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<b>let </b><font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">RAT+</a> ;<br/>



<b>given </b><font color="Maroon" title="c5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">RAT+</a> <b> such that </b><a NAME="E2:94"/><i><font color="Green" title="E77">A1</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">+</a> <font color="Maroon" title="c5">x</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="arytm_3.html#D13" target="_self" title="ARYTM_3:def.13">ARYTM_3:def 13</a><br/>

<b>given </b><font color="Maroon" title="c6">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K7" title="ARYTM_3:func.7">RAT+</a> <b> such that </b><a NAME="E4:94"/><i><font color="Green" title="E78">A2</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">+</a> <font color="Maroon" title="c6">y</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="arytm_3.html#D13" target="_self" title="ARYTM_3:def.13">ARYTM_3:def 13</a><br/>

<font color="Maroon" title="c3">r</font> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">+</a> <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  = 
<font color="Maroon" title="c3">r</font>
<b>by </b><i><a class="ref" href="arytm_3.html#T56" target="_self" title="ARYTM_3:th.56">Th56</a></i>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">x</font> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">+</a> <font color="Maroon" title="c6">y</font></span>)</span>
<b>by </b><i><a class="txt" href="arytm_3.html#E2:94"><i><font color="Green" title="E77">A1</font></i></a>, <a class="txt" href="arytm_3.html#E4:94"><i><font color="Green" title="E78">A2</font></i></a>, <a class="ref" href="arytm_3.html#T57" target="_self" title="ARYTM_3:th.57">Th57</a></i>
;<br/>
<a NAME="E6:94"/><b>then </b>
 <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> <a href="arytm_3.html#K11" title="ARYTM_3:func.11">+</a> <font color="Maroon" title="c6">y</font>
 
<b>by </b><i><a class="ref" href="arytm_3.html#T69" target="_self" title="ARYTM_3:th.69">Th69</a></i>;<br/>
<a NAME="E7:94"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 
<b>by </b><i><a class="ref" href="arytm_3.html#T70" target="_self" title="ARYTM_3:th.70">Th70</a></i>;<br/>
<b>hence </b><a NAME="E8:94"/>
<font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font>
 <b>by </b><i><a class="txt" href="arytm_3.html#E2:94"><i><font color="Green" title="E77">A1</font></i></a>, <a class="ref" href="arytm_3.html#T56" target="_self" title="ARYTM_3:th.56">Th56</a></i>;<br/>


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