DVT Controller providing OJT described a loss of separation event when the developmental issued a runway crossing clearance with conflicting traffic on takeoff; the reporter electing not to issue alternate instructions because of aircraft locations.

Narrative

Aircraft X had just landed on Runway 7L and was holding between the runways waiting to cross at B9. I was providing OJT instruction at the time with my developmental on the Local South position. The developmental then cleared aircraft Y (C172) for departure off Runway 7R; full length. Aircraft Y was slow to depart and my developmental was scanning his pattern containing 4 airplanes. My developmental then picked up his runway crossing placard; in my mind; anticipating going to cross aircraft X after aircraft Y had passed him on his departure. The developmental then keyed the mic; again I am thinking he is going to confirm aircraft X is on frequency; instead keyed the mic and said; 'Aircraft X; without delay cross Runway 7R and contact Ground .8.' As soon as he said the word 'cross' I was in the process of keying my mic to stop his taxi but aircraft X was already moving onto the runway and was past the hold bar and first white line of the runway. I knew aircraft Y was airborne about 200 FT in the air approaching B5 and realized that stopping aircraft X was futile and unnecessary as doing so would have stopped him on the runway and if by chance aircraft Y had to abort his take off; aircraft X would be in his path. My developmental saw the situation as I was alerting him as to where aircraft Y was and keyed the mic and said; 'Aircraft X hold position; disregard.' After getting off position; we debriefed the incident and talked about ways to visually scan first and then get crossing placard second; so that you are sure that the runway is clear. We discussed numerous different scanning techniques; utilizing the crossing placards in a more effective way and emphasized how important scanning the runway is at all times.