Sindbad~EG File Manager

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    <h2>Tarski Formalization Project Archives</h2>
     <p>The posted input files are now all mechanically generated from a master list of theorems.
    For more information about our methodology see the <a href="http://www.michaelbeeson.com/research/FormalTarski/index.php"> top page of this project</a>.
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        <th width="104" scope="col">Input File</th>
        <th width="123" scope="col">Proof</th>
        <th width="315" scope="col">Commentary</th>
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        <td><a href="InputFiles/Satz5.1.in">Satz 5.1</a></td>
        <td><a href="Proofs/Satz5.1.prf">Satz5.1.prf </a><br>127 steps</td>
        <td>connectivity of betweenness <br>(Gupta 1965, one of Quaife's challenge problems)
        <br>Wos has subsequently found a 96-step proof.</td>
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        <td><a href="InputFiles/Satz5.2.in">Satz 5.2</a></td>
        <td><a href="Proofs/Satz5.2.prf">Satz5.2.prf</a></td>
        <td>simple corollary of 5.1</td>
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        <td><a href="InputFiles/Satz5.3.in">Satz 5.3</a></td>
        <td><a href="Proofs/Satz5.3.prf">Satz5.3.prf</a></td>
        <td>simple corollary of 5.1</td>
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        <td><a href="InputFiles/Satz5.5a.in">Satz 5.5a</a></td>
        <td><a href="Proofs/Satz5.5a.prf">Satz5.5a.prf</a></td>
        <td>first half of Satz 5.5</td>
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        <td><a href="InputFiles/Satz5.5b.in">Satz 5.5b</a></td>
        <td><a href="Proofs/Satz5.5b.prf">Satz5.5b.prf</a></td>
        <td>second half of Satz 5.5</td>
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        <td><a href="InputFiles/Satz5.6.in">Satz 5.6</a></td>
        <td><a href="Proofs/Satz5.6.prf">Satz5.6.prf</a></td>
        <td> &le; respects congruence</td>
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        <td><a href="InputFiles/Satz5.7.in">Satz 5.7</a></td>
        <td><a href="Proofs/Satz5.7.prf">Satz5.7.prf</a></td>
        <td> reflexivity of &le; </td>
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        <td><a href="InputFiles/Satz5.8.in">Satz 5.8</a></td>
        <td><a href="Proofs/Satz5.8.prf">Satz5.8.prf</a><br>17 steps</td>
        <td> transitivity of &le; </td>
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        <td><a href="InputFiles/Satz5.9.in">Satz 5.9</a></td>
        <td><a href="Proofs/Satz5.9.prf">Satz5.9.prf</a></td>
        <td> ab &le; cd and cd &le; ef -> ab &le; cd  </td>
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        <td><a href="InputFiles/Satz5.10.in">Satz 5.10</a></td>
        <td><a href="Proofs/Satz5.10.prf">Satz5.10.prf</a></td>
        <td> ab &le; cd  or cd  &le; ab   </td>
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        <td><a href="InputFiles/Satz5.11.in">Satz 5.11</a></td>
        <td><a href="Proofs/Satz5.11.prf">Satz5.11.prf</a></td>
        <td> aa &le; cd  </td>
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        <td><a href="InputFiles/Satz5.12a1.in">Satz 5.12a1</a></td>
        <td><a href="Proofs/Satz5.12a1.prf">Satz5.12a1.prf</a><br>1 step
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        <td> Col(a,b,c) and T(a,b,c) -> ab &le; ac and bc &le; ac </td>
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        <td><a href="InputFiles/Satz5.12a2.in">Satz 5.12a2</a></td>
        <td><a href="Proofs/Satz5.12a2.prf">Satz5.12a2.prf</a><br>3 steps</td>
        <td> Col(a,b,c) and T(a,b,c) ->  bc &le; ac </td>
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        <td><a href="InputFiles/NarbouxLemma1.in">NarbouxLemma1 <br>(not in SST)</a></td>
        <td><a href="Proofs/NarbouxLemma1.prf">NarbouxLemma1.prf</a><br>4 steps</td>
        <td> T(a,b,c) and E(a,c,a,b) -> c=b 
          <br> We used this to prove 5.12b (and nowhere else). Narboux needed this in his formalization too.</td>
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        <td><a href="InputFiles/Satz5.12b.in">Satz 5.12b</a></td>
        <td><a href="Proofs/Satz5.12b.prf">Satz5.12b.prf</a><br>23 steps</td>
        <td> Col(a,b,c) and  ab &le; ac and bc &le; ac ->T(a,b,c) 
            <br> uses Narboux's Lemma 1 above  </td>
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