- \lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq gz a1 a2)).(let TMP_1
-\def (\lambda (a: A).(\lambda (a0: A).(leqz a a0))) in (let TMP_225 \def
-(\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1: nat).(\lambda (n2:
-nat).(\lambda (k: nat).(\lambda (H0: (eq A (aplus gz (ASort h1 n1) k) (aplus
-gz (ASort h2 n2) k))).(let TMP_2 \def (ASort h1 n1) in (let TMP_3 \def (ASort
-h2 n2) in (let TMP_4 \def (leqz TMP_2 TMP_3) in (let TMP_136 \def (\lambda
-(H1: (lt k h1)).(let TMP_5 \def (ASort h1 n1) in (let TMP_6 \def (ASort h2
-n2) in (let TMP_7 \def (leqz TMP_5 TMP_6) in (let TMP_86 \def (\lambda (H2:
-(lt k h2)).(let TMP_8 \def (ASort h1 n1) in (let TMP_9 \def (aplus gz TMP_8
-k) in (let TMP_12 \def (\lambda (a: A).(let TMP_10 \def (ASort h2 n2) in (let
-TMP_11 \def (aplus gz TMP_10 k) in (eq A a TMP_11)))) in (let TMP_13 \def
-(minus h1 k) in (let TMP_14 \def (ASort TMP_13 n1) in (let TMP_15 \def (S k)
-in (let TMP_16 \def (S h1) in (let TMP_17 \def (S k) in (let TMP_18 \def (S
-TMP_17) in (let TMP_19 \def (S h1) in (let TMP_20 \def (S k) in (let TMP_21
-\def (le_n_S TMP_20 h1 H1) in (let TMP_22 \def (le_S TMP_18 TMP_19 TMP_21) in
-(let TMP_23 \def (le_S_n TMP_15 TMP_16 TMP_22) in (let TMP_24 \def (le_S_n k
-h1 TMP_23) in (let TMP_25 \def (aplus_gz_ge n1 k h1 TMP_24) in (let H3 \def
-(eq_ind A TMP_9 TMP_12 H0 TMP_14 TMP_25) in (let TMP_26 \def (ASort h2 n2) in
-(let TMP_27 \def (aplus gz TMP_26 k) in (let TMP_30 \def (\lambda (a: A).(let
-TMP_28 \def (minus h1 k) in (let TMP_29 \def (ASort TMP_28 n1) in (eq A
-TMP_29 a)))) in (let TMP_31 \def (minus h2 k) in (let TMP_32 \def (ASort
-TMP_31 n2) in (let TMP_33 \def (S k) in (let TMP_34 \def (S h2) in (let
-TMP_35 \def (S k) in (let TMP_36 \def (S TMP_35) in (let TMP_37 \def (S h2)
-in (let TMP_38 \def (S k) in (let TMP_39 \def (le_n_S TMP_38 h2 H2) in (let
-TMP_40 \def (le_S TMP_36 TMP_37 TMP_39) in (let TMP_41 \def (le_S_n TMP_33
-TMP_34 TMP_40) in (let TMP_42 \def (le_S_n k h2 TMP_41) in (let TMP_43 \def
-(aplus_gz_ge n2 k h2 TMP_42) in (let H4 \def (eq_ind A TMP_27 TMP_30 H3
-TMP_32 TMP_43) in (let TMP_44 \def (\lambda (e: A).(match e with [(ASort n _)
-\Rightarrow n | (AHead _ _) \Rightarrow (minus h1 k)])) in (let TMP_45 \def
-(minus h1 k) in (let TMP_46 \def (ASort TMP_45 n1) in (let TMP_47 \def (minus
-h2 k) in (let TMP_48 \def (ASort TMP_47 n2) in (let H5 \def (f_equal A nat
-TMP_44 TMP_46 TMP_48 H4) in (let TMP_49 \def (\lambda (e: A).(match e with
