_279 \def (plus TMP_278
+h2) in (let TMP_280 \def (minus TMP_279 h2) in (let TMP_281 \def (plus
+TMP_280 h2) in (let TMP_282 \def (minus n h2) in (let TMP_283 \def (plus
+TMP_282 h2) in (let TMP_284 \def (minus n h2) in (let TMP_285 \def (plus
+TMP_284 h2) in (let TMP_286 \def (minus TMP_285 h2) in (let TMP_287 \def
+(minus n h2) in (let TMP_288 \def (minus n h2) in (let TMP_289 \def
+(minus_plus_r TMP_288 h2) in (let TMP_290 \def (refl_equal nat h2) in (let
+TMP_291 \def (f_equal2 nat nat nat plus TMP_286 TMP_287 h2 h2 TMP_289
+TMP_290) in (let TMP_292 \def (f_equal nat T TLRef TMP_281 TMP_283 TMP_291)
+in (let TMP_293 \def (sym_eq T TMP_274 TMP_277 TMP_292) in (let TMP_294 \def
+(minus n h2) in (let TMP_295 \def (plus TMP_294 h2) in (let TMP_296 \def
+(minus TMP_295 h2) in (let TMP_297 \def (TLRef TMP_296) in (let TMP_298 \def
+(lift h2 d2 TMP_297) in (let TMP_299 \def (minus n h2) in (let TMP_300 \def
+(plus TMP_299 h2) in (let TMP_301 \def (minus TMP_300 h2) in (let TMP_302
+\def (minus n h2) in (let TMP_303 \def (plus TMP_302 h2) in (let TMP_304 \def
+(minus n h2) in (let TMP_305 \def (le_minus d2 n h2 H4) in (let TMP_306 \def
+(le_n h2) in (let TMP_307 \def (le_plus_plus d2 TMP_304 h2 h2 TMP_305
+TMP_306) in (let TMP_308 \def (le_minus d2 TMP_303 h2 TMP_307) in (let
+TMP_309 \def (lift_lref_ge TMP_301 h2 d2 TMP_308) in (let TMP_310 \def
+(eq_ind_r T TMP_265 TMP_269 TMP_293 TMP_298 TMP_309) in (let TMP_311 \def
+(plus d2 h2) in (let TMP_312 \def (le_plus_r d2 h2) in (let TMP_313 \def
+(le_trans h2 TMP_311 n TMP_312 H4) in (let TMP_314 \def (le_plus_minus_sym h2
+n TMP_313) in (let TMP_315 \def (eq_ind_r nat TMP_255 TMP_260 TMP_310 n
+TMP_314) in (let TMP_316 \def (ex_intro2 T TMP_214 TMP_217 TMP_219 TMP_253
+TMP_315) in (let TMP_317 \def (plus d2 h1) in (let TMP_318 \def (plus n h1)
+in (let TMP_319 \def (minus TMP_318 h2) in (let TMP_320 \def (arith0 h2 d2 n
+H4 h1) in (let TMP_321 \def (lift_gen_lref_ge h2 TMP_317 TMP_319 TMP_320 x
+H5) in (eq_ind_r T TMP_203 TMP_209 TMP_316 x
+TMP_321)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
+))))))))))))))))))))))))))))))))))))))) in (lt_le_e n TMP_159 TMP_165 TMP_186
+TMP_322)))))))) in (lt_le_e n d2 TMP_115 TMP_158 TMP_323)))))))))))))) in
+(lt_le_e n d1 TMP_54 TMP_101 TMP_324)))))))))))))) in (let TMP_720 \def
+(\lambda (k: K).(\lambda (t: T).(\lambda (H: ((\forall (x: T).(\forall (h1:
+nat).(\forall (h2: nat).(\forall (d1: nat).(\forall (d2: nat).((le d1 d2) \to
+((eq T (lift h1 d1 t) (lift h2 (plus d2 h1) x)) \to (ex2 T (\lambda (t2:
+T).(eq T x (lift h1 d1 t2))) (\lambda (t2: T).(eq T t (lift h2 d2
+t2))))))))))))).(\lambda (t0: T).(\lambda (H0: ((\forall (x: T).(\forall (h1:
+nat).(\forall (h2: nat).(\forall (d1: nat).(\forall (d2: nat).((le d1 d2) \to
+((eq T (lift h1 d1 t0) (lift h2 (plus d2 h1) x)) \to (ex2 T (\lambda (t2:
+T).(eq T x (lift h1 d1 t2))) (\lambda (t2: T).(eq T t0 (lift h2 d2
+t2))))))))))))).(\lambda (x: T).(\lambda (h1: nat).(\lambda (h2:
+nat).(\lambda (d1: nat).(\lambda (d2: nat).(\lambda (H1: (le d1 d2)).(\lambda
+(H2: (eq T (lift h1 d1 (THead k t t0)) (lift h2 (plus d2 h1) x))).(let
+TMP_331 \def (\lambda (k0: K).((eq T (lift h1 d1 (THead k0 t t0)) (lift h2
