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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:44"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></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="tops_1.html#K1">Int</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<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 class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<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>)</span></span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<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><b>by </b><i><a class="txt" href="kurato_1.html#E1:44"><i><font color="Green">E38</font></i></a>, <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="44_1_1"><b>suppose </b></a><a NAME="E1:44_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:44_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is  non <a href="xboole_0.html#V1">empty</a> <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> 
 <b>by </b><i><a class="ref" href="kurato_1.html#T20" target="_self">Th20</a>, <a class="ref" href="tops_1.html#D1">TOPS_1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_2"><b>suppose </b></a><a NAME="E1:44_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <a href="kurato_1.html#K6" target="_self">KurExSet</a> </span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:44_1_2"/>
<font color="Maroon">c<sub>1</sub></font> is  non <a href="xboole_0.html#V1">empty</a> <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> 
 <b>by </b><i><a class="ref" href="kurato_1.html#T28" target="_self">Th28</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_3"><b>suppose </b></a><a NAME="E1:44_1_3"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<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>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:44_1_3"/>
<font color="Maroon">c<sub>1</sub></font> is  non <a href="xboole_0.html#V1">empty</a> <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> 
 <b>by </b><i><a class="ref" href="kurato_1.html#T27" target="_self">Th27</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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