Snapshot representatives before quick-find union

When merging two blocks in quick-find, let $a=re{p}_0(x)$ and $b=re{p}_0(y)$ be fixed saved labels. Replacing every old occurrence of $b$ by $a$ preserves all other blocks. A scan loop invariant says processed cells already have their specified final labels while unprocessed cells still have their old labels. Recomputing $rep(y)$ during this mutation can change the replacement label after the cell for $y$ is processed, causing remaining old-$b$ cells to be missed. Saving both labels makes the update criterion stable and the invariant provable.