proposition: Lemma finite_mono : forall i j, (i<j)%nat -> F i < F j.
proof: Proof. induction 1. - simpl (finite (S i)); auto with schutte. - apply lt_trans with (finite m);auto. simpl (finite (S m)); apply lt_succ; auto with schutte. Qed.
imports: Coq(Relations Classical Classical_sets) ZornsLemma(CountableTypes) hydras(Well_Orders Lub Countable)