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, Note that the mapping p?q ? [?] ? is undefined whenever either [?] ? = {p?q} or one of p, q occurs in ?, but p?q is not their first communication. Proposition A.5 1. If ? ? ? is defined
,
, From the fact that in any communication sequence ? 1 and ? 2 can be swapped
, Otherwise either ? = [?] ? , in which case we are done, or one of p, q occurs in ?, but ? is not their first communication. We show that this last case is impossible. In fact if one of p, q occurs in ?, then one of p, q occurs in ? ? ?, If ? ? ? is defined by Point 4 ? ? ? < ? ? (? ? ? ) and by Point 2 ? ? (? ? ? ) = ?
G 2 and [p?q] ? ? GE(G i ) for either i = 1 or i = 2 ,
, where in the second case [p?q] ? ? GE(G i ) for all i ? I holds by definition of projection