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<span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"> ( <font color="Maroon" title="c2">n</font> is  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  implies  not <font color="Maroon" title="c2">n</font> is  <a href="number08.html#V1" title="NUMBER08:attr.1">having_exactly_one_prime_divisor</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:128_1_1"/><span class="lab"><font color="Green" title="E101">A1</font></span>: 
<font color="Maroon" title="c2">n</font> is  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</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="c2">n</font> is  <a href="number08.html#V1" title="NUMBER08:attr.1">having_exactly_one_prime_divisor</a> </span><br/>

<span class="kw">given </span><font color="Maroon" title="c3">p</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a><span class="kw"> such that </span><a NAME="E3:128_1_1"/>
<font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">and </span><br/><a NAME="E4:128_1_1"/><span class="lab"><font color="Green" title="E102">A2</font></span>: 
 for <font color="Olive" title="b1">r</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>  st <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">p</font> holds <br/> not <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">n</font>
 ; <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"> contradiction</span><br/>

<a NAME="E5:128_1_1"/>
 ex <font color="Olive" title="b1">p1</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> st <font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T72" onmouseover="rs('newton/T72')" onmouseout="rh()">NEWTON:72</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:128_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:128_1_1"><span class="lab"><font color="Green" title="E101">A1</font></span></a>, <a class="txt" href="#E4:128_1_1"><span class="lab"><font color="Green" title="E102">A2</font></span></a>, <a class="ref" href="int_2.html#T12" onmouseover="rs('int_2/T12')" onmouseout="rh()">INT_2:12</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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