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<b>let </b><font color="Maroon">0L</font> be  <a href="lattices.html#V13">lower-bounded</a> <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">0L</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">0L</font>;<br/>



<b>set </b><font color="Maroon">J</font> = the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">0L</font>;<br/>
<a NAME="E1:25"/><i><font color="Green">E25</font></i>: 
( the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">0L</font> is <a href="binop_1.html#V1">commutative</a> &amp; the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">0L</font> is <a href="binop_1.html#V2">associative</a> &amp; the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">0L</font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="lattice2.html#T27">LATTICE2:27</a>, <a class="ref" href="lattice2.html#T29">LATTICE2:29</a>, <a class="ref" href="lattice2.html#T67">LATTICE2:67</a></i>;<br/>
<b>thus </b> <a href="lattice2.html#K2">FinJoin</a> <span class="p1">(<span class="default"><a href="setwiseo.html#K1">{}.</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">0L</font></span>)</span>,<font color="Maroon">f</font> = 
the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">0L</font> <a href="setwiseo.html#K7">$$</a> <span class="p1">(<span class="default"><a href="setwiseo.html#K1">{}.</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">0L</font></span>)</span>,<font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="lattice2.html#D3">LATTICE2:def 3</a></i>
<br/>.= 
 <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">0L</font>
<b>by </b><i>, <a class="ref" href="setwiseo.html#T40">SETWISEO:40</a></i>
<br/>.= 
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">0L</font>
<b>by </b><i><a class="ref" href="lattice2.html#T68">LATTICE2:68</a></i>
;<br/>


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