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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="robbins1.html#V5" target="_self">Huntington</a>  <a href="robbins1.html#L2" target="_self">ComplLattStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:54"/><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">b</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:54"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">b</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="robbins1.html#K6" target="_self">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="robbins1.html#K7" target="_self">Bot</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="robbins1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E3:54"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">b</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" target="_self">`</a> 
 
<b>by </b><i>, <a class="ref" href="robbins1.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
<font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">b</font></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K6" target="_self">*'</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i/>;<br/>


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