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<div>:: <span class="kw">deftheorem </span>   defines <a href="realset1.html#K3" title="REALSET1:func.3">|||</a> <a onclick="hs(this)" href="javascript:()">REALSET1:def 5 : <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">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">F</font> being  <font color="Olive">b<sub>2</sub></font> <a href="realset1.html#V2" title="REALSET1:attr.2">-subsetpreserving</a>  <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">X</font> holds  <font color="Olive" title="b3">F</font> <a href="realset1.html#K3" title="REALSET1:func.3">|||</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Olive" title="b2">A</font>;<br/></span></div>
