-lemma nat_lt_to_os_lt:
- ∀a,b:nat_ordered_set.a < b → lt nat_ordered_set a b.
-intros 3; split;
-[1: apply nat_le_to_os_le; apply lt_to_le;assumption;
-|2: right; apply H;]
-qed.
-
-lemma os_lt_to_nat_lt:
- ∀a,b:nat_ordered_set. lt nat_ordered_set a b → a < b.
-intros; cases H; clear H; cases H2;
-[2: apply H;| cases (H1 H)]
-qed.
\ No newline at end of file