THESAURUS
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
ROGET THESAURUS
rest on
Support
VB
be supported, lie on, sit on, recline on, lean on, loll on,
rest on, stand on, step on, repose on, abut on, bear on, be based on, have at one's back, bestride, bestraddle, support, bear, carry, hold, sustain, shoulder, hold up, back up, bolster up, shore up, uphold, upbear, prop, under prop, under pin, under set, riprap, bandage, give support, furnish support, afford support, supply support, lend support, give foundations, furnish foundations, afford foundations, supply foundations, lend foundations, bottom, found, base, ground, imbed, embed, maintain, keep on foot, aid.