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<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #), <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <a href="numbers.html#K5">NAT</a> ,<a href="nat_lat.html#K2" target="_self">lcmlat</a> ,<a href="nat_lat.html#K1" target="_self">hcflat</a>  #);<br/>

<b>assume </b><a NAME="E1:9"/>
<font color="Maroon">a</font> <a href="lattices.html#R1">[=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:9"/><b>then </b>
<font color="Maroon">a</font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>
<a NAME="E3:9"/><b>then </b>
<span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K8">lcm</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:9"/><b>then </b>
<span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">a</font></span>)</span> <a href="nat_1.html#K8">lcm</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">b</font>
 
;<br/>
<b>hence </b><a NAME="E5:9"/>
 <a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a>  <a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="newton.html#T57">NEWTON:57</a></i>;<br/>


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