+(plus d2 h1) x)) \to (let TMP_327 \def (\lambda (t2: T).(let TMP_326 \def
+(lift h1 d1 t2) in (eq T x TMP_326))) in (let TMP_330 \def (\lambda (t2:
+T).(let TMP_328 \def (THead k0 t t0) in (let TMP_329 \def (lift h2 d2 t2) in
+(eq T TMP_328 TMP_329)))) in (ex2 T TMP_327 TMP_330))))) in (let TMP_540 \def
+(\lambda (b: B).(\lambda (H3: (eq T (lift h1 d1 (THead (Bind b) t t0)) (lift
+h2 (plus d2 h1) x))).(let TMP_332 \def (Bind b) in (let TMP_333 \def (THead
+TMP_332 t t0) in (let TMP_334 \def (lift h1 d1 TMP_333) in (let TMP_337 \def
+(\lambda (t2: T).(let TMP_335 \def (plus d2 h1) in (let TMP_336 \def (lift h2
+TMP_335 x) in (eq T t2 TMP_336)))) in (let TMP_338 \def (Bind b) in (let
+TMP_339 \def (lift h1 d1 t) in (let TMP_340 \def (S d1) in (let TMP_341 \def
+(lift h1 TMP_340 t0) in (let TMP_342 \def (THead TMP_338 TMP_339 TMP_341) in
+(let TMP_343 \def (lift_bind b t t0 h1 d1) in (let H4 \def (eq_ind T TMP_334
+TMP_337 H3 TMP_342 TMP_343) in (let TMP_346 \def (\lambda (y: T).(\lambda (z:
+T).(let TMP_344 \def (Bind b) in (let TMP_345 \def (THead TMP_344 y z) in (eq
+T x TMP_345))))) in (let TMP_350 \def (\lambda (y: T).(\lambda (_: T).(let
+TMP_347 \def (lift h1 d1 t) in (let TMP_348 \def (plus d2 h1) in (let TMP_349
+\def (lift h2 TMP_348 y) in (eq T TMP_347 TMP_349)))))) in (let TMP_356 \def
+(\lambda (_: T).(\lambda (z: T).(let TMP_351 \def (S d1) in (let TMP_352 \def
+(lift h1 TMP_351 t0) in (let TMP_353 \def (plus d2 h1) in (let TMP_354 \def
+(S TMP_353) in (let TMP_355 \def (lift h2 TMP_354 z) in (eq T TMP_352
+TMP_355)))))))) in (let TMP_358 \def (\lambda (t2: T).(let TMP_357 \def (lift
+h1 d1 t2) in (eq T x TMP_357))) in (let TMP_362 \def (\lambda (t2: T).(let
+TMP_359 \def (Bind b) in (let TMP_360 \def (THead TMP_359 t t0) in (let
+TMP_361 \def (lift h2 d2 t2) in (eq T TMP_360 TMP_361))))) in (let TMP_363
+\def (ex2 T TMP_358 TMP_362) in (let TMP_534 \def (\lambda (x0: T).(\lambda
+(x1: T).(\lambda (H5: (eq T x (THead (Bind b) x0 x1))).(\lambda (H6: (eq T
+(lift h1 d1 t) (lift h2 (plus d2 h1) x0))).(\lambda (H7: (eq T (lift h1 (S
+d1) t0) (lift h2 (S (plus d2 h1)) x1))).(let TMP_364 \def (Bind b) in (let
+TMP_365 \def (THead TMP_364 x0 x1) in (let TMP_372 \def (\lambda (t2: T).(let
+TMP_367 \def (\lambda (t3: T).(let TMP_366 \def (lift h1 d1 t3) in (eq T t2
+TMP_366))) in (let TMP_371 \def (\lambda (t3: T).(let TMP_368 \def (Bind b)
+in (let TMP_369 \def (THead TMP_368 t t0) in (let TMP_370 \def (lift h2 d2
+t3) in (eq T TMP_369 TMP_370))))) in (ex2 T TMP_367 TMP_371)))) in (let
+TMP_374 \def (\lambda (t2: T).(let TMP_373 \def (lift h1 d1 t2) in (eq T x0
+TMP_373))) in (let TMP_376 \def (\lambda (t2: T).(let TMP_375 \def (lift h2
+d2 t2) in (eq T t TMP_375))) in (let TMP_380 \def (\lambda (t2: T).(let
+TMP_377 \def (Bind b) in (let TMP_378 \def (THead TMP_377 x0 x1) in (let
+TMP_379 \def (lift h1 d1 t2) in (eq T TMP_378 TMP_379))))) in (let TMP_384
+\def (\lambda (t2: T).(let TMP_381 \def (Bind b) in (let TMP_382 \def (THead
+TMP_381 t t0) in (let TMP_383 \def (lift h2 d2 t2) in (eq T TMP_382
+TMP_383))))) in (let TMP_385 \def (ex2 T TMP_380 TMP_384) in (let TMP_531
+\def (\lambda (x2: T).(\lambda (H8: (eq T x0 (lift h1 d1 x2))).(\lambda (H9:
+(eq T t (lift h2 d2 x2))).(let TMP_386 \def (lift h1 d1 x2) in (let TMP_395
