<?xml version="1.0"?>
<div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>);<br/>
<a NAME="E1:7_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() holds <br/> ex <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:7_1_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() )
 ;<br/>

<b>take </b>
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">x</font>,<font color="Maroon">y</font>)
;<br/>

<b>thus </b><a NAME="E2:7_1_1"/>
( <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">x</font>,<font color="Maroon">y</font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">x</font>,<font color="Maroon">y</font>)] )
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E2:7_1"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()</span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">F<sub>3</sub></font>() st <br/>for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">f</font> <a href="binop_1.html#K1" target="_self">.</a> <font color="Olive">x</font>,<font color="Olive">y</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S1" target="_self">BINOP_1:sch 1</a>();</i><br/>


</div>
