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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="measure5.html#NM1">Interval</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:51"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:51"/><b>then </b><i><font color="Green">E39</font></i>: 
( (  <a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a> </span>)</span></span><a href="measure5.html#K2">.[</a></span> ) or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a> </span>)</span></span><a href="measure5.html#K3">.]</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a> </span>)</span></span><a href="measure5.html#K1">.]</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a> </span>)</span></span><a href="measure5.html#K4">.[</a></span> )
 
<b>by </b><i><a class="ref" href="measure6.html#T52" target="_self">Th52</a></i>;<br/>
<a NAME="E3:51"/>
 <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="measure6.html#E1:51"><i><font color="Green">E38</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:51"/>
(  <a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a>  )
 <b>by </b><i><a class="txt" href="measure6.html#E2:51"><i><font color="Green">E39</font></i></a>, <a class="ref" href="measure5.html#D1">MEASURE5:def 1</a>, <a class="ref" href="measure5.html#D2">MEASURE5:def 2</a>, <a class="ref" href="measure5.html#D3">MEASURE5:def 3</a>, <a class="ref" href="measure5.html#D4">MEASURE5:def 4</a></i>;<br/>


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