-\Rightarrow True])) I O H3) in (False_ind ((le (S n) m) \to P) H4)) H2))]) in
-(H2 (refl_equal nat O)))))) (\lambda (n1: nat).(\lambda (_: ((\forall (P:
-Prop).((le (S n) n1) \to ((le (S n1) (S n)) \to P))))).(\lambda (P:
-Prop).(\lambda (H1: (le (S n) (S n1))).(\lambda (H2: (le (S (S n1)) (S
+\Rightarrow True])) I O H2) in (False_ind P H3))) | (le_S m0 H2) \Rightarrow
+(\lambda (H3: (eq nat (S m0) O)).((let H4 \def (eq_ind nat (S m0) (\lambda
+(e: nat).(match e in nat return (\lambda (_: nat).Prop) with [O \Rightarrow
+False | (S _) \Rightarrow True])) I O H3) in (False_ind ((le (S n) m0) \to P)
+H4)) H2))]) in (H2 (refl_equal nat O)))))) (\lambda (n1: nat).(\lambda (_:
+((\forall (P: Prop).((le (S n) n1) \to ((le (S n1) (S n)) \to P))))).(\lambda
+(P: Prop).(\lambda (H1: (le (S n) (S n1))).(\lambda (H2: (le (S (S n1)) (S