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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: DIOPHAN1:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">r</font> is  <a href="irrat_1.html#NV1" title="IRRAT_1:NV.1">irrational</a>  holds <br/>(  <a href="real_3.html#NK12" title="REAL_3:NK.12">cocf</a> <font color="Olive" title="b1">r</font> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp;  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <span class="p1">(<span class="default"><a href="real_3.html#NK12" title="REAL_3:NK.12">cocf</a> <font color="Olive" title="b1">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> )</div></div>
