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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> holds  <font color="Olive" title="b1">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> </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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> </span><br/>



<a NAME="E1:19"/><span class="lab"><font color="Green" title="E15">a1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:19_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN: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="ref" href="latstone.html#T6" target="_self" onmouseover="rs('latstone/T6')" onmouseout="rh()">ThD</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:19_1"/>
<font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T25" onmouseover="rs('lattices/T25')" onmouseout="rh()">LATTICES:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:19"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="19_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:19_2"/><span class="lab"><font color="Green" title="E16">a1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN: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="ref" href="lattices.html#T20" onmouseover="rs('lattices/T20')" onmouseout="rh()">LATTICES:20</a></span>;<br/>
<a NAME="E2:19_2"/>
<font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#D3" target="_self" onmouseover="rs('latstone/D3')" onmouseout="rh()">def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:19_2"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_2"><span class="lab"><font color="Green" title="E16">a1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:19"/>
<font color="Maroon" title="c2">x</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E15">a1</font></span></a>, <a class="ref" href="lattices.html#T8" onmouseover="rs('lattices/T8')" onmouseout="rh()">LATTICES:8</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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