Lemma 20 ([Uniform conditional test]). Let I and e be disjoint sets of fields with admissible union. For each ν , let h_I be a function of the labels on I with values in T_ x_ν X_ν , and suppose h_I≤B for a constant independent of ν and …

Lemma 20 ([Uniform conditional test]). Let I and e be disjoint sets of fields with admissible union. For each ν , let h_I be a function of the labels on I with values in T_ x_ν X_ν , and suppose h_I≤B for a constant independent of ν and the match. For either fixed choice σ(s)=s or σ(s)=s^ -1 , _ ν→∞ 𝔼_ μ_ν h_I v_ σ(e) ≤0. Here e in a subscript denotes the letter occupying that field.