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So we have ?, p + ?, q = 1 ? (a + b) for some ?, ? ? P ? , so (a + ?, p ) + (b + ?, q ) = 1. Since u = (p, a) ? (p, a + ?, p ), v = (q, b) ? (q, b + ?, q ), we will assume a + b = 1. Now define w := p ? a(p ? q) = q + (1 ? a)(p ? q) ? P ,
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, + abp ? , q + abq ? ) ? Um(P ? P ), ?, p + abp ? + ?, q + abq ? = 1 ? (a + b)
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