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<b>let </b><font color="Maroon">f</font> be   <a href="newton.html#NM1">Prime</a>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:99"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">f</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">g</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:99"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E3:99"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">f</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:99"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">f</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<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/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:99_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">f</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1"><b>suppose </b></a><a NAME="E1:99_1_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">f</font>
 ;<br/><div class="add"><a NAME="E2:99_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">f</font> &amp; <font color="Maroon">x</font> is <a href="int_2.html#V1">prime</a> )
 <b>by </b><i/>;<br/><a NAME="E3:99_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">g</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="E4:99_1_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">g</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_2"><b>suppose </b></a><a NAME="E1:99_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:99_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:99_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K14" target="_self">SetPrimenumber</a> <font color="Maroon">g</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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