+interpretation "exc_rewr" 'ordered_setrewriter = (exc_rewr _ _ _).
+
+
+lemma lt_rewr: ∀A:ordered_set.∀x,z,y:A. x ≈ y → z < y → z < x.
+intros (A x y z E H); split; cases H;
+[apply (Le≫ ? (eq_sym ??? E));|apply (Ap≫ ? E)] assumption;
+qed.
+
+lemma lt_rewl: ∀A:ordered_set.∀x,z,y:A. x ≈ y → y < z → x < z.
+intros (A x y z E H); split; cases H;
+[apply (Le≪ ? (eq_sym ??? E));| apply (Ap≪ ? E);] assumption;
+qed.
+
+notation > "'Lt'≪" non associative with precedence 50 for @{'ltrewritel}.
+interpretation "lt_rewl" 'ltrewritel = (lt_rewl _ _ _).
+notation > "'Lt'≫" non associative with precedence 50 for @{'ltrewriter}.
+interpretation "lt_rewr" 'ltrewriter = (lt_rewr _ _ _).