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

<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:63_1_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="roughs_1.html#T4" target="_self">Th4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/>
<a NAME="E3:63_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:63_1_1"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="roughs_1.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E5:63_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K4" target="_self">UAp</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="roughs_1.html#E2:63_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="roughs_1.html#E3:63_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="roughs_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E6:63_1_1"/><b>then </b>
 <a href="roughs_1.html#K4" target="_self">UAp</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="roughs_1.html#E2:63_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:63_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> is <a href="roughs_1.html#V4" target="_self">rough</a>
 
<b>by </b><i><a class="ref" href="roughs_1.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E8:63_1_1"/>
ex <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="roughs_1.html#V4" target="_self">rough</a>
 ;<br/>


</div>
