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<div class="add">

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

<b>set </b><font color="Maroon">M</font> = <font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> 0;<br/>
<a NAME="E1:70"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="nat_1.html#K10">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">m</font> <a href="nat_1.html#R1">divides</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T53">NAT_1:53</a></i>;<br/>
<b>hence </b><a NAME="E2:70_1"/>
<font color="Maroon">m</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#D5">NAT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:70"/>
<font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> 0 <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#D5">NAT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:70"/>
<font color="Maroon">m</font> <a href="nat_1.html#K10">hcf</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="newton.html#T5" target="_self">Th5</a>, <a class="ref" href="nat_1.html#T52">NAT_1:52</a></i>;<br/>


</div>
