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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E11">Def4</font></span>   defines <a href="mmlquer2.html#V1" title="MMLQUER2:attr.1">beta-transitive</a> <a onclick="hs(this)" href="javascript:()">MMLQUER2:def 4 : <br/></a><span> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">R</font> being   <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">R</font> is  <a href="mmlquer2.html#V1" title="MMLQUER2:attr.1">beta-transitive</a>  iff  for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font> <a href="mmlquery.html#NR2" title="MMLQUERY:NR.2">nin</a> <font color="Olive" title="b2">R</font> holds <br/> for <font color="Olive" title="b5">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">x</font>,<font color="Olive" title="b5">z</font> <a href="mmlquery.html#R1" title="MMLQUERY:pred.1">in</a> <font color="Olive" title="b2">R</font> holds <br/><font color="Olive" title="b4">y</font>,<font color="Olive" title="b5">z</font> <a href="mmlquery.html#R1" title="MMLQUERY:pred.1">in</a> <font color="Olive" title="b2">R</font> );<br/></span></div>
