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<b>let </b><font color="Maroon">r</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">s</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="E1:117"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">r</font> <a href="arytm_3.html#NR4" target="_self">&lt;</a> <font color="Maroon">s</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</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="E3:117"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T23" target="_self">Th23</a></i>;<br/>
<b>consider </b><font color="Maroon">y</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="E5:117"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T22" target="_self">Th22</a></i>;<br/>
<b>take </b><font color="Maroon">t</font> = <font color="Maroon">r</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">y</font>;<br/>

<a NAME="E6:117"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="arytm_3.html#T34" target="_self">Th34</a>, <a class="ref" href="arytm_3.html#T17" target="_self">Th17</a></i>;<br/>
<a NAME="E7:117"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">s</font> &amp; <font color="Maroon">t</font> <a href="arytm_3.html#K11" target="_self">+</a> <a href="arytm_3.html#K13" target="_self">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">r</font> <a href="arytm_3.html#K11" target="_self">+</a> <a href="arytm_3.html#K13" target="_self">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <a href="arytm_3.html#K13" target="_self">{}</a>  <a href="arytm_3.html#K11" target="_self">+</a> <a href="arytm_3.html#K13" target="_self">{}</a>  <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K13" target="_self">{}</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:117"/>
( <font color="Maroon">r</font> <a href="arytm_3.html#R3" target="_self">&lt;='</a> <font color="Maroon">t</font> &amp; <font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, , <a class="ref" href="arytm_3.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E9:117"/>
<font color="Maroon">r</font> <a href="arytm_3.html#NR4" target="_self">&lt;</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T26" target="_self">Th26</a></i>;<br/>

<a NAME="E10:117"/>
( <font color="Maroon">t</font> <a href="arytm_3.html#R3" target="_self">&lt;='</a> <font color="Maroon">s</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="arytm_3.html#T35" target="_self">Th35</a>, <a class="ref" href="arytm_3.html#T23" target="_self">Th23</a>, <a class="ref" href="arytm_3.html#T24" target="_self">Th24</a></i>;<br/>
<b>hence </b><a NAME="E11:117"/>
<font color="Maroon">t</font> <a href="arytm_3.html#NR4" target="_self">&lt;</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T26" target="_self">Th26</a></i>;<br/>


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