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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></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">c<sub>1</sub></font>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></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">c<sub>4</sub></font> =  <a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<span class="p1">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tsp_2.html#D12" target="_self">Def12</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tex_4.html#T38">TEX_4:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="tex_4.html#K3">MaxADSet</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="tsp_2.html#D12" target="_self">Def12</a></i>
<br/>.= 
<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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K4">\/</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="tsp_2.html#D12" target="_self">Def12</a></i>
;<br/>
<b>hence </b><a NAME="E3:51"/>
<span class="p1">(<span class="default"><a href="tsp_2.html#K4" target="_self">Stone-retraction</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K4">\/</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/>


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