rest on/upon something phrasal verb [not in progressive] ( see also ↑ rest )
1 . formal to depend on something:
Success in management ultimately rests on good judgment.
2 . formal to be based on a particular idea or set of facts:
The case against my client rests entirely on circumstantial evidence.
3 . if your eyes rest on something, you notice it and look at it:
His eyes rested on a small figure in the distance.