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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<i><font color="Green">E35</font></i>:  <a href="tops_1.html#K2" target="_self">Fr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pre_topc.html#T50">PRE_TOPC:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T53">XBOOLE_1:53</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
;<br/>
<a NAME="E2:51"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E3:51"/><b>then </b>
(  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> &amp;  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#T49">PRE_TOPC:49</a></i>;<br/>
<a NAME="E4:51"/><b>then </b>
( <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E5:51"/><b>then </b>
 <a href="tops_1.html#K2" target="_self">Fr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="tops_1.html#E1:51"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E6:51"/><b>then </b>
 <a href="tops_1.html#K2" target="_self">Fr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="tops_1.html#K2" target="_self">Fr</a> <font color="Maroon">c<sub>2</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="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E7:51"/>
 <a href="tops_1.html#K2" target="_self">Fr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="tops_1.html#K2" target="_self">Fr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="tops_1.html#K2" target="_self">Fr</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>


</div>
