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

<a NAME="E1:23"/><i><font color="Green">E24</font></i>: 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font>
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E2:23"/>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> is    <a href="subset_1.html#M2">Element</a> of  <a href="mesfunc1.html#K2" target="_self">INT</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2">INT_1:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:23"/><i><font color="Green">E27</font></i>: 
( <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> or <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="int_1.html#D1">INT_1:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_1"/>
( <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 or <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_1"><b>suppose </b></a><a NAME="E1:23_1_1"/>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_1_1"/>
 ex <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  st  <a href="real_1.html#K1">-</a> <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_1_2"><b>suppose </b></a><a NAME="E1:23_1_2"/><i><font color="Green">E28</font></i>: 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">r</font></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><b>take </b>
0
;<br/><b>thus </b><a NAME="E2:23_1_2"/>
 <a href="real_1.html#K1">-</a> 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font>
 <b>by </b><i>, <a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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