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<b>let </b><font color="Maroon" title="c3">r1</font>, <font color="Maroon" title="c4">r2</font>, <font color="Maroon" title="c5">s1</font>, <font color="Maroon" title="c6">s2</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>assume </b><a NAME="E1:108"/><i><font color="Green" title="E85">A1</font></i>: 
<font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c4">r2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font>
 ;<br/>

<b>assume </b><a NAME="E2:108"/><i><font color="Green" title="E86">A2</font></i>: 
( <font color="Maroon" title="c5">s1</font> <a href="arytm_3.html#NR4" title="ARYTM_3:NR.4">&lt;</a> <font color="Maroon" title="c3">r1</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="arytm_3.html#NR4" title="ARYTM_3:NR.4">&lt;</a> <font color="Maroon" title="c4">r2</font> )
 ;<br/>

<a NAME="E3:108"/><b>then </b><i><font color="Green" title="E87">A3</font></i>: 
( <font color="Maroon" title="c5">s1</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c3">r1</font> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">r1</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c4">r2</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">r2</font> )
 
;<br/>
<a NAME="E4:108"/>
(  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c5">s1</font> &amp;  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c6">s2</font> )
 
<b>by </b><i><a class="ref" href="arytm_3.html#T71" target="_self" title="ARYTM_3:th.71">Th71</a></i>;<br/>
<a NAME="E5:108"/><b>then </b>
<font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c4">r2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a> 
 
<b>by </b><i><a class="txt" href="arytm_3.html#E2:108"><i><font color="Green" title="E86">A2</font></i></a>, <a class="ref" href="arytm_3.html#T86" target="_self" title="ARYTM_3:th.86">Th86</a></i>;<br/>
<a NAME="E6:108"/><b>then </b>
( <font color="Maroon" title="c5">s1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  &amp; <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K13" title="ARYTM_3:func.13">{}</a>  )
 
<b>by </b><i><a class="txt" href="arytm_3.html#E1:108"><i><font color="Green" title="E85">A1</font></i></a>, <a class="ref" href="arytm_3.html#T54" target="_self" title="ARYTM_3:th.54">Th54</a></i>;<br/>
<a NAME="E7:108"/><b>then </b>
( <font color="Maroon" title="c5">s1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> &amp; <font color="Maroon" title="c5">s1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> )
 
<b>by </b><i><a class="txt" href="arytm_3.html#E3:108"><i><font color="Green" title="E87">A3</font></i></a>, <a class="ref" href="arytm_3.html#T62" target="_self" title="ARYTM_3:th.62">Th62</a>, <a class="ref" href="arytm_3.html#T90" target="_self" title="ARYTM_3:th.90">Th90</a></i>;<br/>
<a NAME="E8:108"/><b>then </b>
( <font color="Maroon" title="c5">s1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> <a href="arytm_3.html#NR4" title="ARYTM_3:NR.4">&lt;</a> <font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> &amp; <font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c6">s2</font> <a href="arytm_3.html#R3" title="ARYTM_3:pred.3">&lt;='</a> <font color="Maroon" title="c3">r1</font> <a href="arytm_3.html#K12" title="ARYTM_3:func.12">*'</a> <font color="Maroon" title="c4">r2</font> )
 
<b>by </b><i><a class="txt" href="arytm_3.html#E2:108"><i><font color="Green" title="E86">A2</font></i></a>, <a class="ref" href="arytm_3.html#T73" target="_self" title="ARYTM_3:th.73">Th73</a>, <a class="ref" href="arytm_3.html#T90" target="_self" title="ARYTM_3:th.90">Th90</a></i>;<br/>
<b>hence </b><a NAME="E9:108"/>
contradiction
 <b>by </b><i><a class="txt" href="arytm_3.html#E1:108"><i><font color="Green" title="E85">A1</font></i></a></i>;<br/>


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