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<b>let </b><font color="Maroon">x</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><a NAME="E1:65"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">x</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#K9" target="_self">c[10]</a> </span>)</span>
 ;<br/>

<a NAME="E2:65"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">x</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:65_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">x</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:65_1"/><i><font color="Green">E69</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K8" target="_self">Tunit_circle</a> 2</span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="toprealb.html#K9" target="_self">c[10]</a> </span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E3:65_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</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="txt" href="toprealb.html#E4"><i><font color="Green">Lemma41</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:65_1"/><i><font color="Green">E72</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="toprealb.html#K9" target="_self">c[10]</a> </span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="toprealb.html#E4"><i><font color="Green">Lemma41</font></i></a>, , <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:65_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K21">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="euclid.html#K22">`2</a> </span>)</span></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="ref" href="euclid.html#T57">EUCLID:57</a></i>;<br/><a NAME="E6:65_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K9" target="_self">c[10]</a> 
 <b>by </b><i><a class="txt" href="toprealb.html#E6"><i><font color="Green">Lemma43</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E7:65_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:65"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">x</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i><a class="txt" href="toprealb.html#E4"><i><font color="Green">Lemma41</font></i></a>, <a class="txt" href="toprealb.html#E5"><i><font color="Green">Lemma42</font></i></a>, , <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>


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