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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D19" target="_self">LATTICE3:def 19</a><br/>



<b>set </b><font color="Maroon">B</font> =  <a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font>;<br/>
<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:58"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#R4" target="_self">is_less_than</a> <font color="Maroon">a</font>
 <b>and </b><br/><a NAME="E2:58"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>  st <font color="Maroon">x</font> <a href="lattice3.html#R4" target="_self">is_less_than</a> <font color="Olive">d</font> holds <br/><font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Olive">d</font>
 <b>and </b><br/><a NAME="E3:58"/><i><font color="Green">E25</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  <a href="lattice3.html#R4" target="_self">is_less_than</a> <font color="Maroon">c</font>
 <b>and </b><br/><a NAME="E4:58"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>  st <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  <a href="lattice3.html#R4" target="_self">is_less_than</a> <font color="Olive">d</font> holds <br/><font color="Maroon">c</font> <a href="lattices.html#R3">[=</a> <font color="Olive">d</font>
 ;<br/>

<b>set </b><font color="Maroon">Y</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span> ;<br/>
<a NAME="E5:58"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">H<sub>1</sub></font>( <a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font>) <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:58"/><i><font color="Green">E61</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:58_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span> 
 ;<br/>

<a NAME="E2:58_1"/><b>then </b>
 ex <font color="Olive">a'</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> st <br/>( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font> &amp; <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> )
 
;<br/>
<b>hence </b><a NAME="E3:58_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E7:58"/>
<font color="Maroon">x</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E8:58"/><b>then </b>
(  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> &amp;  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> &amp;  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#T2" target="_self">Th2</a>, <a class="ref" href="zfmisc_1.html#T95">ZFMISC_1:95</a>, <a class="ref" href="zfmisc_1.html#T99">ZFMISC_1:99</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">p</font> =  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span></span>)</span>, <font color="Maroon">q</font> =  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:58_2"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span>
 ;<br/><a NAME="E2:58_2"/><b>then </b><i><font color="Green">E95</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i>, <a class="ref" href="lattice3.html#T3" target="_self">Th3</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:58_2"/>
<font color="Maroon">y'</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="lattice3.html#T4" target="_self">Th4</a>, </i>;<br/><b>hence </b><a NAME="E5:58_2"/>
<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E11:58"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T94">ZFMISC_1:94</a></i>;<br/>
<a NAME="E12:58"/>
<font color="Maroon">x</font> <a href="lattice3.html#R4" target="_self">is_less_than</a> <font color="Maroon">p</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D17" target="_self">LATTICE3:def 17</a><br/>

<b>assume </b><a NAME="E1:58_3"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:58_3"/><b>then </b>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:58_3"/><b>then </b>
<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<b>hence </b><a NAME="E4:58_3"/>
<font color="Maroon">q</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">p</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E13:58"/><b>then </b>
( <font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="lattice3.html#T1" target="_self">Th1</a>, <a class="ref" href="lattice3.html#T3" target="_self">Th3</a>, </i>;<br/>
<a NAME="E14:58"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:58_4"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">a'</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span><b> such that </b><br/><a NAME="E3:58_4"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> )
 ;<br/><a NAME="E4:58_4"/>
<font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a'</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c</font>
 <b>by </b><i>, , , </i>;<br/><b>hence </b><a NAME="E5:58_4"/>
<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E16:58"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T94">ZFMISC_1:94</a></i>;<br/>
<a NAME="E17:58"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  <a href="lattice3.html#R4" target="_self">is_less_than</a> <font color="Maroon">q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D17" target="_self">LATTICE3:def 17</a><br/>

<b>assume </b><a NAME="E1:58_5"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span> 
 ;<br/>

<a NAME="E2:58_5"/><b>then </b>
<font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<b>hence </b><a NAME="E3:58_5"/>
<font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E18:58"/><b>then </b>
( <font color="Maroon">q</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E19:58"/><b>then </b><i><font color="Green">E117</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp; <font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, <a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>
<a NAME="E20:58"/>
<font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:58_6"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E2:58_6"/><b>then </b><i><font color="Green">E118</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:58_6"/><i><font color="Green">E119</font></i>: 
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font></span>)</span> )
 <b>by </b><i><a class="ref" href="lattice3.html#T4" target="_self">Th4</a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E5:58_6"/><i><font color="Green">E120</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:58_6"/>
( <font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">a'</font></span>)</span> where <font color="Olive">a'</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="lattice3.html#K1" target="_self">BooleLatt</a> <font color="Maroon">X</font></span>)</span> : <font color="Olive">a'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> </span>}</span>  &amp; <font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">y</font> )
 
<b>by </b><i>, , , , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:58_6"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E21:58"/>
<font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c</font>
 <b>by </b><i>, </i>;<br/>


</div>
