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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">x'</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x'</font> holds <br/>$2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font>;<br/>
<div><i><font color="Green" title="E21">A1</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" title="c3">q</font>, <font color="Maroon" title="c4">y1</font>, <font color="Maroon" title="c5">y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:29_1_1_1"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">f</font>
 <b>and </b><br/><a NAME="E2:29_1_1_1"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">y1</font>]
 <b>and </b><br/><a NAME="E3:29_1_1_1"/><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">y2</font>]
 ;<br/><b>reconsider </b><font color="Maroon" title="c6">x1</font> = <font color="Maroon" title="c3">q</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <b>by </b><i><a class="txt" href="pralg_3.html#E1:29_1_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="pralg_3.html#E4"><i><font color="Green" title="E4">Lm1</font></i></a></i>;<br/><b>thus </b><font color="Maroon" title="c4">y1</font> = 
<font color="Maroon" title="c6">x1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font>
<b>by </b><i><a class="txt" href="pralg_3.html#E2:29_1_1_1"><i><font color="Green" title="E23">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">y2</font>
<b>by </b><i><a class="txt" href="pralg_3.html#E3:29_1_1_1"><i><font color="Green" title="E24">A4</font></i></a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E22">A5</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" title="c3">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:29_1_1_2"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">f</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c4">q1</font> = <font color="Maroon" title="c3">q</font> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <b>by </b><i><a class="txt" href="pralg_3.html#E4"><i><font color="Green" title="E4">Lm1</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c5">y</font> = <font color="Maroon" title="c4">q1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font>;<br/><b>thus </b><a NAME="E3:29_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">y</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c3">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E4:29_1_1"/><i><font color="Green" title="E23">A6</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">f</font> &amp; ( for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">f</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font>] ) )
 <b>from </b><i><a class="ref" href="funct_1.html#S2" title="FUNCT_1:sch.2">FUNCT_1:sch 2</a>(<a class="txt" href="pralg_3.html#E1:29_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="pralg_3.html#E2:29_1_1"><i><font color="Green" title="E22">A5</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c3">F</font>
;<br/>

<b>thus </b><a NAME="E5:29_1_1"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">f</font> &amp; ( for <font color="Olive" title="b1">y</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">F</font> holds <br/><font color="Maroon" title="c3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> ) )
 <b>by </b><i><a class="txt" href="pralg_3.html#E4:29_1_1"><i><font color="Green" title="E23">A6</font></i></a></i>;<br/>


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