 Of course, if a calculus is to be helpful it would never allow erroneous reasonings: it is not going to drive us from true hypotheses to false conclusions. It must be a sound calculus. Further, it is highly desirable that all the consequences of a set \(\Gamma\) of hypotheses could be derived from \(\Gamma\). That is, we would like to have a strongly complete calculus. In our  section 2.3  you will find the sketch of such a completeness proof.