<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12" title="NORMFORM:func.12">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">zero</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="normform.html#T51" title="NORMFORM:th.51">NORMFORM:51</a></i>;<br/>
<a NAME="E2:40"/><i><font color="Green" title="E39">A1</font></i>: 
 <a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K8" title="HEYTING1:func.8">pseudo_compl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><a href="heyting1.html#K6" title="HEYTING1:func.6">-</a> <span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="heyting1.html#D8" target="_self" title="HEYTING1:def.8">Def8</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c2">u</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K8" title="HEYTING1:func.8">pseudo_compl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">u</font></span>)</span> = 
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">A</font>) <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">u</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K8" title="HEYTING1:func.8">pseudo_compl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">u</font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D2" title="LATTICES:def.2">LATTICES:def 2</a></i>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <span class="p2">(<span class="default"><a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p3">(<span class="default"><a href="heyting1.html#K6" title="HEYTING1:func.6">-</a> <span class="p4">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="heyting1.html#E2:40"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="heyting1.html#E8"><i><font color="Green" title="E5">Lm2</font></i></a></i>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <span class="p2">(<span class="default"><a href="heyting1.html#K6" title="HEYTING1:func.6">-</a> <span class="p3">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T75" title="NORMFORM:th.75">NORMFORM:75</a></i>
<br/>.= 
 <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <font color="Maroon" title="c3">zero</font>
<b>by </b><i><a class="ref" href="heyting1.html#T26" target="_self" title="HEYTING1:th.26">Th26</a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="heyting1.html#T3" target="_self" title="HEYTING1:th.3">Th3</a></i>
<br/>.= 
 <a href="lattices.html#K5" title="LATTICES:func.5">Bottom</a> <span class="p1">(<span class="default"><a href="normform.html#K12" title="NORMFORM:func.12">NormForm</a> <font color="Maroon" title="c1">A</font></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T86" title="NORMFORM:th.86">NORMFORM:86</a></i>
;<br/>


</div>
