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="700" border="1">
      <tr>
        <th width="104" scope="col">Input File</th>
        <th width="123" scope="col">Proof</th>
        <th width="365" scope="col">Commentary</th>
      </tr>
     <tr>
        <td><a href="InputFiles/Satz6.2a.in">Satz 6.2a</a></td>
        <td><a href="Proofs/Satz6.2a.prf">Satz6.2a.prf</a><br>4 steps</td>
        <td> a!=b and b!=p and c!=p and T(a,p,c) and T(b,p,c) -> sameside(a,p,b)  </td>
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        <td><a href="InputFiles/Satz6.2b.in">Satz 6.2b</a></td>
        <td><a href="Proofs/Satz6.2b.prf">Satz6.2b.prf</a><br>4 steps</td>
        <td> a!=b and b!=p and c!=p and T(a,p,c) and sameside(a,p,b)->T(b,p,c)  </td>
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        <td><a href="InputFiles/Satz6.3a.in">Satz 6.3a</a></td>
        <td><a href="Proofs/Satz6.3a.prf">Satz6.3a.prf</a><br>9 steps</td>
        <td> sameside(a,p,b)-><br> a!=p and b !=p and  
             exists c(c !=p and T(a,p,c) and T(b,p,c))  </td>
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        <td><a href="InputFiles/Satz6.3b.in">Satz 6.3b</a></td>
        <td><a href="Proofs/Satz6.3b.prf">Satz6.3b.prf</a><br>1 step</td>
        <td> a!=p and b !=p and  
             exists c(c !=p and T(a,p,c) and T(b,p,c))  <br> -> sameside(a,p,b) </td>
      </tr>
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        <td><a href="InputFiles/Satz6.4a.in">Satz 6.4a</a></td>
        <td><a href="Proofs/Satz6.4a.prf">Satz6.4a.prf</a><br>9 steps</td>
        <td> sameside(a,p,b) -> Col(a,p,b) and not T(a,p,b)  </td>
      </tr>
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        <td><a href="InputFiles/Satz6.4b.in">Satz 6.4b</a></td>
        <td><a href="Proofs/Satz6.4b.prf">Satz6.4b.prf</a><br>33 steps</td>
        <td> Col(a,p,b) and not T(a,p,b)  -> sameside(a,p,b) </td>
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        <td><a href="InputFiles/Satz6.5.in">Satz 6.5</a></td>
        <td><a href="Proofs/Satz6.5.prf">Satz6.5.prf</a><br>1 step</td>
        <td> (reflexivity) a!=p -> sameside(a,p,a)  </td>
      </tr>
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        <td><a href="InputFiles/Satz6.6.in">Satz 6.6</a></td>
        <td><a href="Proofs/Satz6.6.prf">Satz6.6.prf</a><br> 4 steps</td>
        <td> (symmetry) sameside(a,p,b) -> sameside(b,p,a)  </td>
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        <td><a href="InputFiles/Satz6.7.in">Satz 6.7</a></td>
        <td><a href="Proofs/Satz6.7.prf">Satz6.7.prf</a><br>9 steps</td>
        <td> (transitivity) sameside(a,p,b) and sameside(b,p,c) -> sameside(a,p,c)</td>
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        <td><a href="InputFiles/Satz6.11a.in">Satz 6.11a</a></td>
        <td><a href="Proofs/Satz6.11a.prf">Satz6.11a.prf</a><br>23 steps</td>
        <td>r!=a and b!=c -> exists x(sameside(x,a,r) and E(a,x,b,c))  </td>
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        <td><a href="InputFiles/Satz6.11b.in">Satz 6.11b</a></td>
        <td><a href="Proofs/Satz6.11b.prf">Satz6.11b.prf</a><br>12 steps</td>
        <td> uniqueness of the x in 6.11a  </td>
      </tr>
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        <td><a href="InputFiles/Satz6.13a.in">Satz 6.13a</a></td>
        <td><a href="Proofs/Satz6.13a.prf">Satz6.13a.prf</a><br>10 steps</td>
        <td> sameside(a,p,b) and pa &le; pb -> T(p,a,b) </td>
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        <td><a href="InputFiles/Satz6.13b.in">Satz 6.13b</a></td>
        <td><a href="Proofs/Satz6.13b.prf">Satz6.13b.prf</a> <br> 1 step</td>
        <td> sameside(a,p,b) and T(p,a,b) -> pa &le; pb  </td>
