Why? We have, for each node, a "set" of nodes below. Those sets may intersect.

OTOH, ok, suppose a function. Should 'b' know which 'a' gets mapped to it by some function it has no knowledge about? I mean, finding a partial inverse or something is a function of that `f`, not a function on B. But how is it related anway? Do you mean to represent a tree as a function? Not as, e.g., a binary relation?