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<b>let </b><font color="Maroon" title="c1">B</font> be   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</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">FB</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">B</font><br/> for <font color="Olive" title="b2">I</font> being  <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a><br/> for <font color="Olive" title="b3">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">I</font><br/> for <font color="Olive" title="b4">FI</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Olive" title="b2">I</font><br/> for <font color="Olive" title="b5">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b3">i</font>,<font color="Olive" title="b3">i</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Olive" title="b4">FI</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b5">a</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Olive" title="b1">FB</font> )</span><br/><b>let </b><font color="Maroon" title="c2">FB</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c1">B</font>; <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">I</font> being  <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a><br/> for <font color="Olive" title="b2">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">I</font><br/> for <font color="Olive" title="b3">FI</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Olive" title="b1">I</font><br/> for <font color="Olive" title="b4">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b2">i</font>,<font color="Olive" title="b2">i</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Olive" title="b3">FI</font> &amp; <font color="Olive" title="b4">a</font>,<font color="Olive" title="b4">a</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c2">FB</font> )</span><br/><b>let </b><font color="Maroon" title="c3">I</font> be   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</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">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">I</font><br/> for <font color="Olive" title="b2">FI</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c3">I</font><br/> for <font color="Olive" title="b3">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b1">i</font>,<font color="Olive" title="b1">i</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Olive" title="b2">FI</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b3">a</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c2">FB</font> )</span><br/><b>let </b><font color="Maroon" title="c4">i</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">I</font>; <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">FI</font> being   <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c3">I</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c4">i</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Olive" title="b1">FI</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b2">a</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c2">FB</font> )</span><br/><b>let </b><font color="Maroon" title="c5">FI</font> be    <a href="filter_0.html#M1" title="FILTER_0:mode.1">Filter</a> of <font color="Maroon" title="c3">I</font>; <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">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c4">i</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b1">a</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c2">FB</font> )</span><br/><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">i</font>,<font color="Maroon" title="c4">i</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c6">a</font> <a href="filter_0.html#R1" title="FILTER_0:pred.1">are_equivalence_wrt</a> <font color="Maroon" title="c2">FB</font> )</span><br/>











<a NAME="E1:93"/>
<font color="Maroon" title="c1">B</font> is   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a>
 
<b>by </b><i><a class="ref" href="filter_0.html#T40" target="_self" title="FILTER_0:th.40">Th40</a></i>;<br/>
<a NAME="E2:93"/><b>then </b>
( <font color="Maroon" title="c4">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c3">I</font> &amp; <font color="Maroon" title="c6">a</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T38" target="_self" title="FILTER_0:th.38">Th38</a></i>;<br/>
<a NAME="E3:93"/><b>then </b><i><font color="Green" title="E65">A1</font></i>: 
( <font color="Maroon" title="c4">i</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c3">I</font></span>)</span> &amp; <font color="Maroon" title="c6">a</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c3">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c3">I</font> &amp; <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">B</font> )
 
<b>by </b><i><a class="ref" href="lattices.html#T18" title="LATTICES:th.18">LATTICES:18</a></i>;<br/>
<a NAME="E4:93"/>
( <font color="Maroon" title="c3">I</font> is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a> &amp; <font color="Maroon" title="c1">B</font> is   <a href="lattices.html#NM5" title="LATTICES:NM.5">1_Lattice</a> )
 
<b>by </b><i><a class="ref" href="filter_0.html#T37" target="_self" title="FILTER_0:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E5:93"/>
( <font color="Maroon" title="c4">i</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c6">a</font> <a href="filter_0.html#K9" title="FILTER_0:func.9">&lt;=&gt;</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">FB</font> )
 <b>by </b><i><a class="txt" href="#E3:93"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="filter_0.html#T12" target="_self" title="FILTER_0:th.12">Th12</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="filter_0.html#D13" target="_self" title="FILTER_0:def.13">FILTER_0:def 13</a> <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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