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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>given </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><a NAME="E1:94"/><i><font color="Green">E13</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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="arytm_3.html#D13" target="_self">ARYTM_3:def 13</a><br/>

<b>given </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><a NAME="E2:94"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">y</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="arytm_3.html#D13" target="_self">ARYTM_3:def 13</a><br/>

<font color="Maroon">r</font> <a href="arytm_3.html#K11" target="_self">+</a> <a href="arytm_3.html#K13" target="_self">{}</a>  = 
<font color="Maroon">r</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">r</font> <a href="arytm_3.html#K11" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="arytm_3.html#T27" target="_self">Th27</a>, <a class="ref" href="arytm_3.html#T28" target="_self">Th28</a>, <a class="ref" href="arytm_3.html#T17" target="_self">Th17</a></i>
;<br/>
<a NAME="E4:94"/><b>then </b>
 <a href="arytm_3.html#K13" target="_self">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</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#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E5:94"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K13" target="_self">{}</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:94"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T27" target="_self">Th27</a>, </i>;<br/>


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