'rest on' definitions:

Definition of 'rest on'

From: WordNet
verb
Rest on for support; "you can lean on me if you get tired" [syn: lean on, rest on, lean against]
verb
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]

Synonyms of 'rest on'

From: Moby Thesaurus