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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="newton.html#NM1">Prime</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:23"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:23"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E3:23"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:23"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 
<b>by </b><i><a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>
<a NAME="E5:23"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="nat_4.html#E2:23"><i><font color="Green">E25</font></i></a>, <a class="ref" href="power.html#T40">POWER:40</a></i>;<br/>
<a NAME="E6:23"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="power.html#T46">POWER:46</a></i>;<br/>
<a NAME="E7:23"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="nat_4.html#E3:23"><i><font color="Green">E26</font></i></a>, <a class="ref" href="nat_3.html#T6">NAT_3:6</a></i>;<br/>
<a NAME="E8:23"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="nat_4.html#E1:23"><i><font color="Green">E24</font></i></a>, <a class="txt" href="nat_4.html#E4:23"><i><font color="Green">E27</font></i></a>, <a class="ref" href="nat_3.html#T27">NAT_3:27</a></i>;<br/>
<a NAME="E9:23"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_3.html#K10">|-count</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="nat_4.html#E4:23"><i><font color="Green">E27</font></i></a>, <a class="ref" href="nat_3.html#T25">NAT_3:25</a></i>;<br/>
<b>hence </b><a NAME="E10:23"/>
contradiction
 <b>by </b><i><a class="txt" href="nat_4.html#E6:23"><i><font color="Green">E28</font></i></a>, <a class="ref" href="newton.html#T9">NEWTON:9</a></i>;<br/>


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