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<b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> or <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1"><b>suppose </b></a><a NAME="E1:49_1_1"/><i><font color="Green">E37</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font>
 ;<br/><div class="add"><a NAME="E2:49_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:49_1_1"/>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">r</font></span><a href="complex1.html#K17">.|</a></span>
 <b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2"><b>suppose </b></a><a NAME="E1:49_1_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:49_1_2"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font></span>)</span>
 <b>by </b><i><a class="ref" href="extreal1.html#D3">EXTREAL1:def 3</a></i>;<br/><a NAME="E3:49_1_2"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">r</font></span>)</span>
 <b>by </b><i><a class="ref" href="mesfunc2.html#T10">MESFUNC2:10</a></i>;<br/><b>hence </b><a NAME="E4:49_1_2"/>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <font color="Maroon">r</font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><font color="Maroon">r</font></span><a href="complex1.html#K17">.|</a></span>
 <b>by </b><i>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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