<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T10"><span class="comment"><font color="firebrick">:: PDIFF_9:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Olive" title="b1">m</font></span>)</span><br/>  for <font color="Olive" title="b3">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">m</font></span>)</span>  st <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">Y</font> holds <br/>( <font color="Olive" title="b2">X</font> is  <a href="pdiff_7.html#V1" title="PDIFF_7:attr.1">open</a>  iff <font color="Olive" title="b3">Y</font> is  <a href="nfcont_1.html#V3" title="NFCONT_1:attr.3">open</a>  ) ;<br/></div></div>
