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<b>let </b><font color="Maroon">s1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> , <font color="Maroon">t1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> , <font color="Maroon">s2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_3.html#K7" target="_self">RAT+</a> , <font color="Maroon">t2</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="E1:110"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">s1</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">t2</font>
 ;<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="E2:110"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</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>take </b>
<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/>

<a NAME="E3:110"/>
<font color="Maroon">s1</font> <a href="arytm_3.html#K11" target="_self">+</a> <font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</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">t2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="arytm_3.html#E45"><i><font color="Green">Lemma86</font></i></a>, , <a class="ref" href="arytm_3.html#T17" target="_self">Th17</a></i>;<br/>
<b>hence </b><a NAME="E4:110"/>
<font color="Maroon">t1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t2</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#T24" target="_self">Th24</a></i>;<br/>


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