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<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> ] <b>means </b>for <font color="Olive">x'</font> being  <a href="funct_1.html#NM1">Function</a>  st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">x'</font> holds <br/><font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">x'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>;<br/>
<div><i><font color="Green">E38</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">q</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:29_1_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E2:29_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">q</font>,<font color="Maroon">y1</font>]
 <b>and </b><br/><a NAME="E3:29_1_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">q</font>,<font color="Maroon">y2</font>]
 ;<br/><b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">q</font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i>, </i>;<br/><b>thus </b><font color="Maroon">y1</font> = 
<font color="Maroon">x1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">y2</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E45</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">q</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:29_1_1_2"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font>
 ;<br/><b>then reconsider </b><font color="Maroon">q1</font> = <font color="Maroon">q</font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i/>;<br/><b>take </b><font color="Maroon">y</font> = <font color="Maroon">q1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>;<br/><b>thus </b><a NAME="E3:29_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">q</font>,<font color="Maroon">y</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:29_1_1"/><i><font color="Green">E68</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">a</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">a</font>] ) )
 <b>from </b><i><a class="ref" href="funct_1.html#S2">FUNCT_1:sch 2</a>(, );<br/></i>
<b>take </b>
<font color="Maroon">F</font>
;<br/>

<b>thus </b><a NAME="E5:29_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="card_3.html#K4">product</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">y</font> being  <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> ) )
 <b>by </b><i/>;<br/>


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