proposition: Lemma trans_strict : forall R, trans R -> antisym R -> trans (strict R).
proof: Proof. Proof using. introv T S. unfold strict. introv [H1 H2] [H3 H4]. split. { apply* T. } { intros K. subst. apply H2. apply~ S. } Qed.
imports: TLC(LibTactics LibLogic LibBool LibLogic LibProd LibSum)