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<b>let </b><font color="Maroon" title="c3">r</font>, <font color="Maroon" title="c4">s</font>, <font color="Maroon" title="c5">t</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="c6">t0</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="E2:111"/><i><font color="Green" title="E86">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="c6">t0</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>assume </b><a NAME="E3:111"/>
<font color="Maroon" title="c4">s</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</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">t</font>
 ;<br/>

<a NAME="E4:111"/><b>then </b>
<font color="Maroon" title="c6">t0</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c5">t</font>
 
<b>by </b><i><a class="txt" href="arytm_3.html#E2:111"><i><font color="Green" title="E86">A1</font></i></a>, <a class="ref" href="arytm_3.html#T83" target="_self" title="ARYTM_3:th.83">Th83</a></i>;<br/>
<b>hence </b><a NAME="E5:111"/>
 ex <font color="Olive" title="b1">t0</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>  st <br/>( <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="Olive" title="b1">t0</font> &amp; <font color="Olive" title="b1">t0</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c5">t</font> )
 <b>by </b><i><a class="txt" href="arytm_3.html#E2:111"><i><font color="Green" title="E86">A1</font></i></a></i>;<br/>


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