After being cleared to cross a runway; ERJ crew has critical conflict with another aircraft on the far side that has failed to hold short of the intersection as instructed the morning sun was directly in the eyes of the ERJ crew.

Narrative

After landing we were instructed to hold short of Runway 6R on Taxiway K. We complied and were then cleared to cross Runway 6R and contact Ground Control. Both pilots visually confirmed clearance to cross the runway and checked both sides and stated; 'cleared left and right and cleared to cross.' There was an airplane in position and holding at the departure end on Runway 6R. The First Officer confirmed and was monitoring the aircraft while scanning the remaining runway. The sun was very bright out of the east and still rising and was right in our eyes obstructing the taxiway on the other side of the runway. As we came to the runway hold short line on the other side of 6R; we noticed another aircraft crossing Taxiway K on Taxiway L. Both pilots noticed the aircraft and the Captain brought the aircraft to an immediate and abrupt stop. At that point the other aircraft keyed the microphone and apologized profusely for missing what we thought to be a hold short clearance. Ground Control told them that they 'missed it' and should continue through the intersection. We then cleared the runway and had an uneventful taxi in and shut down at the gate.