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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:14_1"/>
( <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> )
 ;<br/><b>then reconsider </b><font color="Maroon">X'</font> = <font color="Maroon">X</font>, <font color="Maroon">Y'</font> = <font color="Maroon">Y</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">A</font> ;<br/><a NAME="E3:14_1"/>
( <font color="Maroon">X'</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y'</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> &amp; <font color="Maroon">X'</font> <a href="subset_1.html#K7">\</a> <font color="Maroon">Y'</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> )
 ;<br/><b>hence </b><a NAME="E4:14_1"/>
( <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> &amp; <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:14"/>
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">A</font> is <a href="finsub_1.html#V4" target="_self">preBoolean</a>
 <b>by </b><i/>;<br/>


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