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<div><span class="kw">theorem </span><a NAME="T36"><span class="comment"><font color="firebrick">:: RUSUB_5:36</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">u</font>, <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">w</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b5">r</font>, <font color="Olive" title="b6">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b2">u</font>,<font color="Olive" title="b5">r</font>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b4">w</font>,<font color="Olive" title="b6">p</font>)</span>)</span> holds <br/> ex <font color="Olive" title="b7">q</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>(  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b7">q</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b2">u</font>,<font color="Olive" title="b5">r</font>) &amp;  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b7">q</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b4">w</font>,<font color="Olive" title="b6">p</font>) )</div></div>
