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<b>let </b><font color="Maroon" title="c1">m</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>set </b><font color="Maroon" title="c2">M</font> = <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> 0;<br/>
<a NAME="E1:70"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1"><b>proof </b></a><div class="add">

<a NAME="E1:70_1"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> 0
 
<b>by </b><i><a class="ref" href="nat_d.html#T6" title="NAT_D:th.6">NAT_D:6</a></i>;<br/>
<b>hence </b><a NAME="E2:70_1"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> 0
 <b>by </b><i><a class="ref" href="nat_d.html#D5" title="NAT_D:def.5">NAT_D:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:70"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> 0 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font>
 
<b>by </b><i><a class="ref" href="nat_d.html#D5" title="NAT_D:def.5">NAT_D:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:70"/>
<font color="Maroon" title="c1">m</font> <a href="nat_d.html#K8" title="NAT_D:func.8">hcf</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font>
 <b>by </b><i><a class="txt" href="newton.html#E1:70"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="nat_d.html#T5" title="NAT_D:th.5">NAT_D:5</a></i>;<br/>


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