[see also: decrease, diminish, lower, cut down]
We claim that, by setting $w$ to zero on this interval, the value of $F(w)$ is reduced.
Kim announces that (by a tedious proof) the upper bound can be reduced to 10.
The length of $F$ is thus reduced by half.
By induction, we are reduced to proving the following lemma.
The problem now reduces to establishing that ......
We first prove a reduced form of the theorem.
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