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

<b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">y</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>and </b><br/><a NAME="E2:2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">y</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E3:2"/>
<font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i>, , <a class="ref" href="real_2.html#T125">REAL_2:125</a></i>;<br/>
<a NAME="E4:2"/><b>then </b>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="int_1.html#T80">INT_1:80</a></i>;<br/>
<a NAME="E5:2"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E6:2"/>
<font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="int_1.html#T52">INT_1:52</a></i>;<br/>
<a NAME="E7:2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2"><a href="int_1.html#K1">[\</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E8:2"/><b>then </b>
<font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2"><a href="int_1.html#K1">[\</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<b>hence </b><a NAME="E9:2"/>
<font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="int_1.html#K1">[\</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">y</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="real_2.html#T178">REAL_2:178</a></i>;<br/>


</div>
