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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:59"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V4" title="LATTICES:attr.4">join-commutative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V5" title="LATTICES:attr.5">join-associative</a> &amp; <font color="Maroon" title="c1">L</font> is <a href="robbins1.html#V5" title="ROBBINS1:attr.5">Huntington</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">L'</font> = <font color="Maroon" title="c1">L</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">z'</font> = <font color="Maroon" title="c3">z</font>, <font color="Maroon" title="c6">x'</font> = <font color="Maroon" title="c2">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">L'</font> ;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">z'</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c6">x'</font></span>)</span> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z'</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> = 
<font color="Maroon" title="c5">z'</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="robbins1.html#K6" title="ROBBINS1:func.6">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">x'</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T32" title="ROBBINS1:th.32">ROBBINS1:32</a></i>
<br/>.= 
<font color="Maroon" title="c5">z'</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><a href="robbins1.html#K7" title="ROBBINS1:func.7">Bot</a> <font color="Maroon" title="c4">L'</font></span>)</span>
<b>by </b><i><a class="ref" href="robbins1.html#T16" title="ROBBINS1:th.16">ROBBINS1:16</a></i>
<br/>.= 
<font color="Maroon" title="c5">z'</font>
<b>by </b><i><a class="ref" href="robbins1.html#T14" title="ROBBINS1:th.14">ROBBINS1:14</a></i>
;<br/>
<b>hence </b><a NAME="E5:59"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="robbins1.html#K4" title="ROBBINS1:func.4">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="robbins1.html#NK4" title="ROBBINS1:NK.4">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font>
 ;<br/>


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