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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: REAL_NS1:12</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">f</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Olive" title="b1">n</font></span>)</span>  st <font color="Olive" title="b2">f</font> is  <a href="rsspace3.html#NV2" title="RSSPACE3:NV.2">Cauchy_sequence_by_Norm</a>  holds <br/><font color="Olive" title="b2">f</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a> </div></div>