+\def (\lambda (t2: T).(let TMP_390 \def (\lambda (t3: T).(let TMP_387 \def
+(Bind b) in (let TMP_388 \def (THead TMP_387 t2 x1) in (let TMP_389 \def
+(lift h1 d1 t3) in (eq T TMP_388 TMP_389))))) in (let TMP_394 \def (\lambda
+(t3: T).(let TMP_391 \def (Bind b) in (let TMP_392 \def (THead TMP_391 t t0)
+in (let TMP_393 \def (lift h2 d2 t3) in (eq T TMP_392 TMP_393))))) in (ex2 T
+TMP_390 TMP_394)))) in (let TMP_396 \def (lift h2 d2 x2) in (let TMP_406 \def
+(\lambda (t2: T).(let TMP_401 \def (\lambda (t3: T).(let TMP_397 \def (Bind
+b) in (let TMP_398 \def (lift h1 d1 x2) in (let TMP_399 \def (THead TMP_397
+TMP_398 x1) in (let TMP_400 \def (lift h1 d1 t3) in (eq T TMP_399
+TMP_400)))))) in (let TMP_405 \def (\lambda (t3: T).(let TMP_402 \def (Bind
+b) in (let TMP_403 \def (THead TMP_402 t2 t0) in (let TMP_404 \def (lift h2
+d2 t3) in (eq T TMP_403 TMP_404))))) in (ex2 T TMP_401 TMP_405)))) in (let
+TMP_407 \def (S d2) in (let TMP_408 \def (plus TMP_407 h1) in (let H10 \def
+(refl_equal nat TMP_408) in (let TMP_409 \def (plus d2 h1) in (let TMP_410
+\def (S TMP_409) in (let TMP_414 \def (\lambda (n: nat).(let TMP_411 \def (S
+d1) in (let TMP_412 \def (lift h1 TMP_411 t0) in (let TMP_413 \def (lift h2 n
+x1) in (eq T TMP_412 TMP_413))))) in (let TMP_415 \def (S d2) in (let TMP_416
+\def (plus TMP_415 h1) in (let H11 \def (eq_ind nat TMP_410 TMP_414 H7
+TMP_416 H10) in (let TMP_419 \def (\lambda (t2: T).(let TMP_417 \def (S d1)
+in (let TMP_418 \def (lift h1 TMP_417 t2) in (eq T x1 TMP_418)))) in (let
+TMP_422 \def (\lambda (t2: T).(let TMP_420 \def (S d2) in (let TMP_421 \def
+(lift h2 TMP_420 t2) in (eq T t0 TMP_421)))) in (let TMP_427 \def (\lambda
+(t2: T).(let TMP_423 \def (Bind b) in (let TMP_424 \def (lift h1 d1 x2) in
+(let TMP_425 \def (THead TMP_423 TMP_424 x1) in (let TMP_426 \def (lift h1 d1
+t2) in (eq T TMP_425 TMP_426)))))) in (let TMP_432 \def (\lambda (t2: T).(let
+TMP_428 \def (Bind b) in (let TMP_429 \def (lift h2 d2 x2) in (let TMP_430
+\def (THead TMP_428 TMP_429 t0) in (let TMP_431 \def (lift h2 d2 t2) in (eq T
+TMP_430 TMP_431)))))) in (let TMP_433 \def (ex2 T TMP_427 TMP_432) in (let
+TMP_524 \def (\lambda (x3: T).(\lambda (H12: (eq T x1 (lift h1 (S d1)
+x3))).(\lambda (H13: (eq T t0 (lift h2 (S d2) x3))).(let TMP_434 \def (S d1)
+in (let TMP_435 \def (lift h1 TMP_434 x3) in (let TMP_446 \def (\lambda (t2:
+T).(let TMP_440 \def (\lambda (t3: T).(let TMP_436 \def (Bind b) in (let
+TMP_437 \def (lift h1 d1 x2) in (let TMP_438 \def (THead TMP_436 TMP_437 t2)
+in (let TMP_439 \def (lift h1 d1 t3) in (eq T TMP_438 TMP_439)))))) in (let
+TMP_445 \def (\lambda (t3: T).(let TMP_441 \def (Bind b) in (let TMP_442 \def
+(lift h2 d2 x2) in (let TMP_443 \def (THead TMP_441 TMP_442 t0) in (let
+TMP_444 \def (lift h2 d2 t3) in (eq T TMP_443 TMP_444)))))) in (ex2 T TMP_440
+TMP_445)))) in (let TMP_447 \def (S d2) in (let TMP_448 \def (lift h2 TMP_447
+x3) in (let TMP_461 \def (\lambda (t2: T).(let TMP_455 \def (\lambda (t3:
+T).(let TMP_449 \def (Bind b) in (let TMP_450 \def (lift h1 d1 x2) in (let
+TMP_451 \def (S d1) in (let TMP_452 \def (lift h1 TMP_451 x3) in (let TMP_453
+\def (THead TMP_449 TMP_450 TMP_452) in (let TMP_454 \def (lift h1 d1 t3) in
