(* Inductive Set nat : O:nat | S:nat->nat. *)
Fixpoint inf_egal (n : nat) : nat -> bool :=
fun m : nat =>
match n, m with
| O, m => true
| S n, O => false
| S n, S m => inf_egal n m
end.

Lemma inf_egal_eq2 : forall n : nat, inf_egal (S n) 0 = false.