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<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> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds   <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> 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">  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font></span><br/>



<a NAME="E1:86"/>
 <a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> is   <a href="lattices.html#NM4" title="LATTICES:NM.4">0_Lattice</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T70" target="_self" title="FILTER_0:th.70">Th70</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">q9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:86"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
for <font color="Olive" title="b1">r9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> holds <br/> ( <font color="Maroon" title="c3">q9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Olive" title="b1">r9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q9</font> &amp; <font color="Olive" title="b1">r9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c3">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q9</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattices.html#D13" title="LATTICES:def.13">LATTICES:def 13</a></span>;<br/>
<a NAME="E4:86"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T63" target="_self" title="FILTER_0:th.63">Th63</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">p9</font> = <font color="Maroon" title="c2">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T19" target="_self" title="FILTER_0:th.19">Th19</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">q</font> = <font color="Maroon" title="c3">q9</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span> <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T63" target="_self" title="FILTER_0:th.63">Th63</a></span>;<br/>
<a NAME="E7:86"/>
<font color="Maroon" title="c3">q9</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c4">p9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E53">A1</font></span></a></span>;<br/>
<a NAME="E8:86"/><span class="kw">then </span>
<font color="Maroon" title="c3">q9</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">p9</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/>
<a NAME="E9:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T65" target="_self" title="FILTER_0:th.65">Th65</a></span>;<br/>
<a NAME="E10:86"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T18" target="_self" title="FILTER_0:th.18">Th18</a></span>;<br/>
<a NAME="E11:86"/>
<font color="Maroon" title="c3">q9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:86"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="ref" href="rlsub_2.html#T84" title="RLSUB_2:th.84">RLSUB_2:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:86"/>
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="filter_0.html#K8" title="FILTER_0:func.8">latt</a> <span class="p2"><a href="filter_0.html#K2" title="FILTER_0:func.2">&lt;.</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="filter_0.html#K2" title="FILTER_0:func.2">.)</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:86"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E10:86"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="ref" href="lattices.html#T26" title="LATTICES:th.26">LATTICES:26</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/>


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