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P. ?a, Q: by definition P = (l)?a. Ql. So f n(P ) = f n(Q) \ {l, a}. By inductive hypothesis we have that

A. Lemma, 5 Be P an HO? + process. If P ? Q then fn(Q) ? fn(P )

. App, V ? F ? with ? = match(V, ?) By definition fn((?)F V ) = (fn(F ) \ dom(?)) ? fn(V ) and fn(F ?) = (fn(F ) \ dom(?))?fn(cod, and we can conclude by noticing that fn(cod(?)) ? fn(V )

R. Q-n-]-?-c-?-1, S. ?. R{-s-?-1, /. Y. , and X. }. , Since identity is included in R (it suffices to consider a 0-ary context), and since (S i , S ? i ) ? R (since they are subterms) we have that (R{ S 1

A. Lemma, 20 Axiom Ex.P and its instantiation are correct with respect to weak bf barbed bisimulation

R. Let, addG(l 1 P | 2 Q | S(l 1