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<div class="add">

<b>let </b><font color="Maroon">IT</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:26_1_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font>
 ;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>take </b><font color="Maroon">a</font> = <font color="Maroon">a</font>;<br/><a NAME="E3:26_1_1_1"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> &amp; <font color="Olive">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" 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">b</font></span>)</span>
<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">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:26_1_1_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> &amp; <font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> )
 ;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E4:26_1_1_1"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
 <b>by </b><i>, <a class="ref" href="lattices.html#D17">LATTICES:def 17</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E2:26_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
 ;<br/>

<a NAME="E3:26_1_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" 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">b</font></span>)</span>
<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">b</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">a</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E2:26_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="robbins1.html#K5" target="_self">+</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:26_1_1"/><b>then </b>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">b</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="robbins1.html#K5" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="robbins1.html#K3" target="_self">`</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E5:26_1_1"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#K6">Top</a> <font color="Maroon">L</font>
 <b>by </b><i>, , <a class="ref" href="lattices.html#D17">LATTICES:def 17</a></i>;<br/>


</div>
