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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  holds not <font color="Olive" title="b1">b</font> <a href="lattice6.html#R1" title="LATTICE6:pred.1">is-upper-neighbour-of</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font></span><br/>

<span class="kw">given </span><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><span class="kw"> such that </span><a NAME="E2:23"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="lattice6.html#R1" title="LATTICE6:pred.1">is-upper-neighbour-of</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:23"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T45" title="LATTICES:th.45">LATTICES:45</a></span>;<br/>
<a NAME="E4:23"/>
(  <a href="lattices.html#K6" title="LATTICES:func.6">Top</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> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="lattice6.html#D5" target="_self" title="LATTICE6:def.5">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:23"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="lattices.html#T26" title="LATTICES:th.26">LATTICES:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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