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R(k,)≤R(R(k-1,),R(k,L-1)+1 n=R-(R(k-1,),R(k,l-1)+1 f:()→{red,blue} remove nfrom [n],consider ([n川={1,2,,n}) define:((red,blue} A∈(-),f'(A)=f(AU{n) n-1=R-(R(k-1,),R(k,l-1) 3Sn-1,lS1=R(k-1,),(3i)byf' Tcn-1,lT|=Rt(k,l-1),(工)byf” Rt(k,l) ≤ Rt-1(Rt(k-1,l), Rt(k,l-1)) + 1 n = Rt-1(Rt(k-1,l), Rt(k,l-1)) + 1 ⇥f : ￾[n] t ⇥ ￾ {red, blue} remove n from [n], consider ￾[n￾1] t￾1 ⇥ ( [n] = {1, 2, ..., n} ) f⇥ : ￾[n￾1] t￾1 ⇥ ￾ {red, blue} ⇥A ￾ ￾[n￾1] t￾1 ⇥ , f⇥ (A) = f(A ⇤ {n}) define n-1 = Rt-1(Rt(k-1,l), Rt(k,l-1)) ⇤S ⇥ [n ￾ 1], |S| = Rt(k ￾ 1, l), ￾ S t￾1 ⇥ by f⇥ ⇤T ⇥ [n ￾ 1], |T| = Rt(k,l ￾ 1), ￾ T t￾1 ⇥ by f⇥ or￾
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