### Table 1: Formal proof method.

"... In PAGE 4: ... All of these proof methods are exploited by the European researchers. Table1 . presents the detailed results concerning the formal proof method used by a particular tool.... ..."

### Table 3. Formalization and verification statistics for the second phase PVS theories LOC proof obligations proof steps

2002

"... In PAGE 25: ....4.1 Statistics We present some statistics concerning the formalization and verification effort in PVS for this compilation step. Table3 summarizes the results. The compiling specification is formalized in 3 theories consisting of the formalization of the representation type and abstraction function, the complete core runtime system, and the compiling relations.... ..."

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### Table 1. Formalization and verification statistics for the first phase PVS theories LOC proof obligations proof steps

2002

"... In PAGE 15: ...We present some statistics concerning the formalization and verification effort for this compilation step. Table1 summarizes the results. First of all, we have extended the built-in PVS library with additional functions and properties for lists, and with a new theory for association lists (finite maps).... ..."

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### Table 5 Summary of Available Federal Commercial Sand Mining Permits from New York District Archive

2006

"... In PAGE 25: ... The New York District recognized that commercial mining would reduce Federal channel maintenance requirements. Eleven permits (including extensions) were granted between 1925 and 1937 to commercial mining interests, 10 of these for removal of sand and gravel from the channel entrance ( Table5 ). It is difficult to evaluate the volume of material removed through this mining.... In PAGE 27: ... If mining operations occurred approximately 200 days/year, this rate amounts to removal of 10,000 cu yd/year. Assuming that partially completed permits finished approximately half of their work, this rate would give an estimated total of 85,000 cu yd from Federal permits listed in Table5 . The permit record does not appear to fully document all mining activities at Mattituck Inlet.... In PAGE 69: ... The practice of sand mining from the Federal inlet channel began in the early 1920s and continued through the late 1930s and early 1940s. Federal permits issued during this time period ( Table5 ) do not record volume of material removed. Most permits were issued for subaerial shoal deposits within the channel entrance to depths between 10 to 20 ft mlw.... ..."

### Table 6: A Larch Prover Sample Proof

2001

"... In PAGE 11: ...able 5: Formal Specification for Composite System................................................. 71 Table6 : A Larch Prover Sample Proof .... ..."

### Table 3: Notation Used in the Formal Theory.

"... In PAGE 22: ... The proofs give sound explanations for the claims and show that the claims are unavoidable consequences of the premises. Parsimony and coherence In the formal theory of Organizations in Action, we used the predicates listed in Table3 . The theory is parsimonious because it uses only ten primitive predicates or concepts.... ..."

### Table 3: Notation Used in the Formal Theory.

"... In PAGE 22: ... The proofs give sound explanations for the claims and show that the claims are unavoidable consequences of the premises. Parsimony and coherence In the formal theory of Organizations in Action, we used the predicates listed in Table3 . The theory is parsimonious because it uses only ten primitive predicates or concepts.... ..."

### Table 1: Features of four universal RPCA models. ( means that the answer seems \no quot;, but no formal proof has been obtained.)

1998

"... In PAGE 9: ... So the size of an F-gate con guration is very large (about 100 200). These features of the four models are summarized in Table1 . If we use the framework of PCA, and assume rotation symmetry, then 64, 16, and 8 are the minimum number of states for each grid type, except the trivial 1-state PCAs.... ..."

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### Table 1: Features of four universal RPCA models. ( means that the answer seems \no quot;, but no formal proof has been obtained.)

"... In PAGE 9: ... So the size of an F-gate con guration is very large (26 220). These features of the four models are summarized in Table1 . If we use the framework of PCA, and assume rotation symmetry, then 64, 16, and 8 are the minimum number of states for each grid type, except the trivial 1-state PCAs.... ..."

### Table 1 Larch traits used in proof

1996

"... In PAGE 12: ... Wewere careful to combine these speci#0Ccations only in ways that did not doubly constrain relations like #3C. Table1 shows the number, structure, and size of our speci#0Ccations and computer- assisted proofs. We speci#0Ced axioms for all relevant data types by Larch traits, and we formalized all relevant lemmas and theorems as implications of those traits.... In PAGE 12: ... We speci#0Ced axioms for all relevant data types by Larch traits, and we formalized all relevant lemmas and theorems as implications of those traits. For each trait, Table1... ..."

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