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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:46"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:46_1"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a>  or <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span> or <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span></span>)</span> )
 </span><b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_1"><b>suppose </b></a><a NAME="E1:46_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 ;<br/><div class="add"><a NAME="E2:46_1_1"/><i><font color="Green">E35</font></i>: 
not 0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">1</span><a href="seq_4.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:46_1_1"/>
not 0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default">2</span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span>
 <b>by </b><i><a class="ref" href="borsuk_5.html#T15">BORSUK_5:15</a></i>;<br/><b>hence </b><a NAME="E4:46_1_1"/>
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i>, , , <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_2"><b>suppose </b></a><a NAME="E1:46_1_2"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_1_2"/>
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i>, <a class="ref" href="borsuk_5.html#T72">BORSUK_5:72</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_1_3"><b>suppose </b></a><a NAME="E1:46_1_3"/>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span></span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:46_1_3"/>
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="kurato_1.html#E1:46"><i><font color="Green">E26</font></i></a>, <a class="ref" href="borsuk_5.html#T72">BORSUK_5:72</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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