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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>   <a href="latstone.html#V1" title="LATSTONE:attr.1">pseudocomplemented</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">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">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">a</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b2">b</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Olive" title="b3">x</font> holds <br/><font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">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">a</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c3">b</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">x</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:11"/><span class="lab"><font color="Green" title="E7">a1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E2:11"/><span class="lab"><font color="Green" title="E8">b1</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="latstone.html#R1" title="LATSTONE:pred.1">is_a_pseudocomplement_of</a> <font color="Maroon" title="c4">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="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font></span><br/>

<a NAME="E3:11"/><span class="lab"><font color="Green" title="E9">a2</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">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="txt" href="#E1:11"><span class="lab"><font color="Green" title="E7">a1</font></span></a></span>;<br/>
<a NAME="E4:11"/><span class="lab"><font color="Green" title="E10">b2</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">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="txt" href="#E2:11"><span class="lab"><font color="Green" title="E8">b1</font></span></a></span>;<br/>
<a NAME="E5:11"/><span class="lab"><font color="Green" title="E11">ab1</font></span>: 
<font color="Maroon" title="c3">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E7">a1</font></span></a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E10">b2</font></span></a></span>;<br/>
<a NAME="E6:11"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E8">b1</font></span></a>, <a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E9">a2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:11"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:11"><span class="lab"><font color="Green" title="E11">ab1</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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