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

<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <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">p</font>, <font color="Olive" title="b2">q</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">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Olive" title="b2">q</font> holds <br/>(  <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>) is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q</font> implies (  <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>) is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:103"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q</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"> (  <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>) is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )</span><br/>

<a NAME="E2:103"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
<font color="Maroon">H<sub>1</sub></font>( <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T72" target="_self" onmouseover="rs('filter_2/T72')" onmouseout="rh()">Th72</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">p9</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">q9</font> = <font color="Maroon" title="c3">q</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="filter_2.html#T62" target="_self" onmouseover="rs('filter_2/T62')" onmouseout="rh()">Th62</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E48">A3</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="103_1"><span class="kw">now </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">  for <font color="Olive" title="b1">a9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> holds <br/> ( <font color="Maroon" title="c5">q9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Olive" title="b1">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q9</font> &amp; <font color="Olive" title="b1">a9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q9</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">a9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</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="c5">q9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q9</font> &amp; <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q9</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">a9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T68" target="_self" onmouseover="rs('filter_2/T68')" onmouseout="rh()">Th68</a></span>;<br/><a NAME="E2:103_1"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E2:103"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="filter_2.html#T62" target="_self" onmouseover="rs('filter_2/T62')" onmouseout="rh()">Th62</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c5">q9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c6">a9</font> = 
<font color="Maroon" title="c3">q</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c7">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T73" target="_self" onmouseover="rs('filter_2/T73')" onmouseout="rh()">Th73</a></span>
<br/>.= 
<font color="Maroon" title="c5">q9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:103_1"><span class="lab"><font color="Green" title="E49">A4</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"> <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q9</font></span><br/><span class="kw">hence </span><a NAME="E4:103_1"/>
<font color="Maroon" title="c6">a9</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q9</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/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E49">A5</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="103_2"><span class="kw">now </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">  for <font color="Olive" title="b1">a9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> holds <br/> ( <font color="Maroon" title="c4">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p9</font> &amp; <font color="Olive" title="b1">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p9</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">a9</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</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="c4">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p9</font> &amp; <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p9</font> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c6">a9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T68" target="_self" onmouseover="rs('filter_2/T68')" onmouseout="rh()">Th68</a></span>;<br/><a NAME="E2:103_2"/><span class="lab"><font color="Green" title="E50">A6</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E2:103"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="filter_2.html#T62" target="_self" onmouseover="rs('filter_2/T62')" onmouseout="rh()">Th62</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c4">p9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">a9</font> = 
<font color="Maroon" title="c2">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c7">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T73" target="_self" onmouseover="rs('filter_2/T73')" onmouseout="rh()">Th73</a></span>
<br/>.= 
<font color="Maroon" title="c4">p9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:103_2"><span class="lab"><font color="Green" title="E50">A6</font></span></a>, <a class="ref" href="lattices.html#T4" onmouseover="rs('lattices/T4')" onmouseout="rh()">LATTICES:4</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"> <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p9</font></span><br/><span class="kw">hence </span><a NAME="E4:103_2"/>
<font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p9</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/></div><span class="kw">end;</span></div>
<a NAME="E6:103"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A7</font></span>: 
 <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>) is   <a href="lattices.html#V13" title="LATTICES:attr.13">lower-bounded</a>   <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:103"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="lattices.html#D13" onmouseover="rs('lattices/D13')" onmouseout="rh()">LATTICES:def 13</a>, <a class="ref" href="lattices.html#D14" onmouseover="rs('lattices/D14')" onmouseout="rh()">LATTICES:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:103"/>
 <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>) is  <a href="lattices.html#V15" title="LATTICES:attr.15">bounded</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"> (  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )</span><br/>

<span class="kw">thus </span><a NAME="E8:103"/>
(  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> &amp;  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K9" title="FILTER_2:func.9">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">#]</a></span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:103"><span class="lab"><font color="Green" title="E49">A5</font></span></a>, <a class="txt" href="#E4:103"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="txt" href="#E6:103"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="lattices.html#D16" onmouseover="rs('lattices/D16')" onmouseout="rh()">LATTICES:def 16</a>, <a class="ref" href="lattices.html#D17" onmouseover="rs('lattices/D17')" onmouseout="rh()">LATTICES:def 17</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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