+(eq T TMP_453 TMP_454)))))))) in (let TMP_460 \def (\lambda (t3: T).(let
+TMP_456 \def (Bind b) in (let TMP_457 \def (lift h2 d2 x2) in (let TMP_458
+\def (THead TMP_456 TMP_457 t2) in (let TMP_459 \def (lift h2 d2 t3) in (eq T
+TMP_458 TMP_459)))))) in (ex2 T TMP_455 TMP_460)))) in (let TMP_468 \def
+(\lambda (t2: T).(let TMP_462 \def (Bind b) in (let TMP_463 \def (lift h1 d1
+x2) in (let TMP_464 \def (S d1) in (let TMP_465 \def (lift h1 TMP_464 x3) in
+(let TMP_466 \def (THead TMP_462 TMP_463 TMP_465) in (let TMP_467 \def (lift
+h1 d1 t2) in (eq T TMP_466 TMP_467)))))))) in (let TMP_475 \def (\lambda (t2:
+T).(let TMP_469 \def (Bind b) in (let TMP_470 \def (lift h2 d2 x2) in (let
+TMP_471 \def (S d2) in (let TMP_472 \def (lift h2 TMP_471 x3) in (let TMP_473
+\def (THead TMP_469 TMP_470 TMP_472) in (let TMP_474 \def (lift h2 d2 t2) in
+(eq T TMP_473 TMP_474)))))))) in (let TMP_476 \def (Bind b) in (let TMP_477
+\def (THead TMP_476 x2 x3) in (let TMP_478 \def (Bind b) in (let TMP_479 \def
+(lift h1 d1 x2) in (let TMP_480 \def (S d1) in (let TMP_481 \def (lift h1
+TMP_480 x3) in (let TMP_482 \def (THead TMP_478 TMP_479 TMP_481) in (let
+TMP_488 \def (\lambda (t2: T).(let TMP_483 \def (Bind b) in (let TMP_484 \def
+(lift h1 d1 x2) in (let TMP_485 \def (S d1) in (let TMP_486 \def (lift h1
+TMP_485 x3) in (let TMP_487 \def (THead TMP_483 TMP_484 TMP_486) in (eq T
+TMP_487 t2))))))) in (let TMP_489 \def (Bind b) in (let TMP_490 \def (lift h1
+d1 x2) in (let TMP_491 \def (S d1) in (let TMP_492 \def (lift h1 TMP_491 x3)
+in (let TMP_493 \def (THead TMP_489 TMP_490 TMP_492) in (let TMP_494 \def
+(refl_equal T TMP_493) in (let TMP_495 \def (Bind b) in (let TMP_496 \def
+(THead TMP_495 x2 x3) in (let TMP_497 \def (lift h1 d1 TMP_496) in (let
+TMP_498 \def (lift_bind b x2 x3 h1 d1) in (let TMP_499 \def (eq_ind_r T
+TMP_482 TMP_488 TMP_494 TMP_497 TMP_498) in (let TMP_500 \def (Bind b) in
+(let TMP_501 \def (lift h2 d2 x2) in (let TMP_502 \def (S d2) in (let TMP_503
+\def (lift h2 TMP_502 x3) in (let TMP_504 \def (THead TMP_500 TMP_501
+TMP_503) in (let TMP_510 \def (\lambda (t2: T).(let TMP_505 \def (Bind b) in
+(let TMP_506 \def (lift h2 d2 x2) in (let TMP_507 \def (S d2) in (let TMP_508
+\def (lift h2 TMP_507 x3) in (let TMP_509 \def (THead TMP_505 TMP_506
+TMP_508) in (eq T TMP_509 t2))))))) in (let TMP_511 \def (Bind b) in (let
+TMP_512 \def (lift h2 d2 x2) in (let TMP_513 \def (S d2) in (let TMP_514 \def
+(lift h2 TMP_513 x3) in (let TMP_515 \def (THead TMP_511 TMP_512 TMP_514) in
+(let TMP_516 \def (refl_equal T TMP_515) in (let TMP_517 \def (Bind b) in
+(let TMP_518 \def (THead TMP_517 x2 x3) in (let TMP_519 \def (lift h2 d2
+TMP_518) in (let TMP_520 \def (lift_bind b x2 x3 h2 d2) in (let TMP_521 \def
+(eq_ind_r T TMP_504 TMP_510 TMP_516 TMP_519 TMP_520) in (let TMP_522 \def
+(ex_intro2 T TMP_468 TMP_475 TMP_477 TMP_499 TMP_521) in (let TMP_523 \def
+(eq_ind_r T TMP_448 TMP_461 TMP_522 t0 H13) in (eq_ind_r T TMP_435 TMP_446
+TMP_523 x1 H12)))))))))))))))))))))))))))))))))))))))))))))))))) in (let
+TMP_525 \def (S d1) in (let TMP_526 \def (S d2) in (let TMP_527 \def (le_n_S
+d1 d2 H1) in (let TMP_528 \def (H0 x1 h1 h2 TMP_525 TMP_526 TMP_527 H11) in
