-a2)).(let TMP_1 \def (\lambda (a: A).(\lambda (a0: A).(\forall (a3: A).((leq
-g a0 a3) \to (leq g a a3))))) in (let TMP_63 \def (\lambda (h1: nat).(\lambda
-(h2: nat).(\lambda (n1: nat).(\lambda (n2: nat).(\lambda (k: nat).(\lambda
-(H0: (eq A (aplus g (ASort h1 n1) k) (aplus g (ASort h2 n2) k))).(\lambda
-(a3: A).(\lambda (H1: (leq g (ASort h2 n2) a3)).(let H_x \def (leq_gen_sort1
-g h2 n2 a3 H1) in (let H2 \def H_x in (let TMP_6 \def (\lambda (n3:
-nat).(\lambda (h3: nat).(\lambda (k0: nat).(let TMP_2 \def (ASort h2 n2) in
-(let TMP_3 \def (aplus g TMP_2 k0) in (let TMP_4 \def (ASort h3 n3) in (let
-TMP_5 \def (aplus g TMP_4 k0) in (eq A TMP_3 TMP_5)))))))) in (let TMP_8 \def
-(\lambda (n3: nat).(\lambda (h3: nat).(\lambda (_: nat).(let TMP_7 \def
-(ASort h3 n3) in (eq A a3 TMP_7))))) in (let TMP_9 \def (ASort h1 n1) in (let
-TMP_10 \def (leq g TMP_9 a3) in (let TMP_62 \def (\lambda (x0: nat).(\lambda
-(x1: nat).(\lambda (x2: nat).(\lambda (H3: (eq A (aplus g (ASort h2 n2) x2)
-(aplus g (ASort x1 x0) x2))).(\lambda (H4: (eq A a3 (ASort x1 x0))).(let
-TMP_11 \def (\lambda (e: A).e) in (let TMP_12 \def (ASort x1 x0) in (let H5
-\def (f_equal A A TMP_11 a3 TMP_12 H4) in (let TMP_13 \def (ASort x1 x0) in
-(let TMP_15 \def (\lambda (a: A).(let TMP_14 \def (ASort h1 n1) in (leq g
-TMP_14 a))) in (let TMP_16 \def (ASort h1 n1) in (let TMP_17 \def (ASort x1
-x0) in (let TMP_18 \def (leq g TMP_16 TMP_17) in (let TMP_41 \def (\lambda
-(H6: (lt k x2)).(let TMP_19 \def (ASort h1 n1) in (let TMP_20 \def (ASort h2
-n2) in (let TMP_21 \def (minus x2 k) in (let H_y \def (aplus_reg_r g TMP_19
-TMP_20 k k H0 TMP_21) in (let TMP_22 \def (minus x2 k) in (let TMP_23 \def
-(plus TMP_22 k) in (let TMP_28 \def (\lambda (n: nat).(let TMP_24 \def (ASort
-h1 n1) in (let TMP_25 \def (aplus g TMP_24 n) in (let TMP_26 \def (ASort h2
-n2) in (let TMP_27 \def (aplus g TMP_26 n) in (eq A TMP_25 TMP_27)))))) in
-(let TMP_29 \def (S k) in (let TMP_30 \def (le_n k) in (let TMP_31 \def (le_S
-k k TMP_30) in (let TMP_32 \def (le_trans k TMP_29 x2 TMP_31 H6) in (let
-TMP_33 \def (le_plus_minus_sym k x2 TMP_32) in (let H7 \def (eq_ind_r nat
-TMP_23 TMP_28 H_y x2 TMP_33) in (let TMP_34 \def (ASort h1 n1) in (let TMP_35
-\def (aplus g TMP_34 x2) in (let TMP_36 \def (ASort h2 n2) in (let TMP_37
-\def (aplus g TMP_36 x2) in (let TMP_38 \def (ASort x1 x0) in (let TMP_39
-\def (aplus g TMP_38 x2) in (let TMP_40 \def (trans_eq A TMP_35 TMP_37 TMP_39
-H7 H3) in (leq_sort g h1 x1 n1 x0 x2 TMP_40)))))))))))))))))))))) in (let
-TMP_60 \def (\lambda (H6: (le x2 k)).(let TMP_42 \def (ASort h2 n2) in (let
-TMP_43 \def (ASort x1 x0) in (let TMP_44 \def (minus k x2) in (let H_y \def
-(aplus_reg_r g TMP_42 TMP_43 x2 x2 H3 TMP_44) in (let TMP_45 \def (minus k
-x2) in (let TMP_46 \def (plus TMP_45 x2) in (let TMP_51 \def (\lambda (n:
