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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</a>;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="binop_1.html#NM2">BinOp</a> of <span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span><b> such that </b><br/><a NAME="E2:102"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font> <a href="realset1.html#K1">||</a> <span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> <a href="realset1.html#K1">||</a> <span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span> &amp;  <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> #) )
 <b>by </b><i><a class="ref" href="filter_2.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E3:102"/><i><font color="Green">E42</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:102"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) )
 
<b>by </b><i><a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>
<b>thus </b><a NAME="E5:102"/>
(  <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1"><a href="filter_2.html#K17" target="_self">(.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K17" target="_self">.&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="filter_2.html#K23" target="_self">latt</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1"><a href="filter_2.html#K1" target="_self">&lt;.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="filter_2.html#K1" target="_self">.)</a></span> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">c<sub>1</sub></font> #) )
 <b>by </b><i><a class="txt" href="filter_2.html#E2:102"><i><font color="Green">E41</font></i></a>, <a class="txt" href="filter_2.html#E3:102"><i><font color="Green">E42</font></i></a>, <a class="txt" href="filter_2.html#E4:102"><i><font color="Green">E43</font></i></a></i>;<br/>


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