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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <a href="topmetr.html#K3">R^1</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:52"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="borsuk_5.html#K3">IRRAT</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="borsuk_5.html#K1">IRRAT</a>  as   <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="topmetr.html#T24">TOPMETR:24</a></i>;<br/>
<a NAME="E3:52"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <a href="borsuk_5.html#K1">IRRAT</a>  <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="txt" href="isomichi.html#E1:52"><i><font color="Green">E21</font></i></a>, <a class="ref" href="borsuk_5.html#D5">BORSUK_5:def 5</a></i>;<br/>
<a NAME="E4:52"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E5:52"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="tops_1.html#V2">boundary</a>
 
<b>by </b><i><a class="ref" href="topgen_1.html#T57">TOPGEN_1:57</a></i>;<br/>
<a NAME="E6:52"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="tops_1.html#V2">boundary</a>
 
<b>by </b><i><a class="txt" href="isomichi.html#E4:52"><i><font color="Green">E22</font></i></a>, <a class="ref" href="tops_3.html#T11">TOPS_3:11</a></i>;<br/>
<b>hence </b><a NAME="E7:52"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="tops_3.html#D1">TOPS_3:def 1</a></i>;<br/>


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