<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="nat_3.html#NK12" target="_self">pfexp</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = <a href="newton.html#K13">SetPrimes</a>  <a href="pre_circ.html#K2">--&gt;</a> 0;<br/>
<a NAME="E1:75"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</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> 1</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> 1</span>)</span> <a href="polynom1.html#K8">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:75_1"/>
<font color="Maroon">c<sub>3</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> 1</span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="newton.html#NM1">Prime</a> <b>by </b><i><a class="ref" href="nat_3.html#T33" target="_self">Th33</a></i>;<br/>
<a NAME="E3:75_1"/><i><font color="Green">E42</font></i>: 
<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/>
<span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> 1</span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_3.html#K10" target="_self">|-count</a> 1
<b>by </b><i><a class="ref" href="nat_3.html#D8" target="_self">Def8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="nat_3.html#E3:75_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="nat_3.html#T21" target="_self">Th21</a></i>
;<br/>
<b>hence </b><a NAME="E5:75_1"/>
<span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> 1</span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:75"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="nat_3.html#NK12" target="_self">pfexp</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> 1</span>)</span></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> 0
 
<b>by </b><i><a class="ref" href="funcop_1.html#T17">FUNCOP_1:17</a></i>;<br/>
<a NAME="E3:75"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK12" target="_self">pfexp</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="newton.html#K13">SetPrimes</a> 
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:75"/>
 <a href="nat_3.html#NK12" target="_self">pfexp</a> 1 <a href="pboole.html#R6">=</a>  <a href="polynom1.html#K16">EmptyBag</a> <a href="newton.html#K13">SetPrimes</a> 
 <b>by </b><i><a class="txt" href="nat_3.html#E2:75"><i><font color="Green">E42</font></i></a></i>;<br/>


</div>
