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

<b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">s</font>,<font color="Olive">t</font></span><a href="borsuk_1.html#K7">]</a></span> where <font color="Olive">s</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Olive">t</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> : <font color="Olive">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">t</font> </span>}</span> ;<br/>
<a NAME="E1:1_1_1"/>
<span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">s</font>,<font color="Olive">t</font></span><a href="borsuk_1.html#K7">]</a></span> where <font color="Olive">s</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Olive">t</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> : <font color="Olive">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">t</font> </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">s</font>,<font color="Olive">t</font></span><a href="borsuk_1.html#K7">]</a></span> where <font color="Olive">s</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Olive">t</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> : <font color="Olive">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">t</font> </span>}</span> 
 ;<br/>

<a NAME="E2:1_1_1_1"/><b>then </b>
 ex <font color="Olive">s</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font> ex <font color="Olive">t</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">s</font>,<font color="Olive">t</font></span><a href="borsuk_1.html#K7">]</a></span> &amp; <font color="Olive">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">t</font> )
 
;<br/>
<b>hence </b><a NAME="E3:1_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:1_1_1"/>
<span class="p1">{<span class="default"> <span class="p2"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Olive">s</font>,<font color="Olive">t</font></span><a href="borsuk_1.html#K7">]</a></span> where <font color="Olive">s</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Olive">t</font> is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> : <font color="Olive">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">t</font> </span>}</span>  is   <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">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>
 ;<br/>


</div>
