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





<b>assume </b><a NAME="E1:6"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then 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="E3:6"/><i><font color="Green">E6</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="nat_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E4:6"/>
<font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="radix_1.html#E3:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="newton.html#T13">NEWTON:13</a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">c<sub>3</sub></font> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>


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