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<b>let </b><font color="Maroon" title="c3">B</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:23"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="arytm_2.html#K1" title="ARYTM_2:func.1">DEDEKIND_CUTS</a> 
 <b>and </b><br/><a NAME="E2:23"/><i><font color="Green" title="E23">A2</font></i>: 
<font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">B</font> = <font color="Maroon" title="c3">B</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="arytm_3.html#K5" title="ARYTM_3:func.5">RAT+</a>  <b>by </b><i><a class="txt" href="arytm_2.html#E1:23"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="arytm_2.html#E2:23"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/>
<a NAME="E4:23"/>
 ex <font color="Olive" title="b1">r</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>  st <font color="Olive" title="b1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<b>hence </b><a NAME="E5:23"/>
 <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="arytm_2.html#E1:23"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="arytm_2.html#E26"><i><font color="Green" title="E20">Lm16</font></i></a>, <a class="ref" href="arytm_3.html#T71" title="ARYTM_3:th.71">ARYTM_3:71</a></i>;<br/>


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