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<div><span class="kw">theorem </span><a NAME="T17"><span class="comment"><font color="firebrick">:: CARDFIL3:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">TopSpaceMetr</a> <span class="p2">(<span class="default"><a href="normsp_2.html#K2" title="NORMSP_2:func.2">MetricSpaceNorm</a> <font color="Olive" title="b1">N</font></span>)</span></span>)</span><br/>  for <font color="Olive" title="b3">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="normsp_2.html#K2" title="NORMSP_2:func.2">MetricSpaceNorm</a> <font color="Olive" title="b1">N</font></span>)</span><br/>  for <font color="Olive" title="b4">n</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> holds <br/> <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Olive" title="b3">y</font>,<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b4">n</font></span>)</span>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="frechet.html#K1" title="FRECHET:func.1">Balls</a> <font color="Olive" title="b2">x</font></div></div>
