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<span class="kw">let </span><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#V6" title="ROBBINS1:attr.6">join-idempotent</a>   <a href="robbins1.html#L2" title="ROBBINS1:struct.2">ComplLattStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>for <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">c</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>
<span class="kw">take </span><font color="Maroon" title="c3">c</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c2">b</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Maroon" title="c3">c</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Olive" title="b1">a</font> <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#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">a</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">c</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c4">a</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> )</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c3">c</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">a</font></span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#T4" target="_self" title="ROBBINS1:th.4">Th4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D5" title="LATTICES:def.5">LATTICES:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <font color="Maroon" title="c4">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#D7" target="_self" title="ROBBINS1:def.7">Def7</a></span>
<br/>.= 
<font color="Maroon" title="c3">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#T4" target="_self" title="ROBBINS1:th.4">Th4</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font></span><br/>

<span class="kw">thus </span><a NAME="E3:23"/>
<font color="Maroon" title="c4">a</font> <a href="robbins1.html#K5" title="ROBBINS1:func.5">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="robbins1.html#T4" target="_self" title="ROBBINS1:th.4">Th4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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