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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_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"> ( <font color="Maroon" title="c1">L</font> is   <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a> iff  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">z</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="b3">y</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">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b2">z</font> &amp; (  for <font color="Olive" title="b4">v</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">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b4">v</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b2">z</font> holds <br/><font color="Olive" title="b4">v</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b3">y</font> ) ) )</span><br/>

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( <font color="Maroon" title="c1">L</font> is   <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a> iff <font color="Maroon" title="c1">L</font> is   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a> )
 
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<span class="kw">hence </span><a NAME="E2:71"/>
( <font color="Maroon" title="c1">L</font> is   <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a> iff  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">z</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="b3">y</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">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b3">y</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b2">z</font> &amp; (  for <font color="Olive" title="b4">v</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">x</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b4">v</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b2">z</font> holds <br/><font color="Olive" title="b4">v</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b3">y</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D6" onmouseover="rs('filter_0/D6')" onmouseout="rh()">FILTER_0:def 6</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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