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

<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k2</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Olive" title="b1">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,1,<font color="Olive" title="b1">k2</font></span><br/><b>let </b><font color="Maroon" title="c2">k2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c2">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,1,<font color="Maroon" title="c2">k2</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c3">k21</font> = <font color="Maroon" title="c2">k2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E2:36"/><i><font color="Green" title="E25">A2</font></i>: 
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,1,<font color="Maroon" title="c2">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <font color="Maroon" title="c3">k21</font>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#T25" target="_self" title="AFINSQ_2:th.25">Th5</a></i>;<br/>
<a NAME="E3:36"/><i><font color="Green" title="E26">A4</font></i>: 
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c2">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="card_fin.html#K3" title="CARD_FIN:func.3">|</a> <font color="Maroon" title="c3">k21</font></span>)</span> <a href="afinsq_2.html#K4" title="AFINSQ_2:func.4">/^</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="afinsq_2.html#D3" target="_self" title="AFINSQ_2:def.3">AB540b</a></i>;<br/>
<a NAME="E4:36"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="nat_2.html#T10" title="NAT_2:th.10">NAT_2:10</a></i>;<br/>
<b>hence </b><a NAME="E5:36"/>
 <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c2">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K6" title="AFINSQ_2:func.6">mid</a> <font color="Maroon" title="c1">f</font>,1,<font color="Maroon" title="c2">k2</font>
 <b>by </b><i><a class="ref" href="afinsq_2.html#T19" target="_self" title="AFINSQ_2:th.19">Th31</a>, <a class="txt" href="#E3:36"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="#E2:36"><i><font color="Green" title="E25">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