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        <td><a href="InputFiles/Satz6.15a.in">Satz 6.15a</a></td>
        <td><a href="Proofs/Satz6.15a.prf">Satz6.15.prf</a><br>16 steps</td>
        <td> p!=q and p!=r and T(q,p,r) and Col(p,q,a) -> <br>
             sameside(a,p,q) or a=p or sameside(a,p,r)
         </td>
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        <td><a href="InputFiles/Satz6.15b.in">Satz 6.15b</a></td>
        <td><a href="Proofs/Satz6.15b.prf">Satz6.15.prf</a><br> 1 step</td>
        <td> p!=q and p!=r and T(q,p,r) and sameside(a,p,q) -> Col(p,q,a)  
        </td>
      </tr>
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        <td><a href="InputFiles/Satz6.15c.in">Satz 6.15c</a></td>
        <td><a href="Proofs/Satz6.15b.prf">Satz6.15.prf</a><br> 10 steps</td>
        <td> p!=q and p!=r and T(q,p,r) and sameside(a,p,r) -> Col(p,q,a)  
        </td>
      </tr>
      <tr>
        <td><a href="InputFiles/Satz6.15d.in">Satz 6.15d</a></td>
        <td><a href="Proofs/Satz6.15b.prf">Satz6.15.prf</a><br>5 steps</td>
        <td> p!=q and p!=r and T(q,p,r) and a=p -> Col(p,q,a)  
        </td>
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        <tr>
        <td><a href="InputFiles/Satz6.16a.in">Satz 6.16a</a></td>
        <td><a href="Proofs/Satz6.16.prf">Satz6.16a.prf</a><br>7 steps</td>
        <td> T(c,a,b) and T(d,a,b) and a!=b -> T(d,c,b) or T(c,d,b)
        </br> We need this to prove Satz 6.16b </td>
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        <td><a href="InputFiles/Satz6.16b.in">Satz 6.16b</a></td>
        <td><a href="Proofs/Satz6.16b.prf">Satz6.16b.prf</a><br>47 steps</td>
        <td> p!=q and s!=p and Col(p,q,s) and Col(p,q,x) ->  Col(p,s,x)
         </td>
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        <td><a href="InputFiles/Satz6.17a.in">Satz 6.17a</a></td>
        <td><a href="Proofs/Satz6.17a.prf">Satz6.17a.prf</a><br> 2 steps</td>
        <td> p!=q -> Col(p,q,p)   </td>
      </tr>
      <tr>
        <td><a href="InputFiles/Satz6.17b.in">Satz 6.17b</a></td>
        <td><a href="Proofs/Satz6.17b.prf">Satz6.17b.prf</a><br> 1 step</td>
        <td> p!=q and Col(p,q,x) -> Col(q,p,x)  </td>
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        <td><a href="InputFiles/Satz6.18.in">Satz 6.18</a></td>
        <td><a href="Proofs/Satz6.18.prf">Satz6.18.prf</a><br>20 steps</td>
        <td> a!=b and p!=q and Col(p,q,a) and Col(p,q,b) and Col(p,q,x) -> Col(a,b,x) 
        <br> This is a special case of Satz 6.21, used in proving Satz 6.21.
        </td>
      </tr>
        <tr>
        <td><a href="InputFiles/Satz6.21.in">Satz 6.21</a></td>
        <td><a href="Proofs/Satz6.21.prf">Satz6.21.prf</a><br>22 steps</td>
        <td> if Line(p,q) and Line(a,b) have two different points in common then they coincide. </td>
      </tr>
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        <td><a href="InputFiles/Satz6.25.in">Satz 6.25</a></td>
        <td><a href="Proofs/Satz6.25.prf">Satz6.25.prf</a><br>3 steps</td>
        <td> There exists a point x not on Line(p,q), that is, such that not Col(p,q,x). </td>
      </tr>
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        <td><a href="InputFiles/Satz6.28.in">Satz 6.28</a></td>
        <td><a href="Proofs/Satz6.28.prf">Satz6.28.prf</a><br>21 steps</td>
        <td>if sameside(a,b,c) and sameside(a1,b1,c1), and ba and bc are respectively
        congruent to b1a1 and b1c1, then ac is congruent to a1c1. <br>
        This is used in Satz 11.4, but is never proved in the book, and belongs in Chapter 6,
        so we give it the name Satz 6.28.
      </tr>
    </table>
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