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B. Lemma, Inversion Lemma for Networks). Let P and N be a process and a network, respectively. We have

. Proof, Follows by the typing system definition (cf. Table 9)

B. Lemma, 8 (Substitution Lemma). Let P be a process

B. ?. Lemma, N. ?-n-then, and ?. , 9 (Subject Congruence) If

. Proof, By induction on the derivation of N ? N , with a case analysis on the last applied rule