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

<b>let </b><font color="Maroon" title="c1">p</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> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>;<br/>



<b>assume </b><a NAME="E1:22"/><i><font color="Green" title="E21">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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c1">p</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> )
 ;<br/>

<a NAME="E2:22"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <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="c1">p</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">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="E4:22"/><i><font color="Green" title="E22">A2</font></i>: 
(  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">q</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="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">q</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="c4">r</font> &amp; <font color="Maroon" title="c3">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">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c3">q</font></span>)</span> &amp; <font color="Maroon" title="c4">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="c4">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c4">r</font></span>)</span> &amp; <font color="Maroon" title="c3">q</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">+</a> <font color="Maroon" title="c4">r</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c1">p</font> )
 <b>by </b><i><a class="txt" href="int_7.html#E7"><i><font color="Green" title="E7">Lm3</font></i></a></i>;<br/>
<a NAME="E5:22"/><i><font color="Green" title="E23">A3</font></i>: 
<span class="p1">(<span class="default"><a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Maroon" title="c3">q</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="c4">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="c1">p</font>
 
<b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="nat_3.html#T19" title="NAT_3:th.19">NAT_3:19</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>$1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a> = <font color="Maroon" title="c2">x</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<b>consider </b><font color="Maroon" title="c5">nx</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E7:22"/><i><font color="Green" title="E24">A4</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">nx</font> &amp; <font color="Maroon" title="c1">p</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c5">nx</font> )
 <b>by </b><i><a class="txt" href="int_7.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="int_7.html#D1" target="_self" title="INT_7:def.1">Def1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">mx</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E9:22"/><i><font color="Green" title="E25">A5</font></i>: 
<font color="Maroon" title="c5">nx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">mx</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="int_7.html#E7:22"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<a NAME="E10:22"/><i><font color="Green" title="E26">A6</font></i>: 
<font color="Maroon" title="c6">mx</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1"/>
<font color="Maroon" title="c6">mx</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<a NAME="E2:22_1"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">mx</font>
 
;<br/>
<a NAME="E3:22_1"/><b>then </b><i><font color="Green" title="E27">A7</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">mx</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E4:22_1"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="int_2.html#D5" title="INT_2:def.5">INT_2:def 5</a></i>;<br/>
<a NAME="E5:22_1"/><b>then </b><i><font color="Green" title="E28">A8</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c5">nx</font>
 
<b>by </b><i><a class="txt" href="int_7.html#E9:22"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="int_7.html#E3:22_1"><i><font color="Green" title="E27">A7</font></i></a>, <a class="ref" href="power.html#T44" title="POWER:th.44">POWER:44</a></i>;<br/>
<a NAME="E6:22_1"/>
<font color="Maroon" title="c2">x</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c5">nx</font>
 
<b>by </b><i><a class="txt" href="int_7.html#E5:22_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="ref" href="power.html#T46" title="POWER:th.46">POWER:46</a></i>;<br/>
<a NAME="E7:22_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c5">nx</font>
 
<b>by </b><i><a class="ref" href="power.html#T46" title="POWER:th.46">POWER:46</a></i>;<br/>
<b>hence </b><a NAME="E8:22_1"/>
contradiction
 <b>by </b><i><a class="txt" href="int_7.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="int_7.html#E7:22"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="newton.html#T10" title="NEWTON:th.10">NEWTON:10</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E11:22"/><i><font color="Green" title="E27">A9</font></i>: 
<font color="Maroon" title="c3">q</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">z</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>;<br/><b>assume </b><a NAME="E1:22_2_1"/><i><font color="Green" title="E28">A10</font></i>: 
<font color="Maroon" title="c7">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">q</font>
 ;<br/><a NAME="E2:22_2_1"/><i><font color="Green" title="E29">A11</font></i>: 
 <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">q</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="c1">p</font>
 <b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/><b>consider </b><font color="Maroon" title="c8">n</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E4:22_2_1"/><i><font color="Green" title="E30">A12</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">n</font> &amp; <font color="Maroon" title="c1">p</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">z</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c8">n</font> )
 <b>by </b><i><a class="txt" href="int_7.html#E1:22"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="int_7.html#E1:22_2_1"><i><font color="Green" title="E28">A10</font></i></a>, <a class="txt" href="int_7.html#E2:22_2_1"><i><font color="Green" title="E29">A11</font></i></a>, <a class="ref" href="int_7.html#D1" target="_self" title="INT_7:def.1">Def1</a></i>;<br/><b>take </b><font color="Maroon" title="c9">n</font> = <font color="Maroon" title="c8">n</font>;<br/><font color="Maroon" title="c3">q</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">z</font>
<b>by </b><i><a class="txt" href="int_7.html#E1:22_2_1"><i><font color="Green" title="E28">A10</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">p</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">z</font>
<b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="int_7.html#E1:22_2_1"><i><font color="Green" title="E28">A10</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><b>hence </b><a NAME="E6:22_2_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">n</font> &amp; <font color="Maroon" title="c3">q</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c7">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">z</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c9">n</font> )
 <b>by </b><i><a class="txt" href="int_7.html#E4:22_2_1"><i><font color="Green" title="E30">A12</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:22_2"/>
<font color="Maroon" title="c3">q</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a>
 <b>by </b><i><a class="ref" href="int_7.html#D1" target="_self" title="INT_7:def.1">Def1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:22"/><i><font color="Green" title="E28">A13</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c4">r</font>
 
<b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<i><font color="Green" title="E29">A14</font></i>: <font color="Maroon" title="c4">r</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="int_7.html#E12:22"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c1">p</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="int_7.html#E12:22"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="int_7.html#E7:22"><i><font color="Green" title="E24">A4</font></i></a>, <a class="txt" href="int_7.html#E9:22"><i><font color="Green" title="E25">A5</font></i></a>, <a class="txt" href="int_7.html#E10:22"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="newton.html#T10" title="NEWTON:th.10">NEWTON:10</a></i>
;<br/>
<a NAME="E14:22"/>
<font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="newton.html#K13" title="NEWTON:func.13">SetPrimes</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">r</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">x</font></span>)</span>
 
<b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="int_7.html#T1" target="_self" title="INT_7:th.1">Th1</a></i>;<br/>
<a NAME="E15:22"/><b>then </b>
 ex <font color="Olive" title="b1">rr1</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>  st <br/>( <font color="Olive" title="b1">rr1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">r</font> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Olive" title="b1">rr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Olive" title="b1">rr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> )
 
<b>by </b><i><a class="txt" href="int_7.html#E13:22"><i><font color="Green" title="E29">A14</font></i></a>, <a class="txt" href="int_7.html#E21"><i><font color="Green" title="E19">Lm8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E16:22"/>
 ex <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">r1</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>  st <br/>( <font color="Olive" title="b1">p1</font> is <a href="int_7.html#V1" title="INT_7:attr.1">prime-factorization-like</a> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Olive" title="b2">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Olive" title="b2">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="polynom2.html#K1" title="POLYNOM2:func.1">support</a> <font color="Olive" title="b1">p1</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="c1">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Olive" title="b1">p1</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="Olive" title="b1">p1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Olive" title="b1">p1</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="nat_3.html#K8" title="NAT_3:func.8">Product</a> <font color="Olive" title="b1">p1</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="txt" href="int_7.html#E4:22"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="int_7.html#E5:22"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="int_7.html#E11:22"><i><font color="Green" title="E27">A9</font></i></a></i>;<br/>


</div>
