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<b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:39"/>
( <font color="Maroon">i</font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="nat_1.html#R1" target="_self">divides</a> <font color="Maroon">i</font> )
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">i</font></span>)</span> &amp; <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">j</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:39"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">i</font> <a href="xcmplx_0.html#K3">*</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E4:39"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:39"/>
( <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> 1 implies <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/>
<span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">i</font></span>)</span> <a href="nat_1.html#K2" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<a NAME="E2:39_1"/><b>then </b>
<font color="Maroon">j</font> <a href="nat_1.html#K5" target="_self">div</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:39_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:39"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/>


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