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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds <br/> ( <font color="Olive" title="b1">A</font> is  <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a>  iff (  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b1">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  &amp;  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A</font> is  <a href="isomichi.html#NV5" title="ISOMICHI:NV.5">regular_closed</a>  &amp;  <a href="isomichi.html#K1" title="ISOMICHI:func.1">Border</a> <font color="Olive" title="b1">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a>  iff (  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  &amp;  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV5" title="ISOMICHI:NV.5">regular_closed</a>  &amp;  <a href="isomichi.html#K1" title="ISOMICHI:func.1">Border</a> <font color="Maroon" title="c2">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  ) )</span><br/>



<span class="kw">thus </span><a NAME="E1:48"/>
( <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a>  implies (  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  &amp;  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV5" title="ISOMICHI:NV.5">regular_closed</a>  &amp;  <a href="isomichi.html#K1" title="ISOMICHI:func.1">Border</a> <font color="Maroon" title="c2">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isomichi.html#T25" target="_self" title="ISOMICHI:th.25">Th25</a>, <a class="ref" href="isomichi.html#T26" target="_self" title="ISOMICHI:th.26">Th26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a>  &amp;  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV5" title="ISOMICHI:NV.5">regular_closed</a>  &amp;  <a href="isomichi.html#K1" title="ISOMICHI:func.1">Border</a> <font color="Maroon" title="c2">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:48"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV4" title="ISOMICHI:NV.4">regular_open</a> 
 <span class="kw">and </span><br/><a NAME="E3:48"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#NV5" title="ISOMICHI:NV.5">regular_closed</a> 
 <span class="kw">and </span><br/><a NAME="E4:48"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
 <a href="isomichi.html#K1" title="ISOMICHI:func.1">Border</a> <font color="Maroon" title="c2">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a> </span><br/>

<a NAME="E5:48"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V2" title="ISOMICHI:attr.2">subcondensed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="isomichi.html#T26" target="_self" title="ISOMICHI:th.26">Th26</a></span>;<br/>
<a NAME="E6:48"/>
<font color="Maroon" title="c2">A</font> is  <a href="isomichi.html#V1" title="ISOMICHI:attr.1">supercondensed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:48"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="isomichi.html#T25" target="_self" title="ISOMICHI:th.25">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:48"/>
<font color="Maroon" title="c2">A</font> is  <a href="tops_1.html#V4" title="TOPS_1:attr.4">condensed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E20">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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