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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</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="Olive" title="b1">P</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a>  &amp; <font color="Olive" title="b2">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a>  holds <br/><font color="Olive" title="b1">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</font>, <font color="Maroon" title="c3">Q</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">P</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a>  &amp; <font color="Maroon" title="c3">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a>  implies <font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a>  )</span><br/>





<a NAME="E1:135"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T54" title="XBOOLE_1:th.54">XBOOLE_1:54</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:135"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
<font color="Maroon" title="c2">P</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a> 
 <span class="kw">and </span><br/><a NAME="E3:135"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
<font color="Maroon" title="c3">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</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">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a> </span><br/>

<a NAME="E4:135"/><span class="lab"><font color="Green" title="E57">A4</font></span>: 
<font color="Maroon" title="c3">Q</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:135"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="ref" href="tops_1.html#T101" target="_self" title="TOPS_1:th.101">Th101</a></span>;<br/>
<a NAME="E5:135"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is  <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:135"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="tops_1.html#T101" target="_self" title="TOPS_1:th.101">Th101</a></span>;<br/>
<a NAME="E6:135"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">Q</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> is  <a href="tops_1.html#V5" title="TOPS_1:attr.5">closed_condensed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:135"><span class="lab"><font color="Green" title="E57">A4</font></span></a>, <a class="ref" href="tops_1.html#T108" target="_self" title="TOPS_1:th.108">Th108</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:135"/>
<font color="Maroon" title="c2">P</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">Q</font> is  <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:135"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="ref" href="tops_1.html#T101" target="_self" title="TOPS_1:th.101">Th101</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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