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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>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>











<b>assume </b><a NAME="E1:23"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>6</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="tsep_1.html#K1">union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span><b> such that </b><br/><a NAME="E3:23"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="tmap_1.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="ref" href="tmap_1.html#T20" target="_self">Th20</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="tmap_1.html#E3:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="connsp_2.html#T5">CONNSP_2:5</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>10</sub></font>
;<br/>

<b>thus </b><a NAME="E5:23"/>
<font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="tmap_1.html#E3:23"><i><font color="Green">E20</font></i></a></i>;<br/>


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