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<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">r1</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">r2</font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><a NAME="E1:34"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r1</font> &amp; <font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r2</font> &amp; <font color="Maroon">r2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1"/>
( <font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</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="34_1_1"><b>suppose </b></a><a NAME="E1:34_1_1"/>
<font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:34_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font>
 <b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><a NAME="E3:34_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E4:34_1_1"/>
<font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/><b>hence </b><a NAME="E5:34_1_1"/>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a</font>
 <b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2"><b>suppose </b></a><a NAME="E1:34_1_2"/>
<font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><b>then </b><i><font color="Green">E37</font></i>:  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font></span>)</span> = 
 <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font></span>)</span>
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<font color="Maroon">r2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r1</font>

;<br/><a NAME="E3:34_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">r2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r1</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E4:34_1_2"/>
<font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/><b>hence </b><a NAME="E5:34_1_2"/>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">r1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">r2</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="real_1.html#K5">-</a> <font color="Maroon">a</font>
 <b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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