$\begin{array}{ccccccccccccc}&&\mathcal{B}&\{B\}&\mathcal{B}&\mathcal{B}&C,C^{\dagger}&\{C\}&B&C&B&B&B\\ L&C^{\dagger}&&&&&Pr&\mathcal{B}&B,C&&&&&\\ Pr&Mo&B,C&&Pr&B&&&&&\\ Pr&\overline{\mathcal{B}}L&C&&Pr&\overline{\mathcal{B}}L&C^{\dagger}&&\frac{\overline{\psi}}{v}+\frac{\psi}{v}&u,\frac{\psi_{L}}{v}&Pr&B&Pr&B\\ Pr&L&C&&Pr&L&C^{\dagger}&&&&&\frac{\psi_{L}}{v}&Pr&B&\gamma&Pr&B\\ &&&&&&&&&&\\ &&&&&&\\ \end{array}$  $\begin{array}{ccccccccccccc}&&\mathcal{B}&\mathcal{B}&\mathcal{B}&C,C^{\dagger}&\{C\}&B&C&B&B&B&\\ Pr&Mo&B,C&&Pr&B&C&\\ Pr&L&C&&Pr&L&C^{\dagger}&&&&&\\ &&&&&&\\ \end{array}$

$\begin{array}{ccccccccccccccccc}&Pr&,&Pr&,&C&&&&&&Pr&,&Pr&,&C&&&&&&\\ &&&&&&Pr&,&CL&C^{\dagger}&&Pr&,&C&,&Pr&,&L&C^{\dagger}&&z&Pr&,&C\\ &&&&&&Pr&,&\overline{CL}&C^{\dagger}&&=&Pr&,&C&,&Pr&,&L&C^{\dagger}&&z&Pr&,&C&.\\&&&&&&&&&z&&&&&&&&&z&&\\ &&&&&&+&&&&&&&&&z&&\\ &&Pr&Mo&C,C^{\dagger}&&Pr&C&&&&&\\ &&&&&&Pr&CL&C^{\dagger}&&Pr&C&,&Pr&L&C^{\dagger}&&z&Pr&C&.\\&&&&&&Pr&Pr&Pr&C&Pr&C&&\\ &&&&&&Pr&Pr&C&P_{T}&C&P_{T}&A&&Pr&A&&\\ &&&&&&Pr&A&&A&&\{B,C\}&&\{C,L&C^{\dagger}\}&&\end{array}$
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Pr BCL C" )) min(Pr BC ; Pr CL C"))) Pr BCL C" )) min(Pr BC ; Pr CL C "))) : By Lemma A.2 with B fBg B B C; C"fCg B C B B and B L C" ), there is probabilistic interpretation Pr over B B ; C with (12). Hence, it holds Pr Mo B ; C and Pr B 0. By Lemma B.4 a), we get: Pr BL C)) Pr BL C" )) min(1; uz v ; u + ux v ; u + ux v Pr B  Pr B Pr L C)) Pr L C" )) uz v Pr B  Pr B : Let C GH We just show b), the claim in c) can be proved analogously. By the in-

Let C GH We just show b), the claim in c) can be proved analogously. By the in- duction hypothesis, there are models Pr ; ; Pr ; Mo B ; G and Pr ; ; Pr ; Mo B ; H with Pr ; B 0, Pr ; B 0, Pr ; B 0, Pr ; B 0, and Pr ; BL G)) Pr ; B ; Pr ; L G)) w Pr ; B Pr ; BL G)) Pr ; B ; Pr ; L G)) w Pr ; B Pr ; BL H)) Pr ; B ; Pr ; L H)) z Pr ; B : Pr ; BL H)) Pr ; B ; Pr ; L H)) z Pr ; B These conditions already entail w w z and z With the results from a), we additionally get w + and z + By Lemma B.3 b), there is
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233