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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><a NAME="E1:8"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>then 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="E3:8"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/>
<a NAME="E4:8"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E5:8"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> 1 <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="nat_3.html#E4:8"><i><font color="Green">E6</font></i></a>, <a class="ref" href="radix_1.html#T7">RADIX_1:7</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="nat_3.html#E3:8"><i><font color="Green">E5</font></i></a>, <a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>


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