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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="yellow_0.html#V3" title="YELLOW_0:attr.3">bounded</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">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>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b2">y</font> <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Olive" title="b1">x</font> iff <font color="Olive" title="b2">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Olive" title="b1">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</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="c3">y</font> <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font> iff <font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  )</span><br/>



<div><span class="kw">hereby </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"> ( <font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  implies <font color="Maroon" title="c3">y</font> <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:39_1"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c3">y</font> <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</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="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a> </span><br/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A2</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T21" target="_self" onmouseover="rs('yellow_7/T21')" onmouseout="rh()">Th21</a></span>
<br/>.= 
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T12" target="_self" onmouseover="rs('yellow_7/T12')" onmouseout="rh()">Th12</a>, <a class="ref" href="yellow_0.html#T42" onmouseover="rs('yellow_0/T42')" onmouseout="rh()">YELLOW_0:42</a></span>
;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> = 
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T23" target="_self" onmouseover="rs('yellow_7/T23')" onmouseout="rh()">Th23</a>, <a class="txt" href="#E1:39_1"><span class="lab"><font color="Green" title="E27">A1</font></span></a></span>
<br/>.= 
 <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T13" target="_self" onmouseover="rs('yellow_7/T13')" onmouseout="rh()">Th13</a>, <a class="ref" href="yellow_0.html#T43" onmouseover="rs('yellow_0/T43')" onmouseout="rh()">YELLOW_0:43</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:39_1"/>
<font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_1"><span class="lab"><font color="Green" title="E28">A2</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">assume </span><span class="kw">that </span><br/><a NAME="E2:39"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:39"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_1.html#D23" onmouseover="rs('waybel_1/D23')" onmouseout="rh()">WAYBEL_1:def 23</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"> <font color="Maroon" title="c3">y</font> <a href="waybel_1.html#R6" title="WAYBEL_1:pred.6">is_a_complement_of</a> <font color="Maroon" title="c2">x</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T23" target="_self" onmouseover="rs('yellow_7/T23')" onmouseout="rh()">Th23</a></span>
<br/>.= 
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="yellow_7.html#T13" target="_self" onmouseover="rs('yellow_7/T13')" onmouseout="rh()">Th13</a>, <a class="ref" href="yellow_0.html#T43" onmouseover="rs('yellow_0/T43')" onmouseout="rh()">YELLOW_0:43</a></span>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_1.html#D23" onmouseover="rs('waybel_1/D23')" onmouseout="rh()">WAYBEL_1:def 23</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"> <font color="Maroon" title="c2">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T21" target="_self" onmouseover="rs('yellow_7/T21')" onmouseout="rh()">Th21</a></span>
<br/>.= 
 <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c1">L</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="yellow_7.html#T12" target="_self" onmouseover="rs('yellow_7/T12')" onmouseout="rh()">Th12</a>, <a class="ref" href="yellow_0.html#T42" onmouseover="rs('yellow_0/T42')" onmouseout="rh()">YELLOW_0:42</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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