proposition: Lemma is_CSetoid_Setoid : forall S eq ap, is_CSetoid S eq ap -> Setoid_Theory S eq.
proof: Proof. intros S eq ap p. destruct p. split. firstorder. intros a b. red in ax_ap_tight0 . repeat rewrite <- ax_ap_tight0. firstorder. intros a b c. red in ax_ap_tight0 . repeat rewrite <- ax_ap_tight0. intros H H0 H1. destruct (ax_ap_cotransitive0 _ _ H1 b); auto. Qed.
imports: CoRN.tactics.CornTac CoRN.logic.CLogic CoRN.tactics.Step CoRN.algebra.RSetoid