B757-200 EXPERIENCES LEADING EDGE SLAT DISAGREE EICAS MESSAGE. FLT CREW RUNS QRH AND CONTINUES TO DEST.

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DURING CLBOUT FROM SFO AURAL CAUTION; MASTER CAUTION; 'LEADING EDGE' DISCRETE CAUTION AND EICAS MESSAGE 'LEADING EDGE SLAT DISAGREEMENT' ALERTED US TO AN UNSURE INDICATION OF SLAT POS. KEPT CLB SPD BELOW 240 KIAS AND CONSULTED QRH FOR GUIDANCE. IT DOES NOT SPECIFY A PROC FOR CONTINUED FLT PER SE; BUT DEALS WITH THE SCENARIO PLAYING OUT DURING APCH. WE DECIDED TO STAY AT FL250. WE INITIATED A PHONE PATCH TO MAINT. WE AGREED THAT THE LEADING EDGE ALTERNATE SYS WORKED AND WOULD EXTINGUISH THE LIGHTS; BUT SHOULD NOT BE RUN CONTINUOUSLY. WE DESELECTED LEADING EDGE ALTERNATE SYS; AFTER WHICH THE EICAS/DISCRETE CAUTIONS REAPPEARED. WE DECIDED THAT CONTINUING TO ZZZ WOULD BE ADVISABLE; GIVING US TIME; A MUCH LOWER LNDG WT; NO THREAT TO SAFETY AND THE PROSPECT OF AN EARLY NOTIFICATION OF GND PERSONNEL. REFILED RTE WITH ATC; MOSTLY DIRECT TO ZZZ WITH DEVS AROUND WX. AT TOP OF DSCNT I DECLARED AN EMER WITH ATC; RESTATING THE LOW RISK; PRECAUTIONARY NATURE OF THE EMER. WX WAS NOT A FACTOR. THE ALTERNATE FLAP/SLAT EXTENSION PROC WAS USED PER THE QRH. LNDG AT 203300 LBS; OTHERWISE NORMAL AT 100 FPM AT TOUCHDOWN; 142K.