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<b>let </b><font color="Maroon" title="c1">q</font>, <font color="Maroon" title="c2">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="nat_lat.html#K3" title="NAT_LAT:func.3">Nat_Lattice</a> ;<br/>



<b>set </b><font color="Maroon" title="c3">s</font> = <font color="Maroon" title="c1">q</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font>;<br/>
<b>thus </b><i><font color="Green" title="E8">A1</font></i>: <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">q</font>,<span class="p1">(<span class="default"><a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">q</font>,<font color="Maroon" title="c2">p</font></span>)</span> = 
<font color="Maroon" title="c1">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c1">q</font>
<b>by </b><i><a class="ref" href="newton.html#T67" title="NEWTON:th.67">NEWTON:67</a></i>
;<br/>

<b>thus </b><i><font color="Green" title="E9">A2</font></i>: <a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">q</font></span>)</span>,<font color="Maroon" title="c1">q</font> = 
<a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c1">q</font></span>)</span>,<font color="Maroon" title="c1">q</font>

<br/>.= 
<font color="Maroon" title="c1">q</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">q</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
<br/>.= 
<font color="Maroon" title="c1">q</font>
<b>by </b><i><a class="ref" href="newton.html#T67" title="NEWTON:th.67">NEWTON:67</a></i>
;<br/>

<b>thus </b><a NAME="E3:16"/>
<a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">q</font>,<span class="p1">(<span class="default"><a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font>
 <b>by </b><i><a class="txt" href="nat_lat.html#E1:16"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="nat_lat.html#T61" target="_self" title="NAT_LAT:th.61">Th61</a></i>;<br/>

<b>thus </b><a NAME="E4:16"/>
<a href="nat_lat.html#K1" title="NAT_LAT:func.1">hcflat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K2" title="NAT_LAT:func.2">lcmlat</a>  <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c1">q</font>,<font color="Maroon" title="c2">p</font></span>)</span>,<font color="Maroon" title="c1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">q</font>
 <b>by </b><i><a class="txt" href="nat_lat.html#E2:16"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="nat_lat.html#T61" target="_self" title="NAT_LAT:th.61">Th61</a></i>;<br/>


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