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>.
  </p>
    <table width="650" border="1">
      <tr>
        <th width="104" scope="col">Input File</th>
        <th width="123" scope="col">Proof</th>
        <th width="315" scope="col">Commentary</th>
      </tr>
       <tr>
        <td><a href="InputFiles/Satz4.2.in">Satz 4.2</a></td>
        <td><a href="Proofs/Satz4.2.prf">Satz4.2.prf </a><br>46 steps</td>
        <td>T(a,b,c) and T(a1,b1,c1) and E(a,c,a1,c1) and E(b,c,b1,c1).
        <br> and E(a,d,a1,d1) and E(c,d,c1,d1) -> E(b,d,b1,d1)<br>
        This is the ``inner five-segment theorem'', similar to the 5-segment axiom but 
        with the segments to be proved equal on the inside, rather than the outside.
        </td>
      </tr>
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        <td><a href="InputFiles/Satz4.3.in">Satz 4.3</a></td>
        <td><a href="Proofs/Satz4.3.prf">Satz4.3.prf</a><br>6 steps</td>
        <td> T(a,b,c) and T(a1,b1,c1) and E(a,c,a1,c1)  <br> and E(b,c,b1,c1) -> E(a,b,a1,b1)</td>
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        <td><a href="InputFiles/Satz4.5.in">Satz 4.5</a></td>
        <td><a href="Proofs/Satz4.5.prf">Satz4.5.prf</a><br>24 steps</td>
        <td> T(a,b,c) and E(a,c,a1,c1) ->  <br> exists b1(T(a1,b1,c1) and E3(a,b,c,a1,b1,c1)).
        <br> We also show that b1 depends only on a,b,a1,c1 (not on c) by an explicit term.
        </td>
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        <td><a href="InputFiles/Satz4.6.in">Satz 4.6</a></td>
        <td><a href="Proofs/Satz4.6.prf">Satz4.6.prf</a><br>10 steps</td>
        <td> T(a,b,c) and E3(a,b,c,a1,b1,c1) -> T(a1,b1,c1)</td>
      </tr>
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        <td><a href="InputFiles/Satz4.11a.in">Satz 4.11a</a>
        <br> <a href="InputFiles/Satz4.11b.in">Satz 4.11b</a>
        <br><a href="InputFiles/Satz4.11c.in">Satz 4.11c</a>
        <br><a href="InputFiles/Satz4.11d.in">Satz 4.11d</a>
        <br><a href="InputFiles/Satz4.11e.in">Satz 4.11e</a>
        </td>
        <td><a href="Proofs/Satz4.11a.prf">Satz4.11a.prf</a> (4 steps) 
         <br>  <a href="Proofs/Satz4.11b.prf">Satz4.11b.prf</a> (4 steps) 
           <br> <a href="Proofs/Satz4.11c.prf">Satz4.11c.prf</a> (7 steps) 
           <br>  <a href="Proofs/Satz4.11d.prf">Satz4.11d.prf</a> (7 steps) 
           <br>   <a href="Proofs/Satz4.11e.prf">Satz4.11e.prf</a> (7 steps) 
        </td>
        <td> Col(a,b,c) -> Col(b,c,a) <br>
         and similarly for all permutations of (a,b,c)
         </td>
      </tr>
    

       <tr>
        <td><a href="InputFiles/Satz4.12.in">Satz 4.12</a>
          <br> <a href="InputFiles/Satz4.12b.in">Satz 4.12b</a>

        </td>
        <td><a href="Proofs/Satz4.12.prf">Satz4.12.prf </a> (1 step)
        <br><a href="Proofs/Satz4.12.prf">Satz4.12b.prf </a> (1 step)
       </td>
        <td> Col(a,a,b)
        <br> Co(a,b,a)
        </td>
      </tr>
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        <td><a href="InputFiles/Satz4.13.in">Satz 4.13</a></td>
        <td><a href="Proofs/Satz4.13.prf">Satz4.13.prf</a><br>19 steps</td>
        <td> Col(a,b,c) and E3(a,b,c,a1,b1,c1) -> Col(a1,b1,c1) </td>
      </tr>
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        <td><a href="InputFiles/Satz4.14.in">Satz 4.14</a></td>
        <td><a href="Proofs/Satz4.14.prf">Satz4.14.prf</a><br>22 steps</td>
        <td> Col(a,b,c) and E(a,b,a1,b1) -> exists c1(E3(a,b,c,a1,b1,c1)) </td>
      </tr>
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        <td><a href="InputFiles/Satz4.16.in">Satz 4.16</a></td>
        <td><a href="Proofs/Satz4.16.prf">Satz4.16.prf</a><br>27 steps</td>
        <td> Col(a,b,c) and E3(a,b,c,a1,b1,c1) and E(a,d,a1,d1)
          <br> and E(b,d,b1,d1) and a!=b -> E(c,d,c1,d1) </td>
      </tr>
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        <td><a href="InputFiles/Satz4.17.in">Satz 4.17</a></td>
        <td><a href="Proofs/Satz4.17.prf">Satz4.17.prf</a><br>3 steps</td>
        <td> a!=b and Col(a,b,c) and E(a,p,a,q) and E(b,p,b,q) -> E(c,p,c,q)  </td>
      </tr>
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        <td><a href="InputFiles/Satz4.18.in">Satz 4.18</a></td>
        <td><a href="Proofs/Satz4.18.prf">Satz4.18.prf</a><br>8 steps</td>
        <td> a!=b and Col(a,b,c) and E(a,c,a,c1) and E(b,c,b,c1) -> c = c1 </td>
      </tr>
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        <td><a href="InputFiles/Satz4.19.in">Satz 4.19</a></td>
        <td><a href="Proofs/Satz4.19.prf">Satz4.19.prf</a><br>11 steps</td>
        <td> T(a,c,b) and E(a,c,a,c1) and E(b,c,b,c1) -> c = c1  </td>
      </tr>
        </tr>
    </table>
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