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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="latstone.html#V3" title="LATSTONE:attr.3">Stone</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> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  ex <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <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> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K3" title="LATSTONE:func.3">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b3">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K6" title="LATSTONE:func.6">DenseElements</a> <font color="Maroon" title="c1">L</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</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">  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b1">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K3" title="LATSTONE:func.3">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b2">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K6" title="LATSTONE:func.6">DenseElements</a> <font color="Maroon" title="c1">L</font> )</span><br/>



<span class="lab"><font color="Green" title="E24">A1</font></span>: <font color="Maroon" title="c2">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T4" onmouseover="rs('lattices/T4')" onmouseout="rh()">LATTICES:4</a>, <a class="ref" href="latstone.html#T7" target="_self" onmouseover="rs('latstone/T7')" onmouseout="rh()">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<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></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span>)</span>
<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="p1">(<span class="default"><span class="p2">(<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></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D11" onmouseover="rs('lattices/D11')" onmouseout="rh()">LATTICES:def 11</a></span>
;<br/>
<span class="kw">take </span><font color="Maroon" title="c3">b</font> = <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> ; <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">  ex <font color="Olive" title="b1">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K3" title="LATSTONE:func.3">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Olive" title="b1">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K6" title="LATSTONE:func.6">DenseElements</a> <font color="Maroon" title="c1">L</font> )</span><br/>

<span class="kw">take </span><font color="Maroon" title="c4">c</font> = <font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</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 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> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K3" title="LATSTONE:func.3">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c4">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K6" title="LATSTONE:func.6">DenseElements</a> <font color="Maroon" title="c1">L</font> )</span><br/>

<a NAME="E2:55"/><span class="lab"><font color="Green" title="E25">G1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></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="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#T5" onmouseover="rs('lattices/T5')" onmouseout="rh()">LATTICES:5</a></span>;<br/>
<a NAME="E3:55"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></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="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> 
 
<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#T5" onmouseover="rs('lattices/T5')" onmouseout="rh()">LATTICES:5</a></span>;<br/>
<a NAME="E4:55"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></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="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<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></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T7" onmouseover="rs('filter_0/T7')" onmouseout="rh()">FILTER_0:7</a>, <a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E25">G1</font></span></a></span>;<br/>
<a NAME="E5:55"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <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>
 
<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/>
<a NAME="E6:55"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a></span>)</span></span>)</span> <a href="latstone.html#K1" title="LATSTONE:func.1">*</a>  <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="boolealg.html#T9" onmouseover="rs('boolealg/T9')" onmouseout="rh()">BOOLEALG:9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:55"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K3" title="LATSTONE:func.3">Skeleton</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c4">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="latstone.html#K6" title="LATSTONE:func.6">DenseElements</a> <font color="Maroon" title="c1">L</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E24">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/>


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