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

<span class="kw">let </span><font color="Maroon" title="c1">BL</font> be   <a href="lattices.html#V17" title="LATTICES:attr.17">Boolean</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">AF</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="lattice4.html#NM2" title="LATTICE4:NM.2">ClosedSubset</a> of <font color="Maroon" title="c1">BL</font>  st  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">AF</font> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">BL</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">AF</font> holds <br/><span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b2">B</font></span>)</span> where <font color="Olive" title="b2">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Olive" title="b1">AF</font> </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K3" title="LATTICE4:func.3">field_by</a> <font color="Olive" title="b1">AF</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">AF</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="lattice4.html#NM2" title="LATTICE4:NM.2">ClosedSubset</a> of <font color="Maroon" title="c1">BL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">BL</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font> implies <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K3" title="LATTICE4:func.3">field_by</a> <font color="Maroon" title="c2">AF</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:54"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font>
 <span class="kw">and </span><br/><a NAME="E2:54"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
 <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">BL</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K3" title="LATTICE4:func.3">field_by</a> <font color="Maroon" title="c2">AF</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">A1</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span> ;<br/>
<a NAME="E3:54"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<font color="Maroon" title="c2">AF</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:54_1"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c4">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">BL</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">B</font> = <span class="p1"><a href="setwiseo.html#K2" title="SETWISEO:func.2">{.</a><span class="default"><font color="Maroon" title="c5">b</font></span><a href="setwiseo.html#K2" title="SETWISEO:func.2">.}</a></span> as   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> ;<br/>
<font color="Maroon" title="c5">b</font> = 
<span class="p1">(<span class="default"><a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <font color="Maroon" title="c1">BL</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T14" title="LATTICES:th.14">LATTICES:14</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">BL</font></span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c5">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T29" target="_self" title="LATTICE4:th.29">Th36</a></span>
;<br/>
<a NAME="E5:54_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E1:54_1"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="lattice4.html#T37" target="_self" title="LATTICE4:th.37">Th44</a></span>;<br/>
<a NAME="E6:54_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A5</font></span>: 
<font color="Maroon" title="c6">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T31" title="ZFMISC_1:th.31">ZFMISC_1:31</a></span>;<br/>
<a NAME="E7:54_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c6">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T10" target="_self" title="LATTICE4:th.10">Th17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:54_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:54_1"><span class="lab"><font color="Green" title="E46">A5</font></span></a></span>; <a class="txt" 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="E4:54"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:54_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font></span><br/>

<a NAME="E2:54_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">B</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> st <br/>( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:54_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font>
 ; <a class="txt" 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>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">A1</font> = <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">BL</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E44">A3</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E45">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="54_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">F</font> be    <a href="lattice4.html#M2" title="LATTICE4:mode.2">Field</a> of <font color="Maroon" title="c1">BL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">AF</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font> implies <font color="Maroon" title="c4">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font> )</span><br/><span class="kw">assume </span><a NAME="E1:54_3"/><span class="lab"><font color="Green" title="E46">A7</font></span>: 
<font color="Maroon" title="c2">AF</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font></span><br/><span class="kw">thus </span><a NAME="E2:54_3"/>
<font color="Maroon" title="c4">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c6">F1</font> = <font color="Maroon" title="c5">F</font> as   <a href="lattice4.html#NM2" title="LATTICE4:NM.2">ClosedSubset</a> of <font color="Maroon" title="c1">BL</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T35" target="_self" title="LATTICE4:th.35">Th42</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> or <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:54_3_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">B</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font><span class="kw"> such that </span><br/><a NAME="E4:54_3_1"/><span class="lab"><font color="Green" title="E47">A8</font></span>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c8">B</font>
 <span class="kw">and </span><br/><a NAME="E5:54_3_1"/><span class="lab"><font color="Green" title="E48">A9</font></span>: 
<font color="Maroon" title="c8">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font>
 ;<br/>
<a NAME="E6:54_3_1"/>
 <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_3_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> or <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:54_3_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font></span><br/>

