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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:22"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:22"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="nat_4.html#E1:22"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:22"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="nat_4.html#E2:22"><i><font color="Green">E24</font></i></a>, <a class="ref" href="nat_4.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E5:22"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> is <a href="int_2.html#V1">prime</a> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="nat_4.html#E1:22"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:22"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="nat_4.html#E5:22"><i><font color="Green">E26</font></i></a>, <a class="ref" href="nat_4.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E8:22"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="nat_4.html#E4:22"><i><font color="Green">E25</font></i></a>, <a class="txt" href="nat_4.html#E7:22"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E9:22"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T7">XCMPLX_1:7</a></i>;<br/>
<a NAME="E10:22"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T40">NAT_1:40</a></i>;<br/>
<b>hence </b><a NAME="E11:22"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="nat_4.html#E4:22"><i><font color="Green">E25</font></i></a></i>;<br/>


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