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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th29</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: EUCLID12:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</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> 2</span>)</span><br/>  for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b4">r</font> is  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  &amp; <font color="Olive" title="b4">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">A</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b3">C</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">A</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b2">B</font></span>)</span></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> holds <br/><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a> </div></div>
