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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">zero</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="chain_1.html#M1" target="_self">Grating</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:94_1"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:94_1"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; ex <font color="Olive">b<sub>1</sub></font> being  <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="chain_1.html#K11" target="_self">del</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) )
 <b>by </b><i><a class="ref" href="chain_1.html#D15" target="_self">Def15</a></i>;<br/><b>thus </b><a NAME="E4:94_1"/>
 <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="chain_1.html#E3:94_1"><i><font color="Green">E67</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:94"/>
(  <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K6" target="_self">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>4</sub></font> is    <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="chain_1.html#D15" target="_self">Def15</a></i>;<br/>


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