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<b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="nat_lat.html#K6" target="_self">Nat_Lattice</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="nat_lat.html#K6" target="_self">Nat_Lattice</a> ;<br/>



<b>set </b><font color="Maroon">r</font> = <font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font>;<br/>
<b>thus </b><i><font color="Green">E25</font></i>: <a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<span class="p1">(<span class="default"><a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<font color="Maroon">p</font></span>)</span> = 
<a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">p</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon">q</font>
<b>by </b><i/>
;<br/>

<b>thus </b><i><font color="Green">E30</font></i>: <a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">p</font>,<font color="Maroon">q</font></span>)</span>,<font color="Maroon">q</font> = 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">q</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>

<br/>.= 
<font color="Maroon">q</font>
<b>by </b><i/>
;<br/>

<b>thus </b><a NAME="E3:22"/>
<a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<span class="p1">(<span class="default"><a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">p</font>,<font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E4:22"/>
<a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">q</font>,<font color="Maroon">p</font></span>)</span>,<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 <b>by </b><i>, </i>;<br/>


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