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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th8</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: TIETZE_2:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">p</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Olive" title="b1">n</font></span>)</span><br/>  for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b4">R</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">R</font> &amp; <font color="Olive" title="b3">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b4">R</font></span>)</span> holds <br/> <a href="tietze_2.html#K2" title="TIETZE_2:func.2">OpenHypercube</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tietze_2.html#K3" title="TIETZE_2:func.3">ClosedHypercube</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b4">R</font>)</div></div>
