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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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="E1:65_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="newton.html#NM1">Prime</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10" target="_self">|-count</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:65_1_2"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="newton.html#NM1">Prime</a> holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10" target="_self">|-count</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:65_1_2_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="newton.html#K13">SetPrimes</a> 
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_3.html#K10" target="_self">|-count</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="nat_3.html#E1:65_1_2"><i><font color="Green">E35</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="nat_3.html#E2:65_1_2"><i><font color="Green">E36</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:65_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


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