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<b>set </b><font color="Maroon">Sq</font> =  <a href="topreal1.html#K2">R^2-unit_square</a> ;<br/>
<b>thus </b><a NAME="E1:19_1_1"/>
 <a href="topreal1.html#K2">R^2-unit_square</a>  is <a href="topreal4.html#V1">special_polygonal</a>
 <b>by </b><i><a class="ref" href="sppol_2.html#T61">SPPOL_2:61</a></i>;<br/>

<a NAME="E2:19_1_1"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K2">R^2-unit_square</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E3:19_1_1"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E4:19_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K2">R^2-unit_square</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:19_1_1"/>
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E6:19_1_1"/><b>then </b>
not  <a href="topreal1.html#K3">LSeg</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span> is <a href="sppol_1.html#V1">horizontal</a>
 
<b>by </b><i><a class="ref" href="sppol_1.html#T36">SPPOL_1:36</a></i>;<br/>
<b>hence </b><a NAME="E7:19_1_1"/>
not  <a href="topreal1.html#K2">R^2-unit_square</a>  is <a href="sppol_1.html#V1">horizontal</a>
 <b>by </b><i>, </i>;<br/>

<a NAME="E8:19_1_1"/>
 <a href="topreal1.html#K3">LSeg</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,0</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="topreal1.html#K3">LSeg</a> <span class="p2"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>,<span class="p2"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E9:19_1_1"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="topreal1.html#K3">LSeg</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span> <a href="tarski.html#R1">c=</a>  <a href="topreal1.html#K2">R^2-unit_square</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E10:19_1_1"/>
( <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E11:19_1_1"/><b>then </b>
not  <a href="topreal1.html#K3">LSeg</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default">0,1</span><a href="euclid.html#K23">]|</a></span>,<span class="p1"><a href="euclid.html#K23">|[</a><span class="default">1,1</span><a href="euclid.html#K23">]|</a></span> is <a href="sppol_1.html#V2">vertical</a>
 
<b>by </b><i><a class="ref" href="sppol_1.html#T37">SPPOL_1:37</a></i>;<br/>
<b>hence </b><a NAME="E12:19_1_1"/>
not  <a href="topreal1.html#K2">R^2-unit_square</a>  is <a href="sppol_1.html#V2">vertical</a>
 <b>by </b><i>, </i>;<br/>


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