The parent and child relations often used with trees can be derived once a root is specified.
Once this is done, the proof continues thus: ......
Once the dissipation relation is in hand, no further work is required.
This procedure, once implemented, can thereafter be applied with great effectiveness.
Moreover, it follows at once from (1) that ......
Let us state once more, in different words, what the preceding result says if $p=1$.
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