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<b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">zero</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="newton.html#NM1">Prime</a>;<br/>



<b>assume </b><a NAME="E1:21"/><i><font color="Green">E41</font></i>: 
not <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK15" target="_self">ppf</a> <font color="Maroon">n</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:21"/>
<font color="Maroon">p</font> <a href="nat_3.html#K11">|-count</a> <font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<a NAME="E3:21"/><b>then </b>
<span class="p1">(<span class="default"><a href="nat_3.html#NK15" target="_self">ppf</a> <font color="Maroon">n</font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="nat_3.html#K11">|-count</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_3.html#T56">NAT_3:56</a></i>;<br/>
<b>hence </b><a NAME="E4:21"/>
contradiction
 <b>by </b><i>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/>


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