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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:98_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 or ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1_1"><b>suppose </b></a><a NAME="E1:98_1_1_1_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:98_1_1_1_1"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K4">card</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> 0 )
 <b>by </b><i><a class="ref" href="card_1.html#T78">CARD_1:78</a></i>;<br/><b>hence </b><a NAME="E3:98_1_1_1_1"/>
 <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="chain_1.html#E1:98_1_1_1_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="chain_1.html#D15" target="_self">Def15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="98_1_1_1_2"><b>suppose </b></a><a NAME="E1:98_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:98_1_1_1_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E4:98_1_1_1_2"/>
 <a href="chain_1.html#K11" target="_self">del</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" target="_self">0_</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="chain_1.html#T61" target="_self">Th61</a></i>;<br/><b>hence </b><a NAME="E5:98_1_1_1_2"/>
 <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="chain_1.html#E3:98_1_1_1_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="chain_1.html#D15" target="_self">Def15</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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