+(let TMP_529 \def (ex2_ind T TMP_419 TMP_422 TMP_433 TMP_524 TMP_528) in (let
+TMP_530 \def (eq_ind_r T TMP_396 TMP_406 TMP_529 t H9) in (eq_ind_r T TMP_386
+TMP_395 TMP_530 x0 H8))))))))))))))))))))))))))))) in (let TMP_532 \def (H x0
+h1 h2 d1 d2 H1 H6) in (let TMP_533 \def (ex2_ind T TMP_374 TMP_376 TMP_385
+TMP_531 TMP_532) in (eq_ind_r T TMP_365 TMP_372 TMP_533 x H5)))))))))))))))))
+in (let TMP_535 \def (lift h1 d1 t) in (let TMP_536 \def (S d1) in (let
+TMP_537 \def (lift h1 TMP_536 t0) in (let TMP_538 \def (plus d2 h1) in (let
+TMP_539 \def (lift_gen_bind b TMP_535 TMP_537 x h2 TMP_538 H4) in (ex3_2_ind
+T T TMP_346 TMP_350 TMP_356 TMP_363 TMP_534 TMP_539))))))))))))))))))))))))))
+in (let TMP_719 \def (\lambda (f: F).(\lambda (H3: (eq T (lift h1 d1 (THead
+(Flat f) t t0)) (lift h2 (plus d2 h1) x))).(let TMP_541 \def (Flat f) in (let
+TMP_542 \def (THead TMP_541 t t0) in (let TMP_543 \def (lift h1 d1 TMP_542)
+in (let TMP_546 \def (\lambda (t2: T).(let TMP_544 \def (plus d2 h1) in (let
+TMP_545 \def (lift h2 TMP_544 x) in (eq T t2 TMP_545)))) in (let TMP_547 \def
+(Flat f) in (let TMP_548 \def (lift h1 d1 t) in (let TMP_549 \def (lift h1 d1
+t0) in (let TMP_550 \def (THead TMP_547 TMP_548 TMP_549) in (let TMP_551 \def
+(lift_flat f t t0 h1 d1) in (let H4 \def (eq_ind T TMP_543 TMP_546 H3 TMP_550
+TMP_551) in (let TMP_554 \def (\lambda (y: T).(\lambda (z: T).(let TMP_552
+\def (Flat f) in (let TMP_553 \def (THead TMP_552 y z) in (eq T x
+TMP_553))))) in (let TMP_558 \def (\lambda (y: T).(\lambda (_: T).(let
+TMP_555 \def (lift h1 d1 t) in (let TMP_556 \def (plus d2 h1) in (let TMP_557
+\def (lift h2 TMP_556 y) in (eq T TMP_555 TMP_557)))))) in (let TMP_562 \def
+(\lambda (_: T).(\lambda (z: T).(let TMP_559 \def (lift h1 d1 t0) in (let
+TMP_560 \def (plus d2 h1) in (let TMP_561 \def (lift h2 TMP_560 z) in (eq T
+TMP_559 TMP_561)))))) in (let TMP_564 \def (\lambda (t2: T).(let TMP_563 \def
+(lift h1 d1 t2) in (eq T x TMP_563))) in (let TMP_568 \def (\lambda (t2:
+T).(let TMP_565 \def (Flat f) in (let TMP_566 \def (THead TMP_565 t t0) in
+(let TMP_567 \def (lift h2 d2 t2) in (eq T TMP_566 TMP_567))))) in (let
+TMP_569 \def (ex2 T TMP_564 TMP_568) in (let TMP_714 \def (\lambda (x0:
+T).(\lambda (x1: T).(\lambda (H5: (eq T x (THead (Flat f) x0 x1))).(\lambda
+(H6: (eq T (lift h1 d1 t) (lift h2 (plus d2 h1) x0))).(\lambda (H7: (eq T
+(lift h1 d1 t0) (lift h2 (plus d2 h1) x1))).(let TMP_570 \def (Flat f) in
+(let TMP_571 \def (THead TMP_570 x0 x1) in (let TMP_578 \def (\lambda (t2:
+T).(let TMP_573 \def (\lambda (t3: T).(let TMP_572 \def (lift h1 d1 t3) in
+(eq T t2 TMP_572))) in (let TMP_577 \def (\lambda (t3: T).(let TMP_574 \def
+(Flat f) in (let TMP_575 \def (THead TMP_574 t t0) in (let TMP_576 \def (lift
+h2 d2 t3) in (eq T TMP_575 TMP_576))))) in (ex2 T TMP_573 TMP_577)))) in (let
+TMP_580 \def (\lambda (t2: T).(let TMP_579 \def (lift h1 d1 t2) in (eq T x0
+TMP_579))) in (let TMP_582 \def (\lambda (t2: T).(let TMP_581 \def (lift h2
+d2 t2) in (eq T t TMP_581))) in (let TMP_586 \def (\lambda (t2: T).(let
+TMP_583 \def (Flat f) in (let TMP_584 \def (THead TMP_583 x0 x1) in (let
+TMP_585 \def (lift h1 d1 t2) in (eq T TMP_584 TMP_585))))) in (let TMP_590
