<?xml version="1.0"?>
<div class="add">

<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="pre_topc.html#NM2">Point</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 <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="borsuk_1.html#K5">:]</a></span>;<br/>







<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:52_1"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="connsp_2.html#M2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span></span><a href="borsuk_1.html#K6">:]</a></span>
 ;<br/><a NAME="E2:52_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is    <a href="connsp_2.html#M2">a_neighborhood</a> of <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T35">ZFMISC_1:35</a></i>;<br/><b>hence </b><a NAME="E3:52_1"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="connsp_2.html#M1">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 <b>by </b><i><a class="ref" href="connsp_2.html#T10">CONNSP_2:10</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:52"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="connsp_2.html#M1">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K7">]</a></span>
 ;<br/>

<a NAME="E3:52"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is    <a href="connsp_2.html#M2">a_neighborhood</a> of <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="connsp_2.html#T10">CONNSP_2:10</a></i>;<br/>
<b>hence </b><a NAME="E4:52"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="connsp_2.html#M2">a_neighborhood</a> of <span class="p1"><a href="borsuk_1.html#K6">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span></span><a href="borsuk_1.html#K6">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T35">ZFMISC_1:35</a></i>;<br/>


</div>
