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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</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>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="t_0topsp.html#D2">T_0TOPSP:def 2</a><br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>



<a NAME="E2:31"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="topgrp_1.html#E1:31"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E3:31"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D1">CONNSP_2:def 1</a></i>;<br/>
<a NAME="E4:31"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> as  <a href="pre_topc.html#V3">open</a>  <a href="connsp_2.html#M1">a_neighborhood</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="topgrp_1.html#E2:31"><i><font color="Green">E23</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>6</sub></font>
;<br/>

<a NAME="E6:31"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="tops_1.html#T44">TOPS_1:44</a></i>;<br/>
<b>hence </b><a NAME="E7:31"/>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#T156">RELAT_1:156</a></i>;<br/>


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