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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="measure5.html#NM1" title="MEASURE5:NM.1">Interval</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>;<br/><b>let </b><font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c6">e</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:37"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="measure5.html#K4" title="MEASURE5:func.4">[.</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="measure5.html#K4" title="MEASURE5:func.4">.[</a></span>
 <b>and </b><br/><a NAME="E2:37"/><i><font color="Green" title="E26">A2</font></i>: 
( <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> )
 <b>and </b><br/><a NAME="E3:37"/><i><font color="Green" title="E27">A3</font></i>: 
( <font color="Maroon" title="c4">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">e</font> &amp; <font color="Maroon" title="c6">e</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">d</font> )
 ;<br/>

<a NAME="E4:37"/>
( <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  &amp; <font color="Maroon" title="c6">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">c</font> = <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c8">e</font> = <font color="Maroon" title="c6">e</font>, <font color="Maroon" title="c9">d</font> = <font color="Maroon" title="c5">d</font> as   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a> ;<br/>
<a NAME="E6:37"/><i><font color="Green" title="E28">A4</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d</font> &amp; <font color="Maroon" title="c9">d</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c9">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 
<b>by </b><i><a class="txt" href="measure6.html#E1:37"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="measure6.html#E2:37"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="measure5.html#D4" title="MEASURE5:def.4">MEASURE5:def 4</a></i>;<br/>
<a NAME="E7:37"/>
( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c7">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">e</font> &amp; <font color="Maroon" title="c8">e</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">d</font> &amp; <font color="Maroon" title="c9">d</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="measure6.html#E1:37"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="measure6.html#E2:37"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="measure6.html#E3:37"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="measure5.html#D4" title="MEASURE5:def.4">MEASURE5:def 4</a></i>;<br/>
<a NAME="E8:37"/><b>then </b><i><font color="Green" title="E29">A5</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">e</font> &amp; <font color="Maroon" title="c8">e</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E9:37"/>
<font color="Maroon" title="c8">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="measure6.html#E3:37"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="measure6.html#E6:37"><i><font color="Green" title="E28">A4</font></i></a></i>;<br/>
<a NAME="E10:37"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">e</font> &amp; <font color="Maroon" title="c8">e</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c8">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 
<b>by </b><i><a class="txt" href="measure6.html#E8:37"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E11:37"/>
<font color="Maroon" title="c6">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="measure6.html#E1:37"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="measure5.html#D4" title="MEASURE5:def.4">MEASURE5:def 4</a></i>;<br/>


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