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

<b>let </b><font color="Maroon">i1</font> be   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">i2</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">n1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> 1 &amp; <font color="Maroon">n2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> <a href="xcmplx_0.html#K2">+</a> 1 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n1</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i1</font> )
 ;<br/>

<a NAME="E2:38"/><b>then </b>
<font color="Maroon">n1</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">n1</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E3:38"/><b>then </b>
<font color="Maroon">i2</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">n1</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>hence </b><a NAME="E4:38"/>
<font color="Maroon">n1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n2</font>
 <b>by </b><i/>;<br/>


</div>
