<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</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="Maroon" title="c1">L</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> holds <br/> <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a></span><br/><b>let </b><font color="Maroon" title="c2">p</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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> implies  <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a> )</span><br/>



<b>assume </b><a NAME="E1:79"/>
<font color="Maroon" title="c1">L</font> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a></span><br/>

<a NAME="E2:79"/><b>then </b>
 <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is  <a href="lattices.html#V11" title="LATTICES:attr.11">distributive</a> <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a> <a href="lattices.html#V16" title="LATTICES:attr.16">complemented</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 
<b>by </b><i><a class="ref" href="filter_0.html#T68" target="_self" title="FILTER_0:th.68">Th68</a>, <a class="ref" href="filter_0.html#T74" target="_self" title="FILTER_0:th.74">Th74</a></i>;<br/>
<b>hence </b><a NAME="E3:79"/>
 <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
