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<b>let </b><font color="Maroon">p</font> be   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">q</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:91"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">p</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">q</font>
 ;<br/>

<a NAME="E2:91"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">p</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:91_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">p</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<a NAME="E3:91_1"/>
( <font color="Maroon">x'</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> &amp; <font color="Maroon">x'</font> is <a href="int_2.html#V1">prime</a> )
 
<b>by </b><i><a class="ref" href="newton.html#T6" target="_self">Th6</a>, </i>;<br/>
<a NAME="E4:91_1"/><b>then </b>
( <font color="Maroon">x'</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">x'</font> is <a href="int_2.html#V1">prime</a> )
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E5:91_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:91"/>
 <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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