<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="realset1.html#K4" title="REALSET1:func.4">!</a> <a onclick="hs(this)" href="javascript:()">REALSET1:def 7 : <br/></a><span> for <font color="Olive" title="b1">A</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">F</font> being  <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <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">A</font> holds  <font color="Olive" title="b3">F</font> <a href="realset1.html#K4" title="REALSET1:func.4">!</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">x</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> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>;<br/></span></div>
