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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>thus </b><i><font color="Green">E17</font></i>: <a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="nat_lat.html#E60"><i><font color="Green">Lemma10</font></i></a></i>
;<br/>

<b>thus </b><i><font color="Green">E18</font></i>: <a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font> = 
<a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="nat_lat.html#E60"><i><font color="Green">Lemma10</font></i></a></i>
;<br/>

<b>thus </b><a NAME="E3:21"/>
<a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="nat_lat.html#E1:21"><i><font color="Green">E17</font></i></a>, <a class="ref" href="nat_lat.html#T61" target="_self">Th61</a></i>;<br/>

<b>thus </b><a NAME="E4:21"/>
<a href="nat_lat.html#K1" target="_self">hcflat</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K2" target="_self">lcmlat</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="nat_lat.html#E2:21"><i><font color="Green">E18</font></i></a>, <a class="ref" href="nat_lat.html#T61" target="_self">Th61</a></i>;<br/>


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