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<b>let </b><font color="Maroon">it1</font> be    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="newton.html#K13">SetPrimes</a> , <font color="Maroon">it2</font> be    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="newton.html#K13">SetPrimes</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:64_1_2"/><i><font color="Green">E95</font></i>: 
 <a href="polynom1.html#K11">support</a> <font color="Maroon">it1</font> <a href="hidden.html#R1">=</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span>
 <b>and </b><br/><a NAME="E2:64_1_2"/><i><font color="Green">E96</font></i>: 
for <font color="Olive">p</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span> holds <br/><font color="Maroon">it1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font>
 <b>and </b><br/><a NAME="E3:64_1_2"/><i><font color="Green">E97</font></i>: 
 <a href="polynom1.html#K11">support</a> <font color="Maroon">it2</font> <a href="hidden.html#R1">=</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span>
 <b>and </b><br/><a NAME="E4:64_1_2"/><i><font color="Green">E98</font></i>: 
for <font color="Olive">p</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span> holds <br/><font color="Maroon">it2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:64_1_2_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K13">SetPrimes</a> 
 ;<br/><b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">i</font> as   <a href="newton.html#NM1">Prime</a> <b>by </b><i>, <a class="ref" href="newton.html#D6">NEWTON:def 6</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:64_1_2_1_1"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span> or  not <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:64_1_2_1_1_1"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">it1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">p</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">it2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:64_1_2_1_1_2"/><i><font color="Green">E103</font></i>: 
not <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" target="_self">pfexp</a> <font color="Maroon">n</font></span>)</span>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">it1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
0
<b>by </b><i>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
<br/>.= 
<font color="Maroon">it2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:64_1_2"/>
<font color="Maroon">it1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">it2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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