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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> ] <b>means </b>$1 is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font>;<br/>
<b>consider </b><font color="Maroon" title="c2">R</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E2:13_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
for <font color="Olive" title="b1">x1</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> iff ( <font color="Olive" title="b1">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x1</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1" title="XBOOLE_0:sch.1">XBOOLE_0:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c2">R</font>
;<br/>

<b>let </b><font color="Maroon" title="c3">x1</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>thus </b><a NAME="E3:13_1_1"/>
( <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> implies <font color="Maroon" title="c3">x1</font> is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font> )
 <b>by </b><i><a class="txt" href="integra1.html#E2:13_1_1"><i><font color="Green" title="E9">A1</font></i></a></i>;<br/>

<b>assume </b><a NAME="E4:13_1_1"/>
<font color="Maroon" title="c3">x1</font> is    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c3">x1</font> as    <a href="integra1.html#M1" title="INTEGRA1:mode.1">DivisionPoint</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E6:13_1_1"/>
<font color="Maroon" title="c4">p</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
;<br/>
<b>hence </b><a NAME="E7:13_1_1"/>
<font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font>
 <b>by </b><i><a class="txt" href="integra1.html#E2:13_1_1"><i><font color="Green" title="E9">A1</font></i></a></i>;<br/>


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