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<b>let </b><font color="Maroon">L</font> be  <a href="group_1.html#V6">finite</a> <a href="lattices.html#NM1">Lattice</a>;<br/>

<a NAME="E1:5"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">L'</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font></span>)</span><b> such that </b><br/><a NAME="E4:5"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font></span>)</span>  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">L'</font> holds <br/><font color="Olive">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:5"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font></span>)</span> holds  <font color="Olive">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_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 <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font></span>)</span>;<br/>

<a NAME="E1:5_1"/>
 <a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>,<span class="p1">(<span class="default"><a href="lattice3.html#K2">LattRel</a> <font color="Maroon">L</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="lattice3.html#D2">LATTICE3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:5_1"/>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:5"/>
 ex <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font></span>)</span> st <br/>for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K3">LattPOSet</a> <font color="Maroon">L</font></span>)</span> holds  <font color="Olive">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">a</font>
 ;<br/>


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