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<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 0,<font color="Maroon">G</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:95_1"/>
<font color="Maroon">C</font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of 0,<font color="Maroon">G</font>
 ;<br/><a NAME="E2:95_1"/><b>then </b>
( ( 0 <a href="hidden.html#R1">=</a> 0 &amp;  <a href="card_1.html#K4">card</a> <font color="Maroon">C</font> is <a href="abian.html#V1">even</a> ) or  ex <font color="Olive">k'</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( 0 <a href="hidden.html#R1">=</a> <font color="Olive">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="Olive">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="Olive">k'</font>,<font color="Maroon">G</font> ) ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:95_1"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">C</font> is <a href="abian.html#V1">even</a>
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:95"/>
(  <a href="card_1.html#K4">card</a> <font color="Maroon">C</font> is <a href="abian.html#V1">even</a> implies <font color="Maroon">C</font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of 0,<font color="Maroon">G</font> )
 <b>by </b><i/>;<br/>


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