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<span class="kw">let </span><font color="Maroon" title="c1">B</font> be   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">FB</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.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#NM1" title="FILTER_0:NM.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/><span class="kw">let </span><font color="Maroon" title="c2">FB</font> be   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NM1" title="FILTER_0:NM.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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NM1" title="FILTER_0:NM.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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">FI</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.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/><span class="kw">let </span><font color="Maroon" title="c5">FI</font> be   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c3">I</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E1:88"/><span class="lab"><font color="Green" title="E58">A1</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T28" target="_self" onmouseover="rs('filter_0/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<a NAME="E2:88"/>
( <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; <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T28" target="_self" onmouseover="rs('filter_0/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:88"/>
( <font color="Maroon" title="c4">i</font> <a href="filter_0.html#K7" title="FILTER_0:func.7">&lt;=&gt;</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">FI</font> &amp; <font color="Maroon" title="c6">a</font> <a href="filter_0.html#K7" title="FILTER_0:func.7">&lt;=&gt;</a> <font color="Maroon" title="c6">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">FB</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:88"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="ref" href="filter_0.html#T11" target="_self" onmouseover="rs('filter_0/T11')" onmouseout="rh()">Th11</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="filter_0.html#D12" target="_self" onmouseover="rs('filter_0/D12')" onmouseout="rh()">FILTER_0:def 12</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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