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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = <span class="p1">(<span class="default"><a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="setwiseo.html#K6">\</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>, <a href="finsub_1.html#K5">Fin</a> <span class="p1">(<span class="default"><a href="normform.html#K7">DISJOINT_PAIRS</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E2:36_4_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">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">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><a NAME="E1:36_4_1_1"/>
<span class="p1">(<span class="default"><a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="setwiseo.html#K6">\</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="heyting1.html#R1" target="_self">c=</a>  <a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">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" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="setwiseo.html#K6">\</a> <span class="p1">(<span class="default"><a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="normform.html#K8">Normal_forms_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="heyting1.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E3:36_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="normform.html#K8">Normal_forms_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="heyting1.html#E2:36_4_1"><i><font color="Green">E32</font></i></a></i>;<br/><b>hence </b><a NAME="E4:36_4_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="normform.html#D14">NORMFORM:def 14</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="binop_1.html#NM1">UnOp</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="heyting1.html#T1" target="_self">Th1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="normform.html#K12">NormForm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>

<a NAME="E5:36_4_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="heyting1.html#K3" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E6:36_4_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="heyting1.html#E2:36_4_1"><i><font color="Green">E32</font></i></a></i>;<br/>


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