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<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] <span class="kw">means </span> ex <font color="Olive" title="b1">B</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">FX</font> st <br/>( <font color="Olive" title="b1">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">FX</font> &amp; $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="pcomps_2.html#K1" title="PCOMPS_2:func.1">PartUnion</a> (<font color="Olive" title="b1">B</font>,<font color="Maroon" title="c2">R</font>)</span>)</span> );<br/>
<span class="kw">thus </span><a NAME="E1:4_1_2"/>
 for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st (  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b3">x</font>] ) ) &amp; (  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b3">x</font>] ) ) holds <br/><font color="Olive" title="b1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X2</font>
 <span class="kw">from</span> <span class="lab"><a class="ref" href="xfamily.html#S3" onmouseover="rs('xfamily/S3')" onmouseout="rh()">XFAMILY:sch 3</a>();</span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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