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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <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>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font></span>)</span> = <span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="setwiseo.html#K6" title="SETWISEO:func.6">\</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> $1</span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c3">IT</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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>, <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7" title="NORMFORM:func.7">DISJOINT_PAIRS</a> <font color="Maroon" title="c1">A</font></span>)</span><b> such that </b><br/><a NAME="E2:36_4_1"/><i><font color="Green" title="E32">A8</font></i>: 
for <font color="Olive" title="b1">v</font> being  <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> holds  <font color="Maroon" title="c3">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">v</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</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/><a NAME="E1:36_4_1_1"/>
<span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="setwiseo.html#K6" title="SETWISEO:func.6">\</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="heyting1.html#R1" title="HEYTING1:pred.1">c=</a>  <a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/><a NAME="E2:36_4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font></span>)</span> <a href="setwiseo.html#K6" title="SETWISEO:func.6">\</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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="heyting1.html#T8" target="_self" title="HEYTING1:th.8">Th8</a></i>;<br/><a NAME="E3:36_4_1_1"/><b>then </b>
<font color="Maroon" title="c3">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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="txt" href="heyting1.html#E2:36_4_1"><i><font color="Green" title="E32">A8</font></i></a></i>;<br/><b>hence </b><a NAME="E4:36_4_1_1"/>
<font color="Maroon" title="c3">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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>
 <b>by </b><i><a class="ref" href="normform.html#D14" title="NORMFORM:def.14">NORMFORM:def 14</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c4">IT</font> = <font color="Maroon" title="c3">IT</font> as   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="heyting1.html#T1" target="_self" title="HEYTING1:th.1">Th1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">IT</font>
;<br/>

<b>let </b><font color="Maroon" title="c5">v</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/>

<a NAME="E5:36_4_1"/>
( <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c5">v</font> &amp; <font color="Maroon" title="c2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="heyting1.html#K3" title="HEYTING1:func.3">@</a> <font color="Maroon" title="c2">u</font> )
 
;<br/>
<b>hence </b><a NAME="E6:36_4_1"/>
<font color="Maroon" title="c4">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c5">v</font>
 <b>by </b><i><a class="txt" href="heyting1.html#E2:36_4_1"><i><font color="Green" title="E32">A8</font></i></a></i>;<br/>


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