-nat).(let TMP_47 \def (ASort h2 n2) in (let TMP_48 \def (aplus g TMP_47 n) in
-(let TMP_49 \def (ASort x1 x0) in (let TMP_50 \def (aplus g TMP_49 n) in (eq
-A TMP_48 TMP_50)))))) in (let TMP_52 \def (le_plus_minus_sym x2 k H6) in (let
-H7 \def (eq_ind_r nat TMP_46 TMP_51 H_y k TMP_52) in (let TMP_53 \def (ASort
-h1 n1) in (let TMP_54 \def (aplus g TMP_53 k) in (let TMP_55 \def (ASort h2
-n2) in (let TMP_56 \def (aplus g TMP_55 k) in (let TMP_57 \def (ASort x1 x0)
-in (let TMP_58 \def (aplus g TMP_57 k) in (let TMP_59 \def (trans_eq A TMP_54
-TMP_56 TMP_58 H0 H7) in (leq_sort g h1 x1 n1 x0 k TMP_59)))))))))))))))))) in
-(let TMP_61 \def (lt_le_e k x2 TMP_18 TMP_41 TMP_60) in (eq_ind_r A TMP_13
-TMP_15 TMP_61 a3 H5))))))))))))))))) in (ex2_3_ind nat nat nat TMP_6 TMP_8
-TMP_10 TMP_62 H2)))))))))))))))) in (let TMP_79 \def (\lambda (a3:
+a2)).(leq_ind g (\lambda (a: A).(\lambda (a0: A).(\forall (a3: A).((leq g a0
+a3) \to (leq g a a3))))) (\lambda (h1: nat).(\lambda (h2: nat).(\lambda (n1:
+nat).(\lambda (n2: nat).(\lambda (k: nat).(\lambda (H0: (eq A (aplus g (ASort
+h1 n1) k) (aplus g (ASort h2 n2) k))).(\lambda (a3: A).(\lambda (H1: (leq g
+(ASort h2 n2) a3)).(let H_x \def (leq_gen_sort1 g h2 n2 a3 H1) in (let H2
+\def H_x in (ex2_3_ind nat nat nat (\lambda (n3: nat).(\lambda (h3:
+nat).(\lambda (k0: nat).(eq A (aplus g (ASort h2 n2) k0) (aplus g (ASort h3
+n3) k0))))) (\lambda (n3: nat).(\lambda (h3: nat).(\lambda (_: nat).(eq A a3
+(ASort h3 n3))))) (leq g (ASort h1 n1) a3) (\lambda (x0: nat).(\lambda (x1:
+nat).(\lambda (x2: nat).(\lambda (H3: (eq A (aplus g (ASort h2 n2) x2) (aplus
+g (ASort x1 x0) x2))).(\lambda (H4: (eq A a3 (ASort x1 x0))).(let H5 \def
+(f_equal A A (\lambda (e: A).e) a3 (ASort x1 x0) H4) in (eq_ind_r A (ASort x1
+x0) (\lambda (a: A).(leq g (ASort h1 n1) a)) (lt_le_e k x2 (leq g (ASort h1
+n1) (ASort x1 x0)) (\lambda (H6: (lt k x2)).(let H_y \def (aplus_reg_r g
+(ASort h1 n1) (ASort h2 n2) k k H0 (minus x2 k)) in (let H7 \def (eq_ind_r
+nat (plus (minus x2 k) k) (\lambda (n: nat).(eq A (aplus g (ASort h1 n1) n)
+(aplus g (ASort h2 n2) n))) H_y x2 (le_plus_minus_sym k x2 (le_trans k (S k)
+x2 (le_S k k (le_n k)) H6))) in (leq_sort g h1 x1 n1 x0 x2 (trans_eq A (aplus
+g (ASort h1 n1) x2) (aplus g (ASort h2 n2) x2) (aplus g (ASort x1 x0) x2) H7
+H3))))) (\lambda (H6: (le x2 k)).(let H_y \def (aplus_reg_r g (ASort h2 n2)
+(ASort x1 x0) x2 x2 H3 (minus k x2)) in (let H7 \def (eq_ind_r nat (plus
+(minus k x2) x2) (\lambda (n: nat).(eq A (aplus g (ASort h2 n2) n) (aplus g
+(ASort x1 x0) n))) H_y k (le_plus_minus_sym x2 k H6)) in (leq_sort g h1 x1 n1
+x0 k (trans_eq A (aplus g (ASort h1 n1) k) (aplus g (ASort h2 n2) k) (aplus g
+(ASort x1 x0) k) H0 H7)))))) a3 H5))))))) H2))))))))))) (\lambda (a3: