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<b>let </b><font color="Maroon">S</font> be  non <a href="pencil_1.html#V3">void</a> non <a href="pencil_1.html#V4">degenerated</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/><b>let </b><font color="Maroon">L</font> be   <a href="pencil_1.html#NM1">Block</a> of <font color="Maroon">S</font>;<br/>



<a NAME="E1:5"/>
<font color="Maroon">L</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font>
 
;<br/>
<a NAME="E2:5"/><b>then </b>
<font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
;<br/>
<a NAME="E3:5"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">L</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D3">PRE_TOPC:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_1"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">L</font>
 ;<br/><a NAME="E2:5_1"/><b>then </b>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/><a NAME="E3:5_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> is   <a href="pencil_1.html#NM1">Block</a> of <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="pre_topc.html#D3">PRE_TOPC:def 3</a></i>;<br/><b>hence </b><a NAME="E4:5_1"/>
contradiction
 <b>by </b><i><a class="ref" href="pencil_1.html#D5">PENCIL_1:def 5</a></i>;<br/></div><b>end;</b></div>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:5"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> &amp; not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">x</font>
;<br/>

<b>thus </b><a NAME="E8:5"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font>
 <b>by </b><i/>;<br/>


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