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<b>let </b><font color="Maroon" title="c1">GX</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>;<br/>



<b>assume </b><a NAME="E1:103"/><i><font color="Green" title="E64">A1</font></i>: 
<font color="Maroon" title="c2">R</font> is <a href="tops_1.html#V6" title="TOPS_1:attr.6">open_condensed</a>
 ;<br/>

<a NAME="E2:103"/><b>then </b><i><font color="Green" title="E65">A2</font></i>: 
<font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tops_1.html#D8" target="_self" title="TOPS_1:def.8">Def8</a></i>;<br/>
<i><font color="Green" title="E66">A3</font></i>:  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c2">R</font> = 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c2">R</font></span>)</span>
<b>by </b><i><a class="txt" href="tops_1.html#E82"><i><font color="Green" title="E39">Lm6</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="tops_1.html#E2:103"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="tops_1.html#T26" target="_self" title="TOPS_1:th.26">Th26</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tops_1.html#T45" target="_self" title="TOPS_1:th.45">Th45</a></i>
<br/>.= 
 <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span>
<b>by </b><i><a class="txt" href="tops_1.html#E82"><i><font color="Green" title="E39">Lm6</font></i></a></i>
;<br/>
 <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="tops_1.html#E82"><i><font color="Green" title="E39">Lm6</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tops_1.html#T26" target="_self" title="TOPS_1:th.26">Th26</a></i>
;<br/>
<b>hence </b><a NAME="E5:103"/>
(  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span> &amp;  <a href="tops_1.html#K2" title="TOPS_1:func.2">Fr</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">R</font> )
 <b>by </b><i><a class="txt" href="tops_1.html#E1:103"><i><font color="Green" title="E64">A1</font></i></a>, <a class="txt" href="tops_1.html#E3:103"><i><font color="Green" title="E66">A3</font></i></a>, <a class="ref" href="tops_1.html#D8" target="_self" title="TOPS_1:def.8">Def8</a></i>;<br/>


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