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<b>let </b><font color="Maroon">r</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">s</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font>
 ;<br/>

<b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:22"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c</font> = <font color="Maroon">c</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E5:22"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">b</font> )
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E6:22"/><b>then </b>
( <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font> )
 
<b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E7:22"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/>


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