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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">X</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> holds <br/><font color="Olive" title="b1">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X</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> implies <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font> )</span><br/>



<a NAME="E1:15"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
 <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">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T16" title="LATTICES:th.16">LATTICES:16</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:15"/>
<font color="Maroon" title="c2">X</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font></span><br/>

<span class="kw">hence </span><a NAME="E3:15"/>
<font color="Maroon" title="c2">X</font> <a href="boolealg.html#R1" title="BOOLEALG:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="lattices.html#T8" title="LATTICES:th.8">LATTICES:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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