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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattices.html#V4">join-commutative</a> <a href="lattices.html#V5">join-associative</a> <a href="lattices.html#V6">meet-commutative</a> <a href="lattices.html#V8">meet-absorbing</a> <a href="lattices.html#V9">join-absorbing</a>  <a href="lattices.html#L3">LattStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">r</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
<b>by </b><i><a class="ref" href="lattices.html#T17">LATTICES:17</a></i>
<br/>.= 
<font color="Maroon">r</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
<b>by </b><i>, <a class="ref" href="lattices.html#D5">LATTICES:def 5</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a><br/>


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