+\def (\lambda (t2: T).(let TMP_587 \def (Flat f) in (let TMP_588 \def (THead
+TMP_587 t t0) in (let TMP_589 \def (lift h2 d2 t2) in (eq T TMP_588
+TMP_589))))) in (let TMP_591 \def (ex2 T TMP_586 TMP_590) in (let TMP_711
+\def (\lambda (x2: T).(\lambda (H8: (eq T x0 (lift h1 d1 x2))).(\lambda (H9:
+(eq T t (lift h2 d2 x2))).(let TMP_592 \def (lift h1 d1 x2) in (let TMP_601
+\def (\lambda (t2: T).(let TMP_596 \def (\lambda (t3: T).(let TMP_593 \def
+(Flat f) in (let TMP_594 \def (THead TMP_593 t2 x1) in (let TMP_595 \def
+(lift h1 d1 t3) in (eq T TMP_594 TMP_595))))) in (let TMP_600 \def (\lambda
+(t3: T).(let TMP_597 \def (Flat f) in (let TMP_598 \def (THead TMP_597 t t0)
+in (let TMP_599 \def (lift h2 d2 t3) in (eq T TMP_598 TMP_599))))) in (ex2 T
+TMP_596 TMP_600)))) in (let TMP_602 \def (lift h2 d2 x2) in (let TMP_612 \def
+(\lambda (t2: T).(let TMP_607 \def (\lambda (t3: T).(let TMP_603 \def (Flat
+f) in (let TMP_604 \def (lift h1 d1 x2) in (let TMP_605 \def (THead TMP_603
+TMP_604 x1) in (let TMP_606 \def (lift h1 d1 t3) in (eq T TMP_605
+TMP_606)))))) in (let TMP_611 \def (\lambda (t3: T).(let TMP_608 \def (Flat
+f) in (let TMP_609 \def (THead TMP_608 t2 t0) in (let TMP_610 \def (lift h2
+d2 t3) in (eq T TMP_609 TMP_610))))) in (ex2 T TMP_607 TMP_611)))) in (let
+TMP_614 \def (\lambda (t2: T).(let TMP_613 \def (lift h1 d1 t2) in (eq T x1
+TMP_613))) in (let TMP_616 \def (\lambda (t2: T).(let TMP_615 \def (lift h2
+d2 t2) in (eq T t0 TMP_615))) in (let TMP_621 \def (\lambda (t2: T).(let
+TMP_617 \def (Flat f) in (let TMP_618 \def (lift h1 d1 x2) in (let TMP_619
+\def (THead TMP_617 TMP_618 x1) in (let TMP_620 \def (lift h1 d1 t2) in (eq T
+TMP_619 TMP_620)))))) in (let TMP_626 \def (\lambda (t2: T).(let TMP_622 \def
+(Flat f) in (let TMP_623 \def (lift h2 d2 x2) in (let TMP_624 \def (THead
+TMP_622 TMP_623 t0) in (let TMP_625 \def (lift h2 d2 t2) in (eq T TMP_624
+TMP_625)))))) in (let TMP_627 \def (ex2 T TMP_621 TMP_626) in (let TMP_707
+\def (\lambda (x3: T).(\lambda (H10: (eq T x1 (lift h1 d1 x3))).(\lambda
+(H11: (eq T t0 (lift h2 d2 x3))).(let TMP_628 \def (lift h1 d1 x3) in (let
+TMP_639 \def (\lambda (t2: T).(let TMP_633 \def (\lambda (t3: T).(let TMP_629
+\def (Flat f) in (let TMP_630 \def (lift h1 d1 x2) in (let TMP_631 \def
+(THead TMP_629 TMP_630 t2) in (let TMP_632 \def (lift h1 d1 t3) in (eq T
+TMP_631 TMP_632)))))) in (let TMP_638 \def (\lambda (t3: T).(let TMP_634 \def
+(Flat f) in (let TMP_635 \def (lift h2 d2 x2) in (let TMP_636 \def (THead
+TMP_634 TMP_635 t0) in (let TMP_637 \def (lift h2 d2 t3) in (eq T TMP_636
+TMP_637)))))) in (ex2 T TMP_633 TMP_638)))) in (let TMP_640 \def (lift h2 d2
+x3) in (let TMP_652 \def (\lambda (t2: T).(let TMP_646 \def (\lambda (t3:
+T).(let TMP_641 \def (Flat f) in (let TMP_642 \def (lift h1 d1 x2) in (let
+TMP_643 \def (lift h1 d1 x3) in (let TMP_644 \def (THead TMP_641 TMP_642
+TMP_643) in (let TMP_645 \def (lift h1 d1 t3) in (eq T TMP_644 TMP_645)))))))
+in (let TMP_651 \def (\lambda (t3: T).(let TMP_647 \def (Flat f) in (let
+TMP_648 \def (lift h2 d2 x2) in (let TMP_649 \def (THead TMP_647 TMP_648 t2)
+in (let TMP_650 \def (lift h2 d2 t3) in (eq T TMP_649 TMP_650)))))) in (ex2 T
+TMP_646 TMP_651)))) in (let TMP_658 \def (\lambda (t2: T).(let TMP_653 \def
