<?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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="Maroon" title="c1">L</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  &amp; <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#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a> </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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  &amp; <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#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:109"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c1">L</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q</font> or  <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">P</font> = <span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">K</font> =  <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:109"/><span class="lab"><font color="Green" title="E43">A2</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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">a9</font>, <font color="Maroon" title="c7">b9</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#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="filter_0.html#D7" title="FILTER_0:def.7">FILTER_0:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span> st <br/>( <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c7">b9</font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span>  holds <br/>(  not <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c7">b9</font> or <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Olive">b<sub>1</sub></font> ) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">a</font> = <font color="Maroon" title="c6">a9</font>, <font color="Maroon" title="c9">b</font> = <font color="Maroon" title="c7">b9</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#T69" target="_self" title="FILTER_2:th.69">Th69</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">c</font> = <font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font>;<br/>
<a NAME="E4:109"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<font color="Maroon">H<sub>1</sub></font>( <a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T73" target="_self" title="FILTER_2:th.73">Th73</a></span>;<br/>
<a NAME="E5:109"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="filter_2.html#T63" target="_self" title="FILTER_2:th.63">Th63</a></span>;<br/>
<a NAME="E6:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:109"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="lattices.html#D12" title="LATTICES:def.12">LATTICES:def 12</a></span>;<br/>
<a NAME="E7:109"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:109"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a></span>;<br/>
<a NAME="E8:109"/>
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E4:109"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="filter_2.html#T63" target="_self" title="FILTER_2:th.63">Th63</a></span>;<br/>
<a NAME="E9:109"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:109"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="filter_0.html#T6" title="FILTER_0:th.6">FILTER_0:6</a></span>;<br/>
<a NAME="E10:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T2" title="FILTER_0:th.2">FILTER_0:2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">d</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font>;<br/>
<a NAME="E11:109"/>
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T22" title="LATTICES:th.22">LATTICES:22</a></span>;<br/>
<a NAME="E12:109"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="filter_0.html#T7" title="FILTER_0:th.7">FILTER_0:7</a>, <a class="ref" href="lattices.html#T23" title="LATTICES:th.23">LATTICES:23</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">d9</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <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#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E4:109"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="filter_2.html#T63" target="_self" title="FILTER_2:th.63">Th63</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c12">d9</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c12">d9</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c7">b9</font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span>  holds <br/>(  not <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c7">b9</font> or <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c12">d9</font> ) ) )</span><br/>

<a NAME="E14:109"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">a</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font></span>)</span> &amp; <font color="Maroon" title="c8">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c12">d9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T74" target="_self" title="FILTER_2:th.74">Th74</a>, <a class="ref" href="lattices.html#D7" title="LATTICES:def.7">LATTICES:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:109"/>
<font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c12">d9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c7">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:109"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="txt" href="#E10:109"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="ref" href="filter_2.html#T75" target="_self" title="FILTER_2:th.75">Th75</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_2.html#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span>  holds <br/>(  not <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c7">b9</font> or <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c12">d9</font> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c13">e9</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#K15" title="FILTER_2:func.15">latt</a> <font color="Maroon" title="c1">L</font>,<span class="p2"><a href="filter_2.html#K14" title="FILTER_2:func.14">[#</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font></span><a href="filter_2.html#K14" title="FILTER_2:func.14">#]</a></span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c13">e9</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c7">b9</font> or <font color="Maroon" title="c13">e9</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c12">d9</font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c14">e</font> = <font color="Maroon" title="c13">e9</font>, <font color="Maroon" title="c15">ae</font> = <font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c13">e9</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#T69" target="_self" title="FILTER_2:th.69">Th69</a></span>;<br/>
<a NAME="E17:109"/>
<font color="Maroon" title="c14">e</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="#E2:109"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E4:109"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="filter_2.html#T63" target="_self" title="FILTER_2:th.63">Th63</a></span>;<br/>
<a NAME="E18:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A7</font></span>: 
<font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">e</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#T21" title="LATTICES:th.21">LATTICES:21</a></span>;<br/>
<span class="kw">assume </span><a NAME="E19:109"/>
<font color="Maroon" title="c6">a9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c13">e9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c7">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">e9</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c12">d9</font></span><br/>

<a NAME="E20:109"/><span class="kw">then </span>
<font color="Maroon" title="c15">ae</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T75" target="_self" title="FILTER_2:th.75">Th75</a></span>;<br/>
<a NAME="E21:109"/><span class="kw">then </span>
<font color="Maroon" title="c8">a</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c14">e</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T74" target="_self" title="FILTER_2:th.74">Th74</a></span>;<br/>
<a NAME="E22:109"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A8</font></span>: 
<font color="Maroon" title="c14">e</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:109"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a></span>;<br/>
<a NAME="E23:109"/>
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c14">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:109"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="txt" href="#E4:109"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="filter_2.html#T63" target="_self" title="FILTER_2:th.63">Th63</a></span>;<br/>
<a NAME="E24:109"/><span class="kw">then </span>
<font color="Maroon" title="c14">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">e</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D3" title="LATTICES:def.3">LATTICES:def 3</a></span>;<br/>
<a NAME="E25:109"/><span class="kw">then </span>
<font color="Maroon" title="c14">e</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:109"><span class="lab"><font color="Green" title="E49">A8</font></span></a>, <a class="ref" href="filter_0.html#T1" title="FILTER_0:th.1">FILTER_0:1</a></span>;<br/>
<a NAME="E26:109"/><span class="kw">then </span>
<font color="Maroon" title="c14">e</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:109"><span class="lab"><font color="Green" title="E48">A7</font></span></a>, <a class="ref" href="lattices.html#T27" title="LATTICES:th.27">LATTICES:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:109"/>
<font color="Maroon" title="c13">e9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c12">d9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T75" target="_self" title="FILTER_2:th.75">Th75</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
