How does Portia manage to save Antonia from Shylock's terrible agreement?

Portia manages to save Antonio from Shylock collecting on his bond by disguising herself as a male doctor and cleverly finding a loophole in the law that prevents Shylock from harming Antonio. Portia secretly travels from Belmont to Venice and disguises herself as "the learned doctor Balthazar," who has been sent by Doctor Bellario to help judge the case. Portia initially declares that Shylock must show Antonio mercy in an attempt to soften Shylock's plea for justice. However, Shylock remains determined to collect his bond, and Portia initially seems to be in favor of Shylock's strict interpretation of the law. Just before Shylock can cut Antonio, Portia halts the process and says that the bond only calls for a pound of flesh and says nothing about blood. She also notes that Shylock must cut exactly a pound of flesh and not one drop of Christian blood can be shed during the procedure. Portia then turns the law against Shylock by declaring that he is attempting to murder Antonio, who is a Venetian citizen. The penalty for any foreigner attempting to murder a Venetian citizen requires that half of the foreigner's assets will be given to the state while the other half of his assets will be given to the Venetian citizen. In summary, Portia saves Antonio's life by disguising herself as a young lawyer named Balthazar and cleverly interpreting the law to prevent Shylock from receiving his bond of a pound of Antonio's flesh.