Pr over fB ; C; L C"g with Pr A Pr A and Pr A Pr A for all atomic
events A and A over fB ; Cg and fC; L C"g respectively, such that:
Pr BCL C"
)) max(0; Pr CL C")) Pr B C))
Pr BCL C "
)) max(0; Pr CL C")) Pr BC)) :
By Lemma A.2 with B fBg B B C; C"nfCg B C B B and B L C"),
there exists 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 B max(0; u u
v + ux
v Pr B Pr BL C")) Pr BL C)) :
Moreover, it is easy to see that Pr BL C)) i L C B

Let C GH By the induction hypothesis, there are models Pr Mo B ; G and
Pr Mo B ; H with Pr B 0, Pr B 0, Pr B Pr BL G)), Pr B
Pr BL H)), Pr BL G)) i L G B and Pr BL H)) i L H B

By Lemma 3.1, we can choose Pr and Pr with Pr B Pr B and Pr B L G))

Pr BL H). By Lemmata A.1 and B.4 b), we can choose the probabilistic interpretation

Pr over fB ; L G ; L H g with Pr A Pr A and Pr A Pr A for all atomic
events A and A over fB ; L G g and fB ; L H g respectively, such that:
Pr BL G L H)) min(Pr BL H)); Pr BL G))
Pr BL G L H)) max(0; Pr BL H)) Pr BL G))) :
By Lemma A.2 with B B B ; G n fBg B B B ; H n fBg B B B L G), and
B L H), there exists probabilistic interpretation Pr over B B ; C with (12). Hence,
it holds Pr Mo B ; C and Pr B 0. By Lemma B.4 b), we get:
max(0; v + 1) Pr B Pr BL G L H)) Pr BL C)) :
Moreover, it is easy to see that Pr BL C)) i L C B 2

  **Proof of Theorem 4.2.**  $H^{\alpha}$$H^{\beta}$$H^{\gamma}$$C$$B$$\ldots B_{k}$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$B$$C$$C$$B$$C$$B$$C$$C$$B$$C$$B$$C$$C$$B$$C$$  

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