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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/>

<b>given </b><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><b> such that </b><a NAME="E2:25"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="lattice6.html#NR2" title="LATTICE6:NR.2">is-lower-neighbour-of</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font>
 ;<br/>

<a NAME="E3:25"/><i><font color="Green" title="E18">A2</font></i>: 
( <font color="Maroon" title="c2">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="txt" href="lattice6.html#E2:25"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="lattice6.html#D5" target="_self" title="LATTICE6:def.5">Def5</a></i>;<br/>
<a NAME="E4:25"/>
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T41" title="LATTICES:th.41">LATTICES:41</a></i>;<br/>
<b>hence </b><a NAME="E5:25"/>
contradiction
 <b>by </b><i><a class="txt" href="lattice6.html#E3:25"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="lattices.html#T26" title="LATTICES:th.26">LATTICES:26</a></i>;<br/>


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