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<b>let </b><font color="Maroon" title="c2">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies ( <font color="Maroon" title="c2">S</font> is <a href="tops_1.html#V6" title="TOPS_1:attr.6">regular_open</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">regular_closed</a> ) )</span><br/>

<b>assume </b><a NAME="E1:22_1_1"/><i><font color="Green" title="E11">Z</font></i>: 
<font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">S</font> is <a href="tops_1.html#V6" title="TOPS_1:attr.6">regular_open</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">regular_closed</a> )</span><br/>

<a NAME="E2:22_1_1"/><b>then </b><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="pcomps_1.html#T2" title="PCOMPS_1:th.2">PCOMPS_1:2</a></i>;<br/>
<a NAME="E3:22_1_1"/>
<font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="#E1:22_1_1"><i><font color="Green" title="E11">Z</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:22_1_1"/>
( <font color="Maroon" title="c2">S</font> is <a href="tops_1.html#V6" title="TOPS_1:attr.6">regular_open</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="tops_1.html#V5" title="TOPS_1:attr.5">regular_closed</a> )
 <b>by </b><i><a class="txt" href="#E2:22_1_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="tops_1.html#D7" title="TOPS_1:def.7">TOPS_1:def 7</a>, <a class="ref" href="tops_1.html#D8" title="TOPS_1:def.8">TOPS_1:def 8</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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