-[(ASort _ n) \Rightarrow n | (AHead _ _) \Rightarrow n1])) in (let TMP_50
-\def (minus h1 k) in (let TMP_51 \def (ASort TMP_50 n1) in (let TMP_52 \def
-(minus h2 k) in (let TMP_53 \def (ASort TMP_52 n2) in (let H6 \def (f_equal A
-nat TMP_49 TMP_51 TMP_53 H4) in (let TMP_85 \def (\lambda (H7: (eq nat (minus
-h1 k) (minus h2 k))).(let TMP_56 \def (\lambda (n: nat).(let TMP_54 \def
-(ASort h1 n1) in (let TMP_55 \def (ASort h2 n) in (leqz TMP_54 TMP_55)))) in
-(let TMP_59 \def (\lambda (n: nat).(let TMP_57 \def (ASort h1 n1) in (let
-TMP_58 \def (ASort n n1) in (leqz TMP_57 TMP_58)))) in (let TMP_60 \def (plus
-h1 n1) in (let TMP_61 \def (refl_equal nat TMP_60) in (let TMP_62 \def
-(leqz_sort h1 h1 n1 n1 TMP_61) in (let TMP_63 \def (S k) in (let TMP_64 \def
-(S h1) in (let TMP_65 \def (S k) in (let TMP_66 \def (S TMP_65) in (let
-TMP_67 \def (S h1) in (let TMP_68 \def (S k) in (let TMP_69 \def (le_n_S
-TMP_68 h1 H1) in (let TMP_70 \def (le_S TMP_66 TMP_67 TMP_69) in (let TMP_71
-\def (le_S_n TMP_63 TMP_64 TMP_70) in (let TMP_72 \def (le_S_n k h1 TMP_71)
-in (let TMP_73 \def (S k) in (let TMP_74 \def (S h2) in (let TMP_75 \def (S
-k) in (let TMP_76 \def (S TMP_75) in (let TMP_77 \def (S h2) in (let TMP_78
-\def (S k) in (let TMP_79 \def (le_n_S TMP_78 h2 H2) in (let TMP_80 \def
-(le_S TMP_76 TMP_77 TMP_79) in (let TMP_81 \def (le_S_n TMP_73 TMP_74 TMP_80)
-in (let TMP_82 \def (le_S_n k h2 TMP_81) in (let TMP_83 \def (minus_minus k
-h1 h2 TMP_72 TMP_82 H7) in (let TMP_84 \def (eq_ind nat h1 TMP_59 TMP_62 h2
-TMP_83) in (eq_ind nat n1 TMP_56 TMP_84 n2 H6))))))))))))))))))))))))))))) in
-(TMP_85 H5))))))))))))))))))))))))))))))))))))))))))))))))) in (let TMP_135
-\def (\lambda (H2: (le h2 k)).(let TMP_87 \def (ASort h1 n1) in (let TMP_88
-\def (aplus gz TMP_87 k) in (let TMP_91 \def (\lambda (a: A).(let TMP_89 \def
-(ASort h2 n2) in (let TMP_90 \def (aplus gz TMP_89 k) in (eq A a TMP_90))))
-in (let TMP_92 \def (minus h1 k) in (let TMP_93 \def (ASort TMP_92 n1) in
-(let TMP_94 \def (S k) in (let TMP_95 \def (S h1) in (let TMP_96 \def (S k)
-in (let TMP_97 \def (S TMP_96) in (let TMP_98 \def (S h1) in (let TMP_99 \def
-(S k) in (let TMP_100 \def (le_n_S TMP_99 h1 H1) in (let TMP_101 \def (le_S
-TMP_97 TMP_98 TMP_100) in (let TMP_102 \def (le_S_n TMP_94 TMP_95 TMP_101) in
-(let TMP_103 \def (le_S_n k h1 TMP_102) in (let TMP_104 \def (aplus_gz_ge n1
-k h1 TMP_103) in (let H3 \def (eq_ind A TMP_88 TMP_91 H0 TMP_93 TMP_104) in
