<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">K</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="robbins1.html#L2">ComplLattStr</a> , <font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="robbins1.html#L2">ComplLattStr</a> ;<br/>

<b>assume </b><a NAME="E1:47"/><i><font color="Green">E22</font></i>: 
(  <a href="robbins1.html#G2">ComplLattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">K</font>,the <a href="robbins1.html#U1">Compl</a> of <font color="Maroon">K</font> #) <a href="hidden.html#R1">=</a>  <a href="robbins1.html#G2">ComplLattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font>,the <a href="robbins1.html#U1">Compl</a> of <font color="Maroon">L</font> #) &amp; <font color="Maroon">K</font> is <a href="robbins3.html#V9" target="_self">with_Top</a> )
 ;<br/>

<a NAME="E2:47"/><i><font color="Green">E23</font></i>: 
 <a href="lattices.html#G2">\/-SemiLattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">K</font> #) <a href="hidden.html#R1">=</a>  <a href="lattices.html#G2">\/-SemiLattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L</font> #)
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:47"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E3:47"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  <font color="Olive">x</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Olive">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Olive">y</font> <a href="robbins1.html#K3">`</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><b>proof </b></a><div class="add">

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

<b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font>, <font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i><a class="txt" href="robbins3.html#E1:47"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E2:47_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">x</font> <a href="robbins1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font> <a href="robbins1.html#K3">`</a>  &amp; <font color="Maroon">y</font> <a href="robbins1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y'</font> <a href="robbins1.html#K3">`</a>  )
 
<b>by </b><i><a class="txt" href="robbins3.html#E1:47"><i><font color="Green">E22</font></i></a>, <a class="ref" href="robbins3.html#D3" target="_self">Def3</a></i>;<br/>
<font color="Maroon">x</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> = 
<font color="Maroon">x'</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Maroon">x'</font> <a href="robbins1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="txt" href="robbins3.html#E2:47"><i><font color="Green">E23</font></i></a>, </i>
<br/>.= 
<font color="Maroon">y'</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Maroon">y'</font> <a href="robbins1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="txt" href="robbins3.html#E1:47"><i><font color="Green">E22</font></i></a>, </i>
<br/>.= 
<font color="Maroon">y</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span>
<b>by </b><i><a class="txt" href="robbins3.html#E2:47"><i><font color="Green">E23</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E4:47_1"/>
<font color="Maroon">x</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="robbins1.html#K3">`</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="robbins3.html#NK1" target="_self">|_|</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="robbins1.html#K3">`</a> </span>)</span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:47"/>
<font color="Maroon">L</font> is <a href="robbins3.html#V9" target="_self">with_Top</a>
 <b>by </b><i/>;<br/>


</div>
