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<b>let </b><font color="Maroon" title="c1">0L</font> be  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">B1</font>, <font color="Maroon" title="c3">B2</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">0L</font>;<br/>





<b>set </b><font color="Maroon" title="c4">J</font> = the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font>;<br/>
<a NAME="E1:24"/><i><font color="Green" title="E20">A1</font></i>: 
( the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> is <a href="binop_1.html#V3" title="BINOP_1:attr.3">idempotent</a> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> is <a href="binop_1.html#V1" title="BINOP_1:attr.1">commutative</a> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> is <a href="binop_1.html#V2" title="BINOP_1:attr.2">associative</a> &amp; the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#NR1" title="SETWISEO:NR.1">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="lattice2.html#T26" title="LATTICE2:th.26">LATTICE2:26</a>, <a class="ref" href="lattice2.html#T27" title="LATTICE2:th.27">LATTICE2:27</a>, <a class="ref" href="lattice2.html#T29" title="LATTICE2:th.29">LATTICE2:29</a>, <a class="ref" href="lattice2.html#T67" title="LATTICE2:th.67">LATTICE2:67</a></i>;<br/>
<b>thus </b> <a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span> = 
the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c3">B2</font></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">0L</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#D3" title="LATTICE2:def.3">LATTICE2:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c2">B1</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">0L</font></span>)</span></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c3">B2</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">0L</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="lattice4.html#E1:24"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="setwiseo.html#T42" title="SETWISEO:th.42">SETWISEO:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c2">B1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c1">0L</font> <a href="setwiseo.html#K7" title="SETWISEO:func.7">$$</a> <font color="Maroon" title="c3">B2</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">0L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#D3" title="LATTICE2:def.3">LATTICE2:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c2">B1</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="lattice4.html#K1" title="LATTICE4:func.1">FinJoin</a> <font color="Maroon" title="c3">B2</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice2.html#D3" title="LATTICE2:def.3">LATTICE2:def 3</a></i>
;<br/>


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