proposition: Lemma seq_mono_inj (s : nat -> Ord) : seq_mono s -> injective s.
proof: Proof. unfold injective;intros H i j H0. case (lt_eq_lt_dec i j). - destruct 1; auto. + generalize (H _ _ l); auto. rewrite H0;intro;case (@Lt_irreflexive Ord lt AX1 (s j));auto. - intro l;generalize (H _ _ l). rewrite H0;intro;case (@Lt_irreflexive Ord lt AX1 (s j));auto. Qed.
imports: Coq(Relations Classical Classical_sets) ZornsLemma(CountableTypes) hydras(Well_Orders Lub Countable)