WordNet (r) 3.0 (2006):

rest on
    v 1: rest on for support; "you can lean on me if you get tired"
         [syn: lean on, rest on, lean against]
    2: be based on; of theories and claims, for example; "What's
       this new evidence based on?" [syn: repose on, rest on,
       build on, build upon]

Moby Thesaurus II by Grady Ward, 1.0:

45 Moby Thesaurus words for "rest on":
   abut on, bank on, be based on, be contingent on, be dependent on,
   be predicated on, bear on, bear upon, bestraddle, bestride, bet on,
   calculate on, count on, depend, depend on, gamble on, hang,
   hang on, hinge, hinge on, lean on, lie on, lie with, perch,
   place reliance on, press, press down, reckon on, rely on,
   rely upon, repose on, rest, rest with, revolve on, ride, sit on,
   stand on, straddle, stride, swear by, trust to, turn on, turn upon,
   weigh on, weigh upon