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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="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:55"/><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> 0
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:55"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/>

<a NAME="E4:55"/>
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 0 <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>;<br/>
<a NAME="E5:55"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 0 <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T53">NAT_1:53</a></i>;<br/>
<a NAME="E6:55"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>
<a NAME="E7:55"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="nat_3.html#E1:55"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E8:55"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="nat_3.html#E2:55"><i><font color="Green">E28</font></i></a>, <a class="txt" href="nat_3.html#E6:55"><i><font color="Green">E31</font></i></a>, <a class="ref" href="nat_1.html#T54">NAT_1:54</a></i>;<br/>
<b>hence </b><a NAME="E9:55"/>
<font color="Maroon">c<sub>2</sub></font> <a href="nat_3.html#K10" target="_self">|-count</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="nat_3.html#E1:55"><i><font color="Green">E27</font></i></a>, <a class="txt" href="nat_3.html#E3:55"><i><font color="Green">E29</font></i></a>, <a class="txt" href="nat_3.html#E5:55"><i><font color="Green">E30</font></i></a>, <a class="ref" href="nat_3.html#D7" target="_self">Def7</a></i>;<br/>


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