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

<b>let </b><font color="Maroon" title="c1">Q</font> be   <a href="quantal1.html#NM5" title="QUANTAL1:NM.5">Girard-Quantale</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">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b2">a</font></span>)</span> where <font color="Olive" title="b2">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span><br/>



<a NAME="E1:63"/>
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="lattice3.html#R3" title="LATTICE3:pred.3">is_less_than</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D16" title="LATTICE3:def.16">LATTICE3:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">b</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="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span>  or  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c3">b</font> )</span><br/>

<b>assume </b><a NAME="E1:63_1"/>
<font color="Maroon" title="c3">b</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="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c3">b</font></span><br/>

<b>then consider </b><font color="Maroon" title="c4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font><b> such that </b><br/><a NAME="E3:63_1"/><i><font color="Green" title="E27">A1</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">a</font> &amp; <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>
<a NAME="E4:63_1"/>
<font color="Maroon" title="c4">a</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font>
 
<b>by </b><i><a class="txt" href="quantal1.html#E3:63_1"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="lattice3.html#T38" title="LATTICE3:th.38">LATTICE3:38</a></i>;<br/>
<b>hence </b><a NAME="E5:63_1"/>
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="quantal1.html#E3:63_1"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="quantal1.html#T13" target="_self" title="QUANTAL1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:63"/><b>then </b><i><font color="Green" title="E27">A2</font></i>: 
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#T40" title="LATTICE3:th.40">LATTICE3:40</a></i>;<br/>
<a NAME="E3:63"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b2">a</font></span>)</span> where <font color="Olive" title="b2">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span>  <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a>  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D17" title="LATTICE3:def.17">LATTICE3:def 17</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b2">a</font></span>)</span> where <font color="Olive" title="b2">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span>  or <font color="Maroon" title="c3">c</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a>  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font> )</span><br/>

<b>assume </b><a NAME="E1:63_2"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b2">a</font></span>)</span> where <font color="Olive" title="b2">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">c</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a>  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font></span><br/>

<b>then consider </b><font color="Maroon" title="c4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font><b> such that </b><br/><a NAME="E3:63_2"/><i><font color="Green" title="E28">A3</font></i>: 
( <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> )
 ;<br/>
<a NAME="E4:63_2"/>
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">b</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="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="quantal1.html#E3:63_2"><i><font color="Green" title="E28">A3</font></i></a></i>;<br/>
<a NAME="E5:63_2"/><b>then </b>
(  <a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">b</font> &amp;  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="quantal1.html#K1" title="QUANTAL1:func.1">-r&gt;</a> <span class="p1">(<span class="default"><a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="lattice3.html#T38" title="LATTICE3:th.38">LATTICE3:38</a></i>;<br/>
<b>hence </b><a NAME="E6:63_2"/>
<font color="Maroon" title="c3">c</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font>
 <b>by </b><i><a class="txt" href="quantal1.html#E3:63_2"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="quantal1.html#T12" target="_self" title="QUANTAL1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:63"/><b>then </b>
 <a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p4">{<span class="default"> <span class="p5">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b2">a</font></span>)</span> where <font color="Olive" title="b2">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D21" title="LATTICE3:def.21">LATTICE3:def 21</a></i>;<br/>
<a NAME="E5:63"/><b>then </b>
( <span class="p1">(<span class="default"><a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="monoid_0.html#NK3" title="MONOID_0:NK.3">[*]</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font> &amp;  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="quantal1.html#K1" title="QUANTAL1:func.1">-r&gt;</a> <span class="p1">(<span class="default"><a href="quantal1.html#K3" title="QUANTAL1:func.3">Bottom</a> <font color="Maroon" title="c1">Q</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="quantal1.html#D5" target="_self" title="QUANTAL1:def.5">Def5</a></i>;<br/>
<a NAME="E6:63"/><b>then </b>
 <a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a>  <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="quantal1.html#T12" target="_self" title="QUANTAL1:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E7:63"/>
 <a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="lattice3.html#K15" title="LATTICE3:func.15">"\/"</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">Q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K16" title="LATTICE3:func.16">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="quantal1.html#K5" title="QUANTAL1:func.5">Bottom</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">Q</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> </span>}</span> ,<font color="Maroon" title="c1">Q</font>
 <b>by </b><i><a class="txt" href="quantal1.html#E2:63"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="lattices.html#T26" title="LATTICES:th.26">LATTICES:26</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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