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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a>] <span class="kw">means </span>$1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <span class="p1">(<span class="default"><a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font></span>)</span>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>3</sub></font>(  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a>) <span class="kw">-&gt; </span>  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a> = $1;<br/>
<a NAME="E1:40_1_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <span class="p1">(<span class="default"><a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font></span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
;<br/>
<a NAME="E2:40_1_1"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<span class="p1"> { <span class="default"> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive" title="b1">Q</font>) where <font color="Olive" title="b1">Q</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> : <font color="Olive" title="b1">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <span class="p1">(<span class="default"><a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font></span>)</span> </span> } </span>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="fraenkel.html#S21" onmouseover="rs('fraenkel/S21')" onmouseout="rh()">FRAENKEL:sch 21</a>(<a class="txt" href="#E1:40_1_1"><span class="lab"><font color="Green" title="E20">A1</font></span></a>);<br/></span>
<a NAME="E3:40_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is   <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">Q</font>] </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="fraenkel.html#S10" onmouseover="rs('fraenkel/S10')" onmouseout="rh()">FRAENKEL:sch 10</a>();<br/></span>
<span class="kw">hence </span><a NAME="E4:40_1_1"/>
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">Q</font> where <font color="Olive" title="b1">Q</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> : <font color="Olive" title="b1">Q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio4.html#K6" title="LTLAXIO4:func.6">comp</a> <span class="p1">(<span class="default"><a href="ltlaxio4.html#K8" title="LTLAXIO4:func.8">untn</a> <font color="Maroon" title="c3">P</font></span>)</span> </span> } </span>  is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span>,<span class="p2">(<span class="default"><a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <a href="ltlaxio3.html#K1" title="LTLAXIO3:func.1">**</a></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:40_1_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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