The algorithm compares $x$ to each entry in turn until a match is found or the list is exhausted.
This process can be repeated until we obtain the promised triangulation.
We postpone the proof until Section 2.
We walk from $X$ to $Y$ until the first place where $G$ changes.
We defer the proof of the `moreover' statement in Theorem 5 until after the proof of the lemma.
There are, however, a few important papers of which we were unaware until fairly recently.