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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></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>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E1:6"/><i><font color="Green">E9</font></i>: 
( <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K6">lcm</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="nat_lat.html#K3" target="_self">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_lat.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E2:6"/><i><font color="Green">E10</font></i>: 
( <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K6">lcm</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="nat_lat.html#K3" target="_self">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="nat_lat.html#D4" target="_self">Def4</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K6">lcm</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K6">lcm</a> <span class="p2">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="nat_lat.html#E1:6"><i><font color="Green">E9</font></i></a>, <a class="ref" href="nat_lat.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K6">lcm</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K3" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="nat_lat.html#E2:6"><i><font color="Green">E10</font></i></a>, <a class="ref" href="newton.html#T56">NEWTON:56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="nat_lat.html#D4" target="_self">Def4</a></i>
;<br/>


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