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<b>let </b><font color="Maroon">1L</font> be  <a href="lattices.html#V14">upper-bounded</a> <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="finsub_1.html#NM1">Finite_Subset</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">1L</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">1L</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="binop_1.html#NM1">UnOp</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">1L</font>;<br/>







<b>set </b><font color="Maroon">M</font> = the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font>;<br/>
<a NAME="E1:29"/><i><font color="Green">E25</font></i>: 
( the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font> is <a href="binop_1.html#V3">idempotent</a> &amp; the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font> is <a href="binop_1.html#V1">commutative</a> &amp; the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font> is <a href="binop_1.html#V2">associative</a> &amp; the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="lattice2.html#T30">LATTICE2:30</a>, <a class="ref" href="lattice2.html#T31">LATTICE2:31</a>, <a class="ref" href="lattice2.html#T32">LATTICE2:32</a>, <a class="ref" href="lattice2.html#T73">LATTICE2:73</a></i>;<br/>
<b>thus </b> <a href="lattice2.html#K3">FinMeet</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="setwiseo.html#K5">\/</a> <span class="p2"><a href="setwiseo.html#K2">{.</a><span class="default"><font color="Maroon">b</font></span><a href="setwiseo.html#K2">.}</a></span></span>)</span>,<font color="Maroon">f</font> = 
the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font> <a href="setwiseo.html#K7">$$</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="setwiseo.html#K5">\/</a> <span class="p2"><a href="setwiseo.html#K2">{.</a><span class="default"><font color="Maroon">b</font></span><a href="setwiseo.html#K2">.}</a></span></span>)</span>,<font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="lattice2.html#D4">LATTICE2:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">1L</font> <a href="setwiseo.html#K7">$$</a> <font color="Maroon">B</font>,<font color="Maroon">f</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="ref" href="setwiseo.html#T41">SETWISEO:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice2.html#K3">FinMeet</a> <font color="Maroon">B</font>,<font color="Maroon">f</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#D4">LATTICE2:def 4</a></i>
;<br/>


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