"... In PAGE 22: ... In order to show that no deviation is beneficial, we systematically explore all deviations. Table1 maps each deviation to the lemma that shows that it is not beneficial. The concern of nodes sending additional messages is covered by Lemmas 11 and 8.... ..."

"... In PAGE 19: ... In order to show that no deviation is beneficial, we system- atically explore all deviations. Table1 maps each deviation to the lemma that shows that it is not beneficial. The concern of nodes sending additional messages is covered by Lemmas 9 and 10.... ..."

"... In PAGE 3: ... In contrast, the surface exposed positions showed few sequence constraints and the nearly perfect alternating polar0nonpolar pat- tern of the wild-type protein was not preserved in the combinato- rial mutants ~Table 3!.All three exposed positions tolerated nonpolar residues; however, the hydrophobic substitutions were somewhat disfavored ~ Table4 !. Interestingly, although the majority of com- binatorial mutants had one nonpolar residue on the surface and almost one-quarter of the mutants had two surface nonpolar resi- dues, there were no mutants with all three surface positions sub- stituted by nonpolar amino acids, despite the fact that 13% of the sequences contain three surface hydrophobic residues in the un- selected population.... In PAGE 3: ... Interestingly, although the majority of com- binatorial mutants had one nonpolar residue on the surface and almost one-quarter of the mutants had two surface nonpolar resi- dues, there were no mutants with all three surface positions sub- stituted by nonpolar amino acids, despite the fact that 13% of the sequences contain three surface hydrophobic residues in the un- selected population. Negative selection was particularly dramatic for residues 59 and 61, which were never simultaneously substi- tuted with hydrophobic amino acids in the recovered mutants ~ Table4 , last column!. The above observations suggested that at least one polar residue on the exposed side of strand 4 is required for the proper folding of protein L.... ..."

"... In PAGE 10: ... For instance, consider to be: 8x: :8y: :P (x;y) Q(x; y) R(x; y) Suppose we choose the rst assertion and choose a parameter t,now is: 8x: :8y: :P (x; y) Q(x; y) R(x; y); 8y: :P (t; y) Q(t; y) R(t; y) Clearly, the number of possible choices grows quickly. Focusing allows the in- stantiation of all parameters and all preconditions of a lemma to occur at once as detailed in Table6 . This formulation is adapted from the discussion presented in [Pfe99].... ..."

"... In PAGE 10: ... For instance, consider to be: 8x: :8y: :P(x; y) Q(x; y) R(x; y) Suppose we choose the rst assertion and choose a parameter t, now is: 8x: :8y: :P(x; y) Q(x; y) R(x; y); 8y: :P(t; y) Q(t; y) R(t; y) Clearly, the number of possible choices grows quickly. Focusing allows the in- stantiation of all parameters and all preconditions of a lemma to occur at once as detailed in Table6 . This formulation is adapted from the discussion presented in [Pfe99].... ..."

"... In PAGE 24: ... This case reduces to the previous one by an appeal to Lemma 21. The above case analysis is summarized in Table2 . In all cases we obtain 1 from by applying one or more transformations [o] 1, [i], [d] 2, [v], [t] together with an additional application of swap in case (1)(d) and (3).... In PAGE 28: ... Proof. According to Table2 we have to consider cases (2) and (3) in the proof of Lemma 36. We consider here only case (2).... ..."

"... In PAGE 9: ...able 2 Taxonomy of Union Services ............................................................................................ 8 Table3 Relationship among theorems (lemmas) and operations .... In PAGE 76: ...67 Table3 shows the relationships among the theorems (lemmas), operations, and the sequence of these operations. If an operation is used for a theorem (lemma), there will be a check mark in the corresponding cell.... ..."