formula_51 is well defined because at least one such edge formula_16 must exist whenever the matching is not yet of maximum possible size (see the following section); it is positive because there are no tight edges between formula_53 and formula_54. Increase formula_14 by formula_51 on the vertices of formula_53 and decrease formula_14 by formula_51 on the vertices of formula_60. The resulting formula_14 is still a potential, and although the graph formula_19 changes, it still contains formula_27 (see the next subsections). We orient the new edges from formula_7 to formula_9. By the definition of formula_51 the set formula_42 of vertices reachable from formula_38 increases (note that the number of tight edges does not necessarily increase).