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<b>let </b><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">t1</font>, <font color="Maroon" title="c5">s2</font>, <font color="Maroon" title="c6">t2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> ;<br/>

<b>assume </b><a NAME="E1:99"/><i><font color="Green" title="E80">A1</font></i>: 
<font color="Maroon" title="c3">s1</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c4">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s2</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c6">t2</font>
 ;<br/>

<b>given </b><font color="Maroon" title="c7">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a> <b> such that </b><a NAME="E3:99"/><i><font color="Green" title="E81">A2</font></i>: 
<font color="Maroon" title="c5">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c7">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>take </b>
<font color="Maroon" title="c7">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/>

<a NAME="E4:99"/>
<font color="Maroon" title="c3">s1</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c4">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">x</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c6">t2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="arytm_3.html#E1:99"><i><font color="Green" title="E80">A1</font></i></a>, <a class="txt" href="arytm_3.html#E3:99"><i><font color="Green" title="E81">A2</font></i></a>, <a class="ref" href="arytm_3.html#T57" target="_self" title="ARYTM_3:th.57">Th57</a></i>;<br/>
<b>hence </b><a NAME="E5:99"/>
<font color="Maroon" title="c4">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t2</font> <a href="arytm_3.html#K9" title="ARYTM_3:func.9">+</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="ref" href="arytm_3.html#T69" target="_self" title="ARYTM_3:th.69">Th69</a></i>;<br/>


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