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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">L'</font> be    <a href="nat_lat.html#M2">SubLattice</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L'</font>, <font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L'</font>;<br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> )
 ;<br/>

<b>thus </b><font color="Maroon">a</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font> = 
the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L'</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a'</font>,<font color="Maroon">b'</font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L'</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="nat_lat.html#D16">NAT_LAT:def 16</a></i>
<br/>.= 
<font color="Maroon">a'</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
;<br/>

<b>thus </b><font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font> = 
the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L'</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a'</font>,<font color="Maroon">b'</font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L'</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">a'</font>,<font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="nat_lat.html#D16">NAT_LAT:def 16</a></i>
<br/>.= 
<font color="Maroon">a'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
;<br/>


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