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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:25"/>
<font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">b</font>
 ;<br/>

<b>then consider </b><font color="Maroon">d</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:25"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>
<a NAME="E4:25"/>
<font color="Maroon">b</font> <a href="wsierp_1.html#K2" target="_self">|^</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="wsierp_1.html#K2" target="_self">|^</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="newton.html#K2">|^</a> <font color="Maroon">c</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="newton.html#T12">NEWTON:12</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
<font color="Maroon">a</font> <a href="wsierp_1.html#K2" target="_self">|^</a> <font color="Maroon">c</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">b</font> <a href="wsierp_1.html#K2" target="_self">|^</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="nat_1.html#D3">NAT_1:def 3</a></i>;<br/>


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