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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a>   <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> 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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font> holds <br/><font color="Olive" title="b1">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font> implies <font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:26"/>
( <font color="Maroon" title="c2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <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="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <font color="Maroon" title="c1">L</font></span><br/>

<a NAME="E2:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A2</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#T16" target="_self" onmouseover="rs('latstone/T16')" onmouseout="rh()">Th13</a></span>;<br/>
<a NAME="E3:26"/>
<font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#T8" target="_self" onmouseover="rs('latstone/T8')" onmouseout="rh()">Th6</a>, <a class="ref" href="lattices.html#T6" onmouseover="rs('lattices/T6')" onmouseout="rh()">LATTICES:6</a></span>;<br/>
<a NAME="E4:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">B2</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <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">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="latstone.html#T8" target="_self" onmouseover="rs('latstone/T8')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E5:26"/>
<font color="Maroon" title="c3">b</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#T8" target="_self" onmouseover="rs('latstone/T8')" onmouseout="rh()">Th6</a>, <a class="ref" href="lattices.html#T6" onmouseover="rs('lattices/T6')" onmouseout="rh()">LATTICES:6</a></span>;<br/>
<a NAME="E6:26"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#T8" target="_self" onmouseover="rs('latstone/T8')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E7:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">B1</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <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">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E18">B2</font></span></a>, <a class="ref" href="filter_0.html#T7" onmouseover="rs('filter_0/T7')" onmouseout="rh()">FILTER_0:7</a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E17">A2</font></span></a></span>;<br/>
<a NAME="E8:26"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="latstone.html#T7" target="_self" onmouseover="rs('latstone/T7')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E9:26"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26"><span class="lab"><font color="Green" title="E19">B1</font></span></a>, <a class="ref" href="lattices.html#T8" onmouseover="rs('lattices/T8')" onmouseout="rh()">LATTICES:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:26"/>
<font color="Maroon" title="c2">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K2" title="LATSTONE:func.2">Skeleton</a> <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"> verum</span><br/>


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