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<b>let </b><font color="Maroon">V</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <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="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/><b>let </b><font color="Maroon">B</font> be    <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="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/><b>let </b><font color="Maroon">D</font> be    <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="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font></span>)</span>;<br/>









<b>assume </b><a NAME="E1:25"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 ;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>,   <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="funct_1.html#NM1">Function</a>,  <a href="funct_1.html#NM1">Function</a>] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">a<sub>2</sub></font> );<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="funct_1.html#NM1">Function</a>,  <a href="funct_1.html#NM1">Function</a>] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">a<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">a<sub>2</sub></font> );<br/>
<b>set </b><font color="Maroon">X1</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">s</font>,<font color="Olive">t</font>] </span>}</span> ;<br/>
<b>set </b><font color="Maroon">X2</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">s</font>,<font color="Olive">t</font>] </span>}</span> ;<br/>
<a NAME="E2:25"/><i><font color="Green">E23</font></i>: 
for <font color="Olive">s</font>, <font color="Olive">t</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">s</font>,<font color="Olive">t</font>] holds <br/><font color="Maroon">S<sub>2</sub></font>[<font color="Olive">s</font>,<font color="Olive">t</font>]
 
<b>by </b><i/>;<br/>
<a NAME="E3:25"/><i><font color="Green">E28</font></i>: 
<span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">s</font>,<font color="Olive">t</font>] </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">s</font>,<font color="Olive">t</font>) where <font color="Olive">s</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>, <font color="Olive">t</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">s</font>,<font color="Olive">t</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="fraenkel.html#S2">FRAENKEL:sch 2</a>();<br/></i>
<b>thus </b><a NAME="E4:25"/>
<font color="Maroon">A</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> <a href="substlat.html#K4" target="_self">^</a> <font color="Maroon">D</font>
 <b>by </b><i/>;<br/>


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