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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="int_2.html#V1" title="INT_2:attr.1">prime</a>  implies <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="E1:127_1_1"/>
<font color="Maroon" title="c2">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</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="number08.html#V1" title="NUMBER08:attr.1">having_exactly_one_prime_divisor</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">n</font> = <font color="Maroon" title="c2">n</font> as   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c3">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">n</font> &amp; (  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">n</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><br/>

<span class="kw">thus </span><a NAME="E3:127_1_1"/>
( <font color="Maroon" title="c3">n</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">n</font> &amp; (  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">n</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="kw">by</span> <span class="lab"><a class="ref" href="number08.html#T7" target="_self" onmouseover="rs('number08/T7')" onmouseout="rh()">Th7</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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