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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">x0</font>, <font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c4">T</font> =  <a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font>;<br/>
<a NAME="E1:39"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="topgen_2.html#D5" target="_self" title="TOPGEN_2:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E2:39"/>
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="topgen_2.html#K5" title="TOPGEN_2:func.5">DiscrWithInfin</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">x0</font></span>)</span> )
 <b>by </b><i><a class="ref" href="topgen_2.html#T22" target="_self" title="TOPGEN_2:th.22">Th22</a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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