<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="bhsp_5.html#K7" title="BHSP_5:func.7">setop_xPROD</a> <a onclick="hs(this)" href="javascript:()">BHSP_5:def 7 : <br/></a><span> for <font color="Olive" title="b1">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">Y</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds <br/> ( ( <font color="Olive" title="b3">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="bhsp_5.html#K7" title="BHSP_5:func.7">setop_xPROD</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">Y</font>,<font color="Olive" title="b1">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_5.html#K6" title="BHSP_5:func.6">setop_xPre_PROD</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">Y</font>,<font color="Olive" title="b1">X</font>) ) &amp; (  not <font color="Olive" title="b3">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="bhsp_5.html#K7" title="BHSP_5:func.7">setop_xPROD</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">Y</font>,<font color="Olive" title="b1">X</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) );<br/></span></div>
