proposition: Lemma all_infinite_is_OO : forall x : Nat, Inf Nat Le x -> EqNat x OO.
proof: Proof. cofix u. rewrite OO_unfold. intros. case H. intros. inversion_clear H0. apply eqSUCC. apply u. assumption. apply eqSUCC. apply u. apply (inf Nat Le m y). assumption. assumption. Qed.
imports: Acc_and_Inf