<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a>  implies <font color="Maroon" title="c1">T</font> is  <a href="compl_sp.html#V8" title="COMPL_SP:attr.8">countably_compact</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:34"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c1">T</font> is  <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">T</font> is  <a href="compl_sp.html#V8" title="COMPL_SP:attr.8">countably_compact</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compl_sp.html#D9" target="_self" title="COMPL_SP:def.9">COMPL_SP:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">F</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Maroon" title="c2">F</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>  &amp; <font color="Maroon" title="c2">F</font> is  <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  implies  ex <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:34"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
<font color="Maroon" title="c2">F</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font>
 <span class="kw">and </span><br/><a NAME="E3:34"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c2">F</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a> 
 <span class="kw">and </span><br/><a NAME="E4:34"/>
<font color="Maroon" title="c2">F</font> is  <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:34"/>
 ex <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> &amp; <font color="Olive" title="b1">G</font> is   <a href="struct_0.html#NM13" title="STRUCT_0:NM.13">Cover</a> of <font color="Maroon" title="c1">T</font> &amp; <font color="Olive" title="b1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="compts_1.html#D1" title="COMPTS_1:def.1">COMPTS_1:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
