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<b>let </b><font color="Maroon">L</font> be  <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">a</font> <a href="yellow_5.html#R2" target="_self">meets</a> <font color="Maroon">b</font>
 ;<br/>

<b>assume </b><a NAME="E2:30"/>
<font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E3:30"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E4:30"/>
not <font color="Maroon">a</font> <a href="yellow_5.html#R2" target="_self">meets</a> <font color="Maroon">c</font>
 ;<br/>

<a NAME="E5:30"/><b>then </b><i><font color="Green">E24</font></i>: 
not <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:30"/>
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T44">YELLOW_0:44</a></i>;<br/>
<a NAME="E7:30"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font>
 
<b>by </b><i>, , <a class="ref" href="yellow_0.html#D3">YELLOW_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:30"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow_5.html#T2" target="_self">Th2</a>, </i>;<br/>


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