+(Flat f) in (let TMP_654 \def (lift h1 d1 x2) in (let TMP_655 \def (lift h1
+d1 x3) in (let TMP_656 \def (THead TMP_653 TMP_654 TMP_655) in (let TMP_657
+\def (lift h1 d1 t2) in (eq T TMP_656 TMP_657))))))) in (let TMP_664 \def
+(\lambda (t2: T).(let TMP_659 \def (Flat f) in (let TMP_660 \def (lift h2 d2
+x2) in (let TMP_661 \def (lift h2 d2 x3) in (let TMP_662 \def (THead TMP_659
+TMP_660 TMP_661) in (let TMP_663 \def (lift h2 d2 t2) in (eq T TMP_662
+TMP_663))))))) in (let TMP_665 \def (Flat f) in (let TMP_666 \def (THead
+TMP_665 x2 x3) in (let TMP_667 \def (Flat f) in (let TMP_668 \def (lift h1 d1
+x2) in (let TMP_669 \def (lift h1 d1 x3) in (let TMP_670 \def (THead TMP_667
+TMP_668 TMP_669) in (let TMP_675 \def (\lambda (t2: T).(let TMP_671 \def
+(Flat f) in (let TMP_672 \def (lift h1 d1 x2) in (let TMP_673 \def (lift h1
+d1 x3) in (let TMP_674 \def (THead TMP_671 TMP_672 TMP_673) in (eq T TMP_674
+t2)))))) in (let TMP_676 \def (Flat f) in (let TMP_677 \def (lift h1 d1 x2)
+in (let TMP_678 \def (lift h1 d1 x3) in (let TMP_679 \def (THead TMP_676
+TMP_677 TMP_678) in (let TMP_680 \def (refl_equal T TMP_679) in (let TMP_681
+\def (Flat f) in (let TMP_682 \def (THead TMP_681 x2 x3) in (let TMP_683 \def
+(lift h1 d1 TMP_682) in (let TMP_684 \def (lift_flat f x2 x3 h1 d1) in (let
+TMP_685 \def (eq_ind_r T TMP_670 TMP_675 TMP_680 TMP_683 TMP_684) in (let
+TMP_686 \def (Flat f) in (let TMP_687 \def (lift h2 d2 x2) in (let TMP_688
+\def (lift h2 d2 x3) in (let TMP_689 \def (THead TMP_686 TMP_687 TMP_688) in
+(let TMP_694 \def (\lambda (t2: T).(let TMP_690 \def (Flat f) in (let TMP_691
+\def (lift h2 d2 x2) in (let TMP_692 \def (lift h2 d2 x3) in (let TMP_693
+\def (THead TMP_690 TMP_691 TMP_692) in (eq T TMP_693 t2)))))) in (let
+TMP_695 \def (Flat f) in (let TMP_696 \def (lift h2 d2 x2) in (let TMP_697
+\def (lift h2 d2 x3) in (let TMP_698 \def (THead TMP_695 TMP_696 TMP_697) in
+(let TMP_699 \def (refl_equal T TMP_698) in (let TMP_700 \def (Flat f) in
+(let TMP_701 \def (THead TMP_700 x2 x3) in (let TMP_702 \def (lift h2 d2
+TMP_701) in (let TMP_703 \def (lift_flat f x2 x3 h2 d2) in (let TMP_704 \def
+(eq_ind_r T TMP_689 TMP_694 TMP_699 TMP_702 TMP_703) in (let TMP_705 \def
+(ex_intro2 T TMP_658 TMP_664 TMP_666 TMP_685 TMP_704) in (let TMP_706 \def
+(eq_ind_r T TMP_640 TMP_652 TMP_705 t0 H11) in (eq_ind_r T TMP_628 TMP_639
+TMP_706 x1 H10)))))))))))))))))))))))))))))))))))))))))))) in (let TMP_708
+\def (H0 x1 h1 h2 d1 d2 H1 H7) in (let TMP_709 \def (ex2_ind T TMP_614
+TMP_616 TMP_627 TMP_707 TMP_708) in (let TMP_710 \def (eq_ind_r T TMP_602
+TMP_612 TMP_709 t H9) in (eq_ind_r T TMP_592 TMP_601 TMP_710 x0
+H8))))))))))))))))) in (let TMP_712 \def (H x0 h1 h2 d1 d2 H1 H6) in (let
+TMP_713 \def (ex2_ind T TMP_580 TMP_582 TMP_591 TMP_711 TMP_712) in (eq_ind_r
+T TMP_571 TMP_578 TMP_713 x H5))))))))))))))))) in (let TMP_715 \def (lift h1
+d1 t) in (let TMP_716 \def (lift h1 d1 t0) in (let TMP_717 \def (plus d2 h1)
+in (let TMP_718 \def (lift_gen_flat f TMP_715 TMP_716 x h2 TMP_717 H4) in
+(ex3_2_ind T T TMP_554 TMP_558 TMP_562 TMP_569 TMP_714
+TMP_718)))))))))))))))))))))))) in (K_ind TMP_331 TMP_540 TMP_719 k
+H2)))))))))))))))) in (T_ind TMP_5 TMP_48 TMP_325 TMP_720 t1))))).
