(* LL: Why was it easier to do it like this? :P *)
Fixpoint listToTree (l : list SplitPath) (f : SplitPath -> RandomSeed)
        ( Pref : PrefixFree l) : {s : SeedTree | correspondingSeedTree l f s}.

(* Specifications: *)
Theorem SplitPathCompleteness (l : list SplitPath) (f : SplitPath -> RandomSeed) : PrefixFree l -> exists (s : RandomSeed), forall p, In p l -> varySeed p s = f p.