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<b>let </b><font color="Maroon">S</font> be  non <a href="pencil_1.html#V3" target="_self">void</a>  <a href="pre_topc.html#L1">TopStruct</a> ;<br/>

<b>thus </b><a NAME="E1:59"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> is <a href="pencil_1.html#V1" target="_self">closed_under_lines</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">K</font> be   <a href="pencil_1.html#NM1">Block</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D2" target="_self">PENCIL_1:def 2</a><br/>

<b>assume </b><a NAME="E1:59_1"/>
2 <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:59_1"/>
<font color="Maroon">K</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="E3:59_1"/><b>then </b>
<font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
;<br/>
<b>hence </b><a NAME="E4:59_1"/>
<font color="Maroon">K</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#T12">PRE_TOPC:12</a></i>;<br/>


</div><b>end;</b></div>


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