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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of  <a href="newton.html#K13" title="NEWTON:func.13">SetPrimes</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp;  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> implies <font color="Maroon" title="c1">p</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">q</font> )</span><br/>

<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E26">A1</font></i>: 
( <font color="Maroon" title="c1">p</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp; <font color="Maroon" title="c2">q</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp;  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">p</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">q</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c3">n</font> =  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<a NAME="E3:27"/>
<font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <font color="Maroon" title="c3">n</font>
 
<b>by </b><i><a class="ref" href="newton.html#T105" title="NEWTON:th.105">NEWTON:105</a></i>;<br/>
<b>hence </b><a NAME="E4:27"/>
<font color="Maroon" title="c1">p</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="txt" href="#E1:27"><i><font color="Green" title="E26">A1</font></i></a>, <a class="txt" href="int_7.html#E26"><i><font color="Green" title="E24">Lm11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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