These derivations also emphasize the strictly formal structure of the sequent calculus. In single-conclusion sequent calculi, "modus ponens" is the Cut rule. Thus, one can use the same proof objects as before in sequent calculus derivations. One way of defining linear logic is as a sequent calculus. In proof theory, Gerhard Gentzen developed natural deduction and the sequent calculus. Sequent calculus systems are more suited to theoretical analysis. The sequent calculus was developed to study the properties of natural deduction systems. The duality between the two systems is best seen within a sequent calculus framework. Proof theorists often prefer to work on cut-free sequent calculus formulations because of such properties. In the sequent calculus all inference rules have a purely bottom-up reading. In the sequent calculus, the rule of cut is admissible. The elimination rules on the other hand turn into "left rules" in the sequent calculus. For instance, in a sequent calculus where cut elimination holds, the "cut" rule is admissible. Tableaux can be intuitively seen as sequent systems upside-down. Most proof systems provide ways to deduce one sequent from another.