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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">set</a> ] <span class="kw">means </span>( $1 is    <a href="waybel35.html#M1" title="WAYBEL35:mode.1">strict_chain</a> of <font color="Maroon" title="c2">R</font> &amp; <font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> $1 );<br/>
<span class="kw">thus </span><a NAME="E1:26_1_2"/>
for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st ( for <font color="Olive" title="b3">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN: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#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN: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="xboole_0.html#S3" title="XBOOLE_0:sch.3">XBOOLE_0:sch 3</a>();</span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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