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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a>  <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Olive" title="b3">c</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c4">c</font></span>)</span></span><br/>



<a NAME="E1:54"/><i><font color="Green" title="E34">A1</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="robbins1.html#T29" target="_self" title="ROBBINS1:th.29">Th29</a></i>;<br/>
<a NAME="E2:54"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="robbins1.html#K7" title="ROBBINS1:func.7">Bot</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="robbins1.html#T30" target="_self" title="ROBBINS1:th.30">Th30</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" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 
<b>by </b><i><a class="txt" href="#E1:54"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="robbins1.html#T24" target="_self" title="ROBBINS1:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
<font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <font color="Maroon" title="c4">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="robbins1.html#T11" target="_self" title="ROBBINS1:th.11">Th11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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