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<b>let </b><font color="Maroon" title="c1">1L</font> be  <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">B</font> be   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">1L</font>;<br/><b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">1L</font>;<br/>







<b>set </b><font color="Maroon" title="c5">M</font> = the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font>;<br/>
<a NAME="E1:31"/><i><font color="Green" title="E31">A1</font></i>: 
( the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font> is <a href="binop_1.html#V3" title="BINOP_1:attr.3">idempotent</a> &amp; the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="lattice2.html#T30" title="LATTICE2:th.30">LATTICE2:30</a>, <a class="ref" href="lattice2.html#T31" title="LATTICE2:th.31">LATTICE2:31</a>, <a class="ref" href="lattice2.html#T32" title="LATTICE2:th.32">LATTICE2:32</a>, <a class="ref" href="lattice2.html#T73" title="LATTICE2:th.73">LATTICE2:73</a></i>;<br/>
<b>thus </b> <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c2">B</font></span>)</span>,<font color="Maroon" title="c4">g</font> = 
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="setwiseo.html#K8" title="SETWISEO:func.8">.:</a> <font color="Maroon" title="c2">B</font></span>)</span>,<font color="Maroon" title="c4">g</font>
<b>by </b><i><a class="ref" href="lattice2.html#D4" title="LATTICE2:def.4">LATTICE2:def 4</a></i>
<br/>.= 
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c1">1L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="txt" href="lattice4.html#E1:31"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="setwiseo.html#T44" title="SETWISEO:th.44">SETWISEO:44</a></i>
<br/>.= 
 <a href="lattice2.html#K3" title="LATTICE2:func.3">FinMeet</a> <font color="Maroon" title="c2">B</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#D4" title="LATTICE2:def.4">LATTICE2:def 4</a></i>
;<br/>


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