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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 <a href="armstrng.html#R1" title="ARMSTRNG:pred.1">is_/\-irreducible_in</a> <font color="Maroon" title="c1">X</font>;<br/>
<b>thus </b><a NAME="E1:9_1_2"/>
for <font color="Olive" title="b1">X1</font>, <font color="Olive" title="b2">X2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st ( for <font color="Olive" title="b3">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b3">y</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">y</font>] ) ) &amp; ( for <font color="Olive" title="b3">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b3">y</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">y</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>
 <b>from </b><i><a class="ref" href="armstrng.html#S1" target="_self" title="ARMSTRNG:sch.1">ARMSTRNG:sch 1</a>();</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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