<a NAME="E2:54_3_1_1"/><span class="kw">then </span>
 ex <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">BL</font> st <br/>( <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">AF</font> )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:54_3_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_3"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="ref" href="lattice4.html#T33" target="_self" title="LATTICE4:th.33">Th40</a></span>; <a class="txt" 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="E7:54_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:54_3_1"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:54_3_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E1:54_3"><span class="lab"><font color="Green" title="E46">A7</font></span></a>, <a class="txt" href="#E4:54_3_1"><span class="lab"><font color="Green" title="E47">A8</font></span></a>, <a class="ref" href="lattice4.html#T24" target="_self" title="LATTICE4:th.24">Th31</a></span>; <a class="txt" 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="kw">end;</span></div>
<a NAME="E7:54"/>
<font color="Maroon" title="c4">A1</font> is    <a href="lattice4.html#M2" title="LATTICE4:mode.2">Field</a> of <font color="Maroon" title="c1">BL</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">BL</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="lattice4.html#D9" target="_self" title="LATTICE4:def.9">LATTICE4:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">BL</font>  st <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> &amp; <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> holds <br/>( <font color="Maroon" title="c5">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> &amp; <font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">BL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> &amp; <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> implies ( <font color="Maroon" title="c5">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> &amp; <font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:54_4"/><span class="lab"><font color="Green" title="E46">A10</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
 <span class="kw">and </span><br/><a NAME="E2:54_4"/><span class="lab"><font color="Green" title="E47">A11</font></span>: 
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> &amp; <font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:54_4"/>
<font color="Maroon" title="c5">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c7">B2</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font><span class="kw"> such that </span><br/><a NAME="E2:54_4_1"/><span class="lab"><font color="Green" title="E48">A12</font></span>: 
( <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c7">B2</font> &amp; <font color="Maroon" title="c7">B2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_4"><span class="lab"><font color="Green" title="E47">A11</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">B1</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font><span class="kw"> such that </span><br/><a NAME="E4:54_4_1"/><span class="lab"><font color="Green" title="E49">A13</font></span>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c8">B1</font> &amp; <font color="Maroon" title="c8">B1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_4"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">B0</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font><span class="kw"> such that </span><br/><a NAME="E6:54_4_1"/><span class="lab"><font color="Green" title="E50">A14</font></span>: 
<font color="Maroon" title="c9">B0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">B1</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Maroon" title="c7">B2</font>
 ;<br/>
<a NAME="E7:54_4_1"/>
( <font color="Maroon" title="c9">B0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> &amp; <font color="Maroon" title="c5">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c9">B0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54_4_1"><span class="lab"><font color="Green" title="E49">A13</font></span></a>, <a class="txt" href="#E2:54_4_1"><span class="lab"><font color="Green" title="E48">A12</font></span></a>, <a class="txt" href="#E6:54_4_1"><span class="lab"><font color="Green" title="E50">A14</font></span></a>, <a class="ref" href="lattice4.html#T23" target="_self" title="LATTICE4:th.23">Th30</a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:54_4_1"/>
<font color="Maroon" title="c5">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
 ; <a class="txt" 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>

<span class="kw">thus </span><a NAME="E4:54_4"/>
<font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_4_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c7">B</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font><span class="kw"> such that </span><br/><a NAME="E2:54_4_2"/><span class="lab"><font color="Green" title="E48">A15</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E3:54_4_2"/><span class="lab"><font color="Green" title="E49">A16</font></span>: 
<font color="Maroon" title="c7">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_4"><span class="lab"><font color="Green" title="E46">A10</font></span></a></span>;<br/>
<a NAME="E4:54_4_2"/>
<font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice2.html#K2" title="LATTICE2:func.2">FinJoin</a> (<font color="Maroon" title="c7">B</font>,<span class="p1">(<span class="default"><a href="lattice4.html#K5" title="LATTICE4:func.5">comp</a> <font color="Maroon" title="c1">BL</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54_4_2"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="lattice4.html#T41" target="_self" title="LATTICE4:th.41">Th48</a></span>;<br/>
<a NAME="E5:54_4_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">B0</font> being   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> st <br/>( <font color="Olive" title="b1">B0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> &amp; <font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B0</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E3:54_4_2"><span class="lab"><font color="Green" title="E49">A16</font></span></a>, <a class="ref" href="lattice4.html#T42" target="_self" title="LATTICE4:th.42">Th49</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:54_4_2"/>
<font color="Maroon" title="c5">p</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A1</font>
 ; <a class="txt" 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="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E8:54"/>
<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="lattice4.html#K2" title="LATTICE4:func.2">FinMeet</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="finsub_1.html#NM1" title="FINSUB_1:NM.1">Finite_Subset</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">BL</font> : <font color="Olive" title="b1">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="lattice4.html#K4" title="LATTICE4:func.4">SetImp</a> <font color="Maroon" title="c2">AF</font> </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice4.html#K3" title="LATTICE4:func.3">field_by</a> <font color="Maroon" title="c2">AF</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E6:54"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="ref" href="lattice4.html#D10" target="_self" title="LATTICE4:def.10">Def15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
