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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="nat_3.html#NK12" target="_self">pfexp</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:69"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:69"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_1"/>
(  not <font color="Maroon">c<sub>4</sub></font> is <a href="int_2.html#V1">prime</a> or <font color="Maroon">c<sub>4</sub></font> is <a href="int_2.html#V1">prime</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1"><b>suppose </b></a><a NAME="E1:69_1_1"/>
not <font color="Maroon">c<sub>4</sub></font> is <a href="int_2.html#V1">prime</a>
 ;<br/><div class="add"><a NAME="E2:69_1_1"/><b>then </b>
not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_3.html#T33" target="_self">Th33</a></i>;<br/><b>hence </b><a NAME="E3:69_1_1"/>
<span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_2"><b>suppose </b></a><a NAME="E1:69_1_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="int_2.html#V1">prime</a>
 ;<br/><div class="add"><a NAME="E2:69_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>by </b><i><a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/><a NAME="E3:69_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_3.html#K10" target="_self">|-count</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="nat_3.html#E1:69"><i><font color="Green">E39</font></i></a>, <a class="txt" href="nat_3.html#E2:69"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nat_3.html#T23" target="_self">Th23</a></i>;<br/><b>hence </b><a NAME="E4:69_1_2"/>
<span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="nat_3.html#E1:69_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="nat_3.html#D8" target="_self">Def8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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