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

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> ;<br/>





<b>assume </b><a NAME="E1:82"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="arytm_3.html#K13" target="_self">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">r</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> <b> such that </b><br/><a NAME="E3:82"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i/>;<br/>
<a NAME="E4:82"/>
( <font color="Maroon">r</font> <a href="arytm_3.html#K12" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="arytm_3.html#K14" target="_self">one</a>  <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">y</font> &amp; <font color="Maroon">r</font> <a href="arytm_3.html#K12" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <a href="arytm_3.html#K14" target="_self">one</a>  <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">z</font> )
 
<b>by </b><i><a class="ref" href="arytm_3.html#T20" target="_self">Th20</a>, <a class="ref" href="arytm_3.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E5:82"/><b>then </b>
( <font color="Maroon">r</font> <a href="arytm_3.html#K12" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">r</font> <a href="arytm_3.html#K12" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 
<b>by </b><i><a class="ref" href="arytm_3.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E6:82"/>
(  not <font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="arytm_3.html#K12" target="_self">*'</a> <font color="Maroon">z</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/>


</div>
