Helmer Daniel Sullivan suffered four fractured ribs and a collapsed lung Tuesday after falling through the trap door on the stage of the Delacorte Theater in Central Park, where he is directing the Public Theater/New York Shakespeare Fest production of “A Midsummer Night’s Dream.”Production had just begun technical rehearsals. Sullivan (“Proof”) was taken to a nearby hospital but he is expected to recover quickly from his injuries. The Public hopes to have him back in rehearsals in a few days. It’s not yet certain whether the “Midsummer” timeline will be at all delayed. Production, starring Tim Blake Nelson, Martha Plimpton, Keith David and Mireille Enos, was set to begin previews Tuesday and run through Sept. 9.