-\def (match H in le with [le_n \Rightarrow (\lambda (H0: (eq nat (S y)
-O)).(let H1 \def (eq_ind nat (S y) (\lambda (e: nat).(match e in nat with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H0) in (False_ind (eq bool
-(blt y O) true) H1))) | (le_S m H0) \Rightarrow (\lambda (H1: (eq nat (S m)
-O)).((let H2 \def (eq_ind nat (S m) (\lambda (e: nat).(match e in nat with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H1) in (False_ind ((le (S
-y) m) \to (eq bool (blt y O) true)) H2)) H0))]) in (H0 (refl_equal nat O)))))
-(\lambda (n: nat).(\lambda (H: ((\forall (y: nat).((lt y n) \to (eq bool (blt
-y n) true))))).(\lambda (y: nat).(nat_ind (\lambda (n0: nat).((lt n0 (S n))
-\to (eq bool (blt n0 (S n)) true))) (\lambda (_: (lt O (S n))).(refl_equal
-bool true)) (\lambda (n0: nat).(\lambda (_: (((lt n0 (S n)) \to (eq bool
-(match n0 with [O \Rightarrow true | (S m) \Rightarrow (blt m n)])
-true)))).(\lambda (H1: (lt (S n0) (S n))).(H n0 (le_S_n (S n0) n H1)))))
-y)))) x).
+\def (match H with [le_n \Rightarrow (\lambda (H0: (eq nat (S y) O)).(let H1
+\def (eq_ind nat (S y) (\lambda (e: nat).(match e with [O \Rightarrow False |
+(S _) \Rightarrow True])) I O H0) in (False_ind (eq bool (blt y O) true)
+H1))) | (le_S m H0) \Rightarrow (\lambda (H1: (eq nat (S m) O)).((let H2 \def
+(eq_ind nat (S m) (\lambda (e: nat).(match e with [O \Rightarrow False | (S
+_) \Rightarrow True])) I O H1) in (False_ind ((le (S y) m) \to (eq bool (blt
+y O) true)) H2)) H0))]) in (H0 (refl_equal nat O))))) (\lambda (n:
+nat).(\lambda (H: ((\forall (y: nat).((lt y n) \to (eq bool (blt y n)
+true))))).(\lambda (y: nat).(nat_ind (\lambda (n0: nat).((lt n0 (S n)) \to
+(eq bool (blt n0 (S n)) true))) (\lambda (_: (lt O (S n))).(refl_equal bool
+true)) (\lambda (n0: nat).(\lambda (_: (((lt n0 (S n)) \to (eq bool (match n0
+with [O \Rightarrow true | (S m) \Rightarrow (blt m n)]) true)))).(\lambda
+(H1: (lt (S n0) (S n))).(H n0 (le_S_n (S n0) n H1))))) y)))) x).