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<b>let </b><font color="Maroon">X</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">X0</font> be  non <a href="struct_0.html#V3">empty</a> <a href="tsp_2.html#NM1">maximal_Kolmogorov_subspace</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>





<b>reconsider </b><font color="Maroon">C</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>set </b><font color="Maroon">r</font> =  <a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">X</font>,<font color="Maroon">X0</font>;<br/>
<a NAME="E2:49"/>
<font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">B</font> = <span class="p1">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">X</font>,<font color="Maroon">X0</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:49"/><i><font color="Green">E17</font></i>: 
<span class="p1">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">X</font>,<font color="Maroon">X0</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">X</font>,<font color="Maroon">X0</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:49"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T50">FUNCT_2:50</a></i>;<br/>
<a NAME="E6:49"/>
<font color="Maroon">C</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:49"/><b>then </b>
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>hence </b><a NAME="E8:49"/>
<span class="p1">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">X</font>,<font color="Maroon">X0</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">X</font>,<font color="Maroon">X0</font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">A</font>
 <b>by </b><i>, , <a class="ref" href="tex_4.html#T37">TEX_4:37</a></i>;<br/>


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