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<span class="kw">let </span><font color="Maroon" title="c3">p1</font> be   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="number08.html#D6" target="_self" onmouseover="rs('number08/D6')" onmouseout="rh()">NUMBER08:def 6</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">p1</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">p</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> or  ex <font color="Olive" title="b1">r</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> st <br/>( <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p1</font> &amp; <font color="Olive" title="b1">r</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">p</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ) )</span><br/>

<a NAME="E1:129_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T4" onmouseover="rs('newton/T4')" onmouseout="rh()">NEWTON:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:129_1_1"/>
(  not <font color="Maroon" title="c3">p1</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">p</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> or  ex <font color="Olive" title="b1">r</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> st <br/>( <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p1</font> &amp; <font color="Olive" title="b1">r</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">p</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_d.html#T7" onmouseover="rs('nat_d/T7')" onmouseout="rh()">NAT_D:7</a>, <a class="ref" href="int_2.html#D4" onmouseover="rs('int_2/D4')" onmouseout="rh()">INT_2:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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