<?xml version="1.0"?>
<div class="add">

<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"> (  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c1">p</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font></span>)</span> implies  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font> )</span><br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E16">A1</font></i>: 
(  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c2">q</font> &amp; <font color="Maroon" title="c1">p</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font></span><br/>

<b>consider </b><font color="Maroon" title="c3">r</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of  <a href="newton.html#K13" title="NEWTON:func.13">SetPrimes</a> <b> such that </b><br/><a NAME="E3:16"/><i><font color="Green" title="E17">A2</font></i>: 
(  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font></span>)</span> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">r</font> &amp; <font color="Maroon" title="c3">r</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">q</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">r</font></span>)</span> &amp; <font color="Maroon" title="c1">p</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">+</a> <font color="Maroon" title="c3">r</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="int_7.html#E1:16"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="int_7.html#E6"><i><font color="Green" title="E6">Lm2</font></i></a></i>;<br/>
<a NAME="E4:16"/>
<span class="p1">(<span class="default"><a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c3">r</font></span>)</span> <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>
 
<b>by </b><i><a class="txt" href="int_7.html#E3:16"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="nat_3.html#T19" title="NAT_3:th.19">NAT_3:19</a></i>;<br/>
<b>hence </b><a NAME="E5:16"/>
 <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c1">p</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a>  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c2">q</font>
 <b>by </b><i><a class="ref" href="int_1.html#D9" title="INT_1:def.9">INT_1:def 9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
