<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="realset1.html#R1" title="REALSET1:pred.1">is_Bin_Op_Preserv</a> <a onclick="hs(this)" href="javascript:()">REALSET1:def 3 : <br/></a><span> for <font color="Olive" title="b1">X</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">F</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">F</font> <a href="realset1.html#R1" title="REALSET1:pred.1">is_Bin_Op_Preserv</a> <font color="Olive" title="b3">x</font> iff ( <font color="Olive" title="b1">X</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" title="b3">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is    <a href="realset1.html#M1" title="REALSET1:mode.1">Preserv</a> of <font color="Olive" title="b2">F</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Olive" title="b1">X</font></span>)</span> <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" title="b3">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">X</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="b3">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> ) );<br/></span></div>
