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<b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:41"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="arytm_2.html#K2" target="_self">REAL+</a> 
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <a href="arytm_3.html#K7">RAT+</a>  <a href="xboole_0.html#K2">\/</a> <a href="arytm_2.html#K1" target="_self">DEDEKIND_CUTS</a> 
 
;<br/>
<a NAME="E3:41"/><b>then </b>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="arytm_3.html#K7">RAT+</a>  or <font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="arytm_2.html#K1" target="_self">DEDEKIND_CUTS</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:41"/>
<font color="Maroon">e</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="arytm_3.html#K7">RAT+</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>


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