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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th45</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: NFCONT_4:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">i</font> being    <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="b3">x0</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</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">n</font></span>)</span>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i</font> &amp; <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> holds <br/> <a href="pdiff_1.html#K4" title="PDIFF_1:func.4">Proj</a> (<font color="Olive" title="b2">i</font>,<font color="Olive" title="b1">n</font>) <a href="nfcont_1.html#R1" title="NFCONT_1:pred.1">is_continuous_in</a> <font color="Olive" title="b3">x0</font></div></div>
