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<b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:63"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">p</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K10" target="_self">c[-10]</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:63"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E3:63"/>
<font color="Maroon">p</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K8" target="_self">Tunit_circle</a> 2</span>)</span>
 
<b>by </b><i>, <a class="ref" href="topmetr.html#T2">TOPMETR:2</a></i>;<br/>
<b>then </b>1 <a href="square_1.html#K5">^2</a>  = 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">p</font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a> 
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K21">`1</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="euclid.html#K22">`2</a> </span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>
;<br/>
<a NAME="E5:63"/><b>then </b><i><font color="Green">E68</font></i>: 
( <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1 )
 
<b>by </b><i>, <a class="ref" href="square_1.html#T110">SQUARE_1:110</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:63_2"/>
<font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/><a NAME="E2:63_2"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K10" target="_self">c[-10]</a> 
 <b>by </b><i>, <a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/><b>hence </b><a NAME="E3:63_2"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:63"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K9" target="_self">c[10]</a> 
 <b>by </b><i>, , <a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/>


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