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<b>let </b><font color="Maroon" title="c1">TS</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">PS</font>, <font color="Olive" title="b2">QS</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>  st <font color="Maroon" title="c1">TS</font> is <a href="pre_topc.html#V8" title="PRE_TOPC:attr.8">Hausdorff</a> &amp; <font color="Olive" title="b1">PS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> &amp; <font color="Olive" title="b2">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> holds <br/><font color="Olive" title="b1">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a></span><br/><b>let </b><font color="Maroon" title="c2">PS</font>, <font color="Maroon" title="c3">QS</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">TS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">TS</font> is <a href="pre_topc.html#V8" title="PRE_TOPC:attr.8">Hausdorff</a> &amp; <font color="Maroon" title="c2">PS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> &amp; <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> implies <font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )</span><br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E12">A1</font></i>: 
( <font color="Maroon" title="c1">TS</font> is <a href="pre_topc.html#V8" title="PRE_TOPC:attr.8">Hausdorff</a> &amp; <font color="Maroon" title="c2">PS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> &amp; <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a></span><br/>

<a NAME="E2:16"/><b>then </b>
( <font color="Maroon" title="c2">PS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> &amp; <font color="Maroon" title="c3">QS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> )
 
<b>by </b><i><a class="ref" href="compts_1.html#T16" target="_self" title="COMPTS_1:th.16">Th16</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
<font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T35" title="TOPS_1:th.35">TOPS_1:35</a></i>;<br/>
<b>hence </b><a NAME="E4:16"/>
<font color="Maroon" title="c2">PS</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">QS</font> is <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>
 <b>by </b><i><a class="txt" href="#E1:16"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="compts_1.html#T18" target="_self" title="COMPTS_1:th.18">Th18</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</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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