+
+theorem lifts_inj:
+ \forall (xs: TList).(\forall (ts: TList).(\forall (h: nat).(\forall (d:
+nat).((eq TList (lifts h d xs) (lifts h d ts)) \to (eq TList xs ts)))))
+\def
+ \lambda (xs: TList).(let TMP_1 \def (\lambda (t: TList).(\forall (ts:
+TList).(\forall (h: nat).(\forall (d: nat).((eq TList (lifts h d t) (lifts h
+d ts)) \to (eq TList t ts)))))) in (let TMP_11 \def (\lambda (ts: TList).(let
+TMP_2 \def (\lambda (t: TList).(\forall (h: nat).(\forall (d: nat).((eq TList
+(lifts h d TNil) (lifts h d t)) \to (eq TList TNil t))))) in (let TMP_3 \def
+(\lambda (_: nat).(\lambda (_: nat).(\lambda (_: (eq TList TNil
+TNil)).(refl_equal TList TNil)))) in (let TMP_10 \def (\lambda (t:
+T).(\lambda (t0: TList).(\lambda (_: ((\forall (h: nat).(\forall (d:
+nat).((eq TList TNil (lifts h d t0)) \to (eq TList TNil t0)))))).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (H0: (eq TList TNil (TCons (lift h d t)
+(lifts h d t0)))).(let TMP_4 \def (\lambda (ee: TList).(match ee with [TNil
+\Rightarrow True | (TCons _ _) \Rightarrow False])) in (let TMP_5 \def (lift
+h d t) in (let TMP_6 \def (lifts h d t0) in (let TMP_7 \def (TCons TMP_5
+TMP_6) in (let H1 \def (eq_ind TList TNil TMP_4 I TMP_7 H0) in (let TMP_8
+\def (TCons t t0) in (let TMP_9 \def (eq TList TNil TMP_8) in (False_ind
+TMP_9 H1)))))))))))))) in (TList_ind TMP_2 TMP_3 TMP_10 ts))))) in (let
+TMP_53 \def (\lambda (t: T).(\lambda (t0: TList).(\lambda (H: ((\forall (ts:
+TList).(\forall (h: nat).(\forall (d: nat).((eq TList (lifts h d t0) (lifts h
+d ts)) \to (eq TList t0 ts))))))).(\lambda (ts: TList).(let TMP_13 \def
+(\lambda (t1: TList).(\forall (h: nat).(\forall (d: nat).((eq TList (lifts h
+d (TCons t t0)) (lifts h d t1)) \to (let TMP_12 \def (TCons t t0) in (eq
+TList TMP_12 t1)))))) in (let TMP_20 \def (\lambda (h: nat).(\lambda (d:
+nat).(\lambda (H0: (eq TList (TCons (lift h d t) (lifts h d t0)) TNil)).(let
+TMP_14 \def (lift h d t) in (let TMP_15 \def (lifts h d t0) in (let TMP_16
+\def (TCons TMP_14 TMP_15) in (let TMP_17 \def (\lambda (ee: TList).(match ee
+with [TNil \Rightarrow False | (TCons _ _) \Rightarrow True])) in (let H1
+\def (eq_ind TList TMP_16 TMP_17 I TNil H0) in (let TMP_18 \def (TCons t t0)
+in (let TMP_19 \def (eq TList TMP_18 TNil) in (False_ind TMP_19 H1)))))))))))
+in (let TMP_52 \def (\lambda (t1: T).(\lambda (t2: TList).(\lambda (_:
+((\forall (h: nat).(\forall (d: nat).((eq TList (TCons (lift h d t) (lifts h
+d t0)) (lifts h d t2)) \to (eq TList (TCons t t0) t2)))))).(\lambda (h:
+nat).(\lambda (d: nat).(\lambda (H1: (eq TList (TCons (lift h d t) (lifts h d
+t0)) (TCons (lift h d t1) (lifts h d t2)))).(let TMP_27 \def (\lambda (e:
+TList).(match e with [TNil \Rightarrow (let TMP_25 \def lref_map in (let
+TMP_26 \def (\lambda (x: nat).(plus x h)) in (TMP_25 TMP_26 d t))) | (TCons
+t3 _) \Rightarrow t3])) in (let TMP_28 \def (lift h d t) in (let TMP_29 \def
+(lifts h d t0) in (let TMP_30 \def (TCons TMP_28 TMP_29) in (let TMP_31 \def
+(lift h d t1) in (let TMP_32 \def (lifts h d t2) in (let TMP_33 \def (TCons
+TMP_31 TMP_32) in (let H2 \def (f_equal TList T TMP_27 TMP_30 TMP_33 H1) in
+(let TMP_37 \def (\lambda (e: TList).(match e with [TNil \Rightarrow (let
+TMP_36 \def lifts in (TMP_36 h d t0)) | (TCons _ t3) \Rightarrow t3])) in
+(let TMP_38 \def (lift h d t) in (let TMP_39 \def (lifts h d t0) in (let
+TMP_40 \def (TCons TMP_38 TMP_39) in (let TMP_41 \def (lift h d t1) in (let
+TMP_42 \def (lifts h d t2) in (let TMP_43 \def (TCons TMP_41 TMP_42) in (let
+H3 \def (f_equal TList TList TMP_37 TMP_40 TMP_43 H1) in (let TMP_51 \def
+(\lambda (H4: (eq T (lift h d t) (lift h d t1))).(let TMP_46 \def (\lambda
+(t3: T).(let TMP_44 \def (TCons t t0) in (let TMP_45 \def (TCons t3 t2) in
+(eq TList TMP_44 TMP_45)))) in (let TMP_47 \def (refl_equal T t) in (let
+TMP_48 \def (H t2 h d H3) in (let TMP_49 \def (f_equal2 T TList TList TCons t
+t t0 t2 TMP_47 TMP_48) in (let TMP_50 \def (lift_inj t t1 h d H4) in (eq_ind
+T t TMP_46 TMP_49 t1 TMP_50))))))) in (TMP_51 H2)))))))))))))))))))))))) in
+(TList_ind TMP_13 TMP_20 TMP_52 ts)))))))) in (TList_ind TMP_1 TMP_11 TMP_53
+xs)))).