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

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">d</font> be  non <a href="xboole_0.html#V1">zero</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">G</font> be    <a href="chain_1.html#M1" target="_self">Grating</a> of <font color="Maroon">d</font>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font>;<br/>







<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:93_1"/>
<font color="Maroon">C</font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">G</font>
 ;<br/><b>then consider </b><font color="Maroon">k'</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:93_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">k'</font> <a href="nat_1.html#K1">+</a> 1 &amp;  ex <font color="Olive">C'</font> being  <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">k'</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font> st <br/>( <font color="Olive">C'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp;  <a href="chain_1.html#K11" target="_self">del</a> <font color="Olive">C'</font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">k'</font>,<font color="Maroon">G</font> ) )
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E4:93_1"/>
 <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">k</font>,<font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="chain_1.html#T6" target="_self">Th6</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:93"/>
(  <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">k</font>,<font color="Maroon">G</font> implies <font color="Maroon">C</font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">G</font> )
 <b>by </b><i/>;<br/>


</div>
