[see also: adaptation, adjustment, change, variant, variation, version]
The proof is similar to the proof of Theorem 4, with two principal modifications.
We write $\beta= ......$, which is a slight modification to the previous version of $\beta$.
The only modification to be made is that we define ......
with minor modifications
(with the usual modification for $p=\infty$)
a considerable $\langle$extensive/major/significant$\rangle$ modification
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