-(let TMP_105 \def (ASort h2 n2) in (let TMP_106 \def (aplus gz TMP_105 k) in
-(let TMP_109 \def (\lambda (a: A).(let TMP_107 \def (minus h1 k) in (let
-TMP_108 \def (ASort TMP_107 n1) in (eq A TMP_108 a)))) in (let TMP_110 \def
-(minus k h2) in (let TMP_111 \def (plus TMP_110 n2) in (let TMP_112 \def
-(ASort O TMP_111) in (let TMP_113 \def (aplus_gz_le k h2 n2 H2) in (let H4
-\def (eq_ind A TMP_106 TMP_109 H3 TMP_112 TMP_113) in (let TMP_114 \def
-(minus h1 k) in (let TMP_119 \def (\lambda (n: nat).(let TMP_115 \def (ASort
-n n1) in (let TMP_116 \def (minus k h2) in (let TMP_117 \def (plus TMP_116
-n2) in (let TMP_118 \def (ASort O TMP_117) in (eq A TMP_115 TMP_118)))))) in
-(let TMP_120 \def (S k) in (let TMP_121 \def (minus h1 TMP_120) in (let
-TMP_122 \def (S TMP_121) in (let TMP_123 \def (minus_x_Sy h1 k H1) in (let H5
-\def (eq_ind nat TMP_114 TMP_119 H4 TMP_122 TMP_123) in (let TMP_124 \def (S
-k) in (let TMP_125 \def (minus h1 TMP_124) in (let TMP_126 \def (S TMP_125)
-in (let TMP_127 \def (ASort TMP_126 n1) in (let TMP_128 \def (\lambda (ee:
-A).(match ee with [(ASort n _) \Rightarrow (match n with [O \Rightarrow False
-| (S _) \Rightarrow True]) | (AHead _ _) \Rightarrow False])) in (let TMP_129
-\def (minus k h2) in (let TMP_130 \def (plus TMP_129 n2) in (let TMP_131 \def
-(ASort O TMP_130) in (let H6 \def (eq_ind A TMP_127 TMP_128 I TMP_131 H5) in
-(let TMP_132 \def (ASort h1 n1) in (let TMP_133 \def (ASort h2 n2) in (let
-TMP_134 \def (leqz TMP_132 TMP_133) in (False_ind TMP_134
-H6)))))))))))))))))))))))))))))))))))))))))))))) in (lt_le_e k h2 TMP_7
-TMP_86 TMP_135))))))) in (let TMP_224 \def (\lambda (H1: (le h1 k)).(let
-TMP_137 \def (ASort h1 n1) in (let TMP_138 \def (ASort h2 n2) in (let TMP_139
-\def (leqz TMP_137 TMP_138) in (let TMP_194 \def (\lambda (H2: (lt k
-h2)).(let TMP_140 \def (ASort h1 n1) in (let TMP_141 \def (aplus gz TMP_140
-k) in (let TMP_144 \def (\lambda (a: A).(let TMP_142 \def (ASort h2 n2) in
-(let TMP_143 \def (aplus gz TMP_142 k) in (eq A a TMP_143)))) in (let TMP_145
-\def (minus k h1) in (let TMP_146 \def (plus TMP_145 n1) in (let TMP_147 \def
-(ASort O TMP_146) in (let TMP_148 \def (aplus_gz_le k h1 n1 H1) in (let H3
-\def (eq_ind A TMP_141 TMP_144 H0 TMP_147 TMP_148) in (let TMP_149 \def
-(ASort h2 n2) in (let TMP_150 \def (aplus gz TMP_149 k) in (let TMP_154 \def
-(\lambda (a: A).(let TMP_151 \def (minus k h1) in (let TMP_152 \def (plus
-TMP_151 n1) in (let TMP_153 \def (ASort O TMP_152) in (eq A TMP_153 a))))) in
