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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(),   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(),   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(),   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(),   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()] <b>means </b>for <font color="Olive">r</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()  st <font color="Olive">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>5</sub></font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font>,<font color="Maroon">a<sub>4</sub></font>,<font color="Maroon">a<sub>5</sub></font>];<br/>
<a NAME="E1:18_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font>, <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()  ex <font color="Olive">t</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font>,<font color="Olive">s</font>,<font color="Olive">t</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">z</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">s</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<b>consider </b><font color="Maroon">t</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E2:18_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">s</font>,<font color="Maroon">t</font>]
 <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">t</font>
;<br/>

<b>thus </b><a NAME="E3:18_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>,<font color="Maroon">s</font>,<font color="Maroon">t</font>]
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>()</span><a href="zfmisc_1.html#K4">:]</a></span>,<font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E3:18_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">d</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">d</font></span><a href="domain_1.html#K5">]</a></span>]
 <b>from </b><i><a class="ref" href="multop_1.html#S5" target="_self">MULTOP_1:sch 5</a>();<br/></i>
<b>take </b><font color="Maroon">o</font> = <font color="Maroon">f</font>;<br/>

<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<b>thus </b><a NAME="E4:18_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">o</font> <a href="multop_1.html#K4" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>]
 <b>by </b><i/>;<br/>


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