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<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>assume </b><a NAME="E1:94"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">d</font>
 ;<br/>

<b>let </b><font color="Maroon">C</font> be   <a href="chain_1.html#NM4">Chain</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font>;<br/>

<b>consider </b><font color="Maroon">k'</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:94"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k'</font> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="chain_1.html#T6" target="_self">Th6</a>, <a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<b>reconsider </b><font color="Maroon">k'</font> = <font color="Maroon">k'</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>reconsider </b><font color="Maroon">C'</font> = <font color="Maroon">C</font> as   <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> <b>by </b><i/>;<br/>
<a NAME="E6:94"/>
( <font color="Maroon">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="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/>
<b>hence </b><a NAME="E7:94"/>
<font color="Maroon">C</font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font>
 <b>by </b><i>, </i>;<br/>


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