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<b>let </b><font color="Maroon">f</font> be    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="newton.html#K13">SetPrimes</a> , <font color="Maroon">g</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="E1:66_1_2"/><i><font color="Green">E47</font></i>: 
for <font color="Olive">i</font> being  <a href="newton.html#NM1">Prime</a> holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">i</font> <a href="nat_3.html#K11" target="_self">|-count</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:66_1_2"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">i</font> being  <a href="newton.html#NM1">Prime</a> holds  <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">i</font> <a href="nat_3.html#K11" target="_self">|-count</a> <font color="Maroon">n</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_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="E1:66_1_2_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K13">SetPrimes</a> 
 ;<br/><b>then reconsider </b><font color="Maroon">a</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/><b>thus </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<font color="Maroon">a</font> <a href="nat_3.html#K11" target="_self">|-count</a> <font color="Maroon">n</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:66_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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