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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>





<b>assume </b><a NAME="E1:66"/><i><font color="Green" title="E49">A1</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c1">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">b</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c3">c</font> )
 ;<br/>

<a NAME="E2:66"/><b>then </b><i><font color="Green" title="E50">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E18"><i><font color="Green" title="E13">Lm8</font></i></a></i>;<br/>
<a NAME="E3:66"/>
<font color="Maroon" title="c1">a</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c2">b</font> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E1:66"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="wsierp_1.html#E12"><i><font color="Green" title="E7">Lm4</font></i></a></i>;<br/>
<a NAME="E4:66"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="int_1.html#R2" title="INT_1:pred.2">divides</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="wsierp_1.html#E2:66"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="wsierp_1.html#T36" target="_self" title="WSIERP_1:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E5:66"/>
<font color="Maroon" title="c1">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E12"><i><font color="Green" title="E7">Lm4</font></i></a></i>;<br/>


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