<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">r</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="E1:6"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <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="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<b>assume </b><a NAME="E2:6"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<a NAME="E3:6"/><b>then </b><i><font color="Green">E42</font></i>: 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">a</font></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a> <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="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:6"/><i><font color="Green">E43</font></i>: 
(  <a href="int_1.html#K4">frac</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><font color="Maroon">a</font></span><a href="int_1.html#K1">/]</a></span> &amp;  <a href="int_1.html#K4">frac</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K6">-</a> <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> )
 
<b>by </b><i><a class="ref" href="int_1.html#D6">INT_1:def 6</a></i>;<br/>
<a NAME="E5:6"/>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">r</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<a NAME="E6:6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <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> <a href="xcmplx_0.html#K6">-</a> <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>
 
<b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<b>hence </b><a NAME="E7:6"/>
 <a href="int_1.html#K4">frac</a> <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="int_1.html#K4">frac</a> <font color="Maroon">r</font>
 <b>by </b><i>, </i>;<br/>


</div>
