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Lemma 6 ([Transfer between temperatures]). Let j≥0 and let m>k≥2 be even. Suppose e_k(j)<1 and 0<q<1 with q≥ρ_ j+1 ^ m-k . Define, for 0≤e<1 and 0<t≤1 , F(q,e,t)=(q)/(1-q)((1)/((1-e)^2t)-1). Then e_m(j+1)≤F(q,e_k(j),A(m,j)). In particular, an upper bound strictly below one on the right proves c_ j+1 >0 without presupposing it.