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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c3">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">p'</font> = <font color="Maroon" title="c3">p</font>;<br/>
<a NAME="E1:7"/>
not <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="ref" href="realset1.html#T4" title="REALSET1:th.4">REALSET1:4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">q</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:7"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">p</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E4:7"/>
<font color="Maroon" title="c5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="txt" href="borsuk_4.html#E3:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">q</font> = <font color="Maroon" title="c5">q</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c6">q</font>
;<br/>

<b>thus </b><a NAME="E6:7"/>
( <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c6">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p</font> )
 <b>by </b><i><a class="txt" href="borsuk_4.html#E3:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>


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