-(let TMP_155 \def (minus h2 k) in (let TMP_156 \def (ASort TMP_155 n2) in
-(let TMP_157 \def (S k) in (let TMP_158 \def (S h2) in (let TMP_159 \def (S
-k) in (let TMP_160 \def (S TMP_159) in (let TMP_161 \def (S h2) in (let
-TMP_162 \def (S k) in (let TMP_163 \def (le_n_S TMP_162 h2 H2) in (let
-TMP_164 \def (le_S TMP_160 TMP_161 TMP_163) in (let TMP_165 \def (le_S_n
-TMP_157 TMP_158 TMP_164) in (let TMP_166 \def (le_S_n k h2 TMP_165) in (let
-TMP_167 \def (aplus_gz_ge n2 k h2 TMP_166) in (let H4 \def (eq_ind A TMP_150
-TMP_154 H3 TMP_156 TMP_167) in (let TMP_168 \def (minus k h1) in (let TMP_169
-\def (plus TMP_168 n1) in (let TMP_170 \def (ASort O TMP_169) in (let TMP_171
-\def (minus h2 k) in (let TMP_172 \def (ASort TMP_171 n2) in (let H5 \def
-(sym_eq A TMP_170 TMP_172 H4) in (let TMP_173 \def (minus h2 k) in (let
-TMP_178 \def (\lambda (n: nat).(let TMP_174 \def (ASort n n2) in (let TMP_175
-\def (minus k h1) in (let TMP_176 \def (plus TMP_175 n1) in (let TMP_177 \def
-(ASort O TMP_176) in (eq A TMP_174 TMP_177)))))) in (let TMP_179 \def (S k)
-in (let TMP_180 \def (minus h2 TMP_179) in (let TMP_181 \def (S TMP_180) in
-(let TMP_182 \def (minus_x_Sy h2 k H2) in (let H6 \def (eq_ind nat TMP_173
-TMP_178 H5 TMP_181 TMP_182) in (let TMP_183 \def (S k) in (let TMP_184 \def
-(minus h2 TMP_183) in (let TMP_185 \def (S TMP_184) in (let TMP_186 \def
-(ASort TMP_185 n2) in (let TMP_187 \def (\lambda (ee: A).(match ee with
+ \lambda (a1: A).(\lambda (a2: A).(\lambda (H: (leq gz a1 a2)).(leq_ind gz
+(\lambda (a: A).(\lambda (a0: A).(leqz a a0))) (\lambda (h1: nat).(\lambda
+(h2: nat).(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (k: nat).(\lambda
+(H0: (eq A (aplus gz (ASort h1 n1) k) (aplus gz (ASort h2 n2) k))).(lt_le_e k
+h1 (leqz (ASort h1 n1) (ASort h2 n2)) (\lambda (H1: (lt k h1)).(lt_le_e k h2
+(leqz (ASort h1 n1) (ASort h2 n2)) (\lambda (H2: (lt k h2)).(let H3 \def
+(eq_ind A (aplus gz (ASort h1 n1) k) (\lambda (a: A).(eq A a (aplus gz (ASort
+h2 n2) k))) H0 (ASort (minus h1 k) n1) (aplus_gz_ge n1 k h1 (le_S_n k h1
+(le_S_n (S k) (S h1) (le_S (S (S k)) (S h1) (le_n_S (S k) h1 H1)))))) in (let
+H4 \def (eq_ind A (aplus gz (ASort h2 n2) k) (\lambda (a: A).(eq A (ASort
+(minus h1 k) n1) a)) H3 (ASort (minus h2 k) n2) (aplus_gz_ge n2 k h2 (le_S_n
+k h2 (le_S_n (S k) (S h2) (le_S (S (S k)) (S h2) (le_n_S (S k) h2 H2)))))) in
+(let H5 \def (f_equal A nat (\lambda (e: A).(match e with [(ASort n _)
