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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">F</font> being  <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c1">L</font> is   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a> holds <br/> <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">F</font> be   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</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#NM2" title="FILTER_0:NM.2">I_Lattice</a> implies  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:101"/>
<font color="Maroon" title="c1">L</font> is   <a href="filter_0.html#NM2" title="FILTER_0:NM.2">I_Lattice</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font></span><br/>

<a NAME="E2:101"/><span class="kw">then </span>
 <a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font> is   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T84" target="_self" title="FILTER_0:th.84">Th84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:101"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="filter_0.html#K10" title="FILTER_0:func.10">equivalence_wrt</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</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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