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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="measure5.html#NM1">Interval</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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="E1:52"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:52"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="measure6.html#K5" target="_self">^^</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:52"/>
(  <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>3</sub></font> &amp;  <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>3</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;  <a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>2</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>4</sub></font> &amp;  <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K5" target="_self">^^</a>  )
 
<b>by </b><i><a class="txt" href="measure6.html#E1:52"><i><font color="Green">E39</font></i></a>, <a class="ref" href="measure6.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E4:52"/><b>then </b>
(  <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="measure6.html#K4" target="_self">^^</a> <font color="Maroon">c<sub>2</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>4</sub></font> )
 
<b>by </b><i><a class="txt" href="measure6.html#E2:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/>
<a NAME="E5:52"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="measure6.html#K1" target="_self">R_EAL</a> <font color="Maroon">c<sub>3</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>4</sub></font>
 
<b>by </b><i><a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="supinf_1.html#NM3">R_eal</a> <b>by </b><i><a class="ref" href="supinf_1.html#T10">SUPINF_1:10</a></i>;<br/>
<a NAME="E8:52"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="measure6.html#E5:52"><i><font color="Green">E41</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:52"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


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