+\Rightarrow n | (AHead _ _) \Rightarrow (minus h1 k)])) (ASort (minus h1 k)
+n1) (ASort (minus h2 k) n2) H4) in ((let H6 \def (f_equal A nat (\lambda (e:
+A).(match e with [(ASort _ n) \Rightarrow n | (AHead _ _) \Rightarrow n1]))
+(ASort (minus h1 k) n1) (ASort (minus h2 k) n2) H4) in (\lambda (H7: (eq nat
+(minus h1 k) (minus h2 k))).(eq_ind nat n1 (\lambda (n: nat).(leqz (ASort h1
+n1) (ASort h2 n))) (eq_ind nat h1 (\lambda (n: nat).(leqz (ASort h1 n1)
+(ASort n n1))) (leqz_sort h1 h1 n1 n1 (refl_equal nat (plus h1 n1))) h2
+(minus_minus k h1 h2 (le_S_n k h1 (le_S_n (S k) (S h1) (le_S (S (S k)) (S h1)
+(le_n_S (S k) h1 H1)))) (le_S_n k h2 (le_S_n (S k) (S h2) (le_S (S (S k)) (S
+h2) (le_n_S (S k) h2 H2)))) H7)) n2 H6))) H5))))) (\lambda (H2: (le h2
+k)).(let H3 \def (eq_ind A (aplus gz (ASort h1 n1) k) (\lambda (a: A).(eq A a
+(aplus gz (ASort h2 n2) k))) H0 (ASort (minus h1 k) n1) (aplus_gz_ge n1 k h1
+(le_S_n k h1 (le_S_n (S k) (S h1) (le_S (S (S k)) (S h1) (le_n_S (S k) h1
+H1)))))) in (let H4 \def (eq_ind A (aplus gz (ASort h2 n2) k) (\lambda (a:
+A).(eq A (ASort (minus h1 k) n1) a)) H3 (ASort O (plus (minus k h2) n2))
+(aplus_gz_le k h2 n2 H2)) in (let H5 \def (eq_ind nat (minus h1 k) (\lambda
+(n: nat).(eq A (ASort n n1) (ASort O (plus (minus k h2) n2)))) H4 (S (minus
+h1 (S k))) (minus_x_Sy h1 k H1)) in (let H6 \def (eq_ind A (ASort (S (minus
+h1 (S k))) n1) (\lambda (ee: A).(match ee with [(ASort n _) \Rightarrow
+(match n with [O \Rightarrow False | (S _) \Rightarrow True]) | (AHead _ _)
+\Rightarrow False])) I (ASort O (plus (minus k h2) n2)) H5) in (False_ind
+(leqz (ASort h1 n1) (ASort h2 n2)) H6)))))))) (\lambda (H1: (le h1
+k)).(lt_le_e k h2 (leqz (ASort h1 n1) (ASort h2 n2)) (\lambda (H2: (lt k
+h2)).(let H3 \def (eq_ind A (aplus gz (ASort h1 n1) k) (\lambda (a: A).(eq A
+a (aplus gz (ASort h2 n2) k))) H0 (ASort O (plus (minus k h1) n1))
+(aplus_gz_le k h1 n1 H1)) in (let H4 \def (eq_ind A (aplus gz (ASort h2 n2)
+k) (\lambda (a: A).(eq A (ASort O (plus (minus k h1) n1)) a)) H3 (ASort
+(minus h2 k) n2) (aplus_gz_ge n2 k h2 (le_S_n k h2 (le_S_n (S k) (S h2) (le_S
+(S (S k)) (S h2) (le_n_S (S k) h2 H2)))))) in (let H5 \def (sym_eq A (ASort O
+(plus (minus k h1) n1)) (ASort (minus h2 k) n2) H4) in (let H6 \def (eq_ind
+nat (minus h2 k) (\lambda (n: nat).(eq A (ASort n n2) (ASort O (plus (minus k
+h1) n1)))) H5 (S (minus h2 (S k))) (minus_x_Sy h2 k H2)) in (let H7 \def
+(eq_ind A (ASort (S (minus h2 (S k))) n2) (\lambda (ee: A).(match ee with