Sequent calculus is a different style in which proof systems can be formulated, where for each connective, we have a left rule for introducing it (in the conclusion of the rule) in the left part of a sequent G => D (i.e., in G), and similarly a right rule for introducing it in the right part (D).  The beauty of sequent calculus is disjunction is handled without any departure from the general form for sequent calculus rules (unlike disjunction in natural deduction, as we discussed last time).