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<b>let </b><font color="Maroon">L</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/>

<b>set </b><font color="Maroon">J</font> = the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font>;<br/>
<b>given </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:23"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">u</font> <a href="binop_1.html#R3">is_a_unity_wrt</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="setwiseo.html#D2">SETWISEO:def 2</a><br/>

<a NAME="E2:23"/>
the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> is <a href="binop_1.html#V1">commutative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:23"/><b>then </b>
for <font color="Olive">v</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  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">u</font>,<font color="Olive">v</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font>
 
<b>by </b><i>, <a class="ref" href="binop_1.html#T12">BINOP_1:12</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:23"/>
 <a href="lattices.html#K5">Bottom</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="binop_1.html#D8">BINOP_1:def 8</a></i>;<br/>


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