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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: JORDAN1K:19</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="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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>  holds <br/>(  not <font color="Olive" title="b2">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">Q</font> or <font color="Olive" title="b2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K2" title="JORDAN2C:func.2">UBD</a> <font color="Olive" title="b3">Q</font> or <font color="Olive" title="b2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="jordan2c.html#K1" title="JORDAN2C:func.1">BDD</a> <font color="Olive" title="b3">Q</font> )</div></div>
