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

<b>let </b><font color="Maroon">s</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:33"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">s</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">t</font>
 ;<br/>

<b>let </b><font color="Maroon">r</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E2:33"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">t</font>
 ;<br/>

<a NAME="E3:33"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">s</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">r</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<a NAME="E1:33_1"/>
<font color="Maroon">t</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">s</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E2:33_1"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T26">XREAL_1:26</a></i>;<br/>
<b>hence </b><a NAME="E3:33_1"/>
<font color="Maroon">s</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">r</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E4:33"/>
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:33"/><b>then </b>
<font color="Maroon">s</font> <a href="newton.html#K8" target="_self">choose</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="newton.html#K6" target="_self">!</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="newton.html#K6" target="_self">!</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">t</font> <a href="newton.html#K6" target="_self">!</a> </span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:33"/>
<font color="Maroon">s</font> <a href="newton.html#K8" target="_self">choose</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="newton.html#K8" target="_self">choose</a> <font color="Maroon">r</font>
 <b>by </b><i>, , </i>;<br/>


</div>
