interpretation "ap_rewr" 'aprewriter = (ap_rewr _ _ _).
lemma exc_rewl: ∀A:ordered_set.∀x,z,y:A. x ≈ y → y ≰ z → x ≰ z.
-intros (A x z y Exy Ayz); cases (os_cotransitive ??? x Ayz); [2:assumption]
+intros (A x z y Exy Ayz); cases (hos_cotransitive ??? x Ayz); [2:assumption]
cases Exy; right; assumption;
qed.
lemma exc_rewr: ∀A:ordered_set.∀x,z,y:A. x ≈ y → z ≰ y → z ≰ x.
-intros (A x z y Exy Azy); cases (os_cotransitive ???x Azy); [assumption]
+intros (A x z y Exy Azy); cases (hos_cotransitive ???x Azy); [assumption]
cases (Exy); left; assumption;
qed.