We introduce the sequent calculus as a means to search for normal natural deductions in a purely bottom-up fashion. We then relate it normal natural deductions by appropriate soundness and completeness theorems. In order to model arbitrary natural deductions have to add the rule of cut. If we can show that cut is redundant (whenever the premises of a cut have a cut-free proof, then does the conclusion), we can see immediately that the system must be consistent. Moreover, we obtain a procedure for translating an arbitrary natural deduction to a normal one.