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

<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c3">k1</font>, <font color="Maroon" title="c4">k2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k2</font>
 ;<br/>

<a NAME="E2:6"/><b>then </b><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">k1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E1:6"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">k1</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k1</font>
<b>by </b><i><a class="txt" href="finseq_8.html#E2:6"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>
;<br/>
<b>hence </b><a NAME="E4:6"/>
 <a href="finseq_8.html#K2" title="FINSEQ_8:func.2">smid</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:6"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="jordan3.html#D1" title="JORDAN3:def.1">JORDAN3:def 1</a></i>;<br/>


</div>
