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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th121</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: DUALSP01:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">S</font> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  holds <br/>( <font color="Olive" title="b1">S</font> <a href="dualsp01.html#K10" title="DUALSP01:func.10">-</a> <font color="Olive" title="b2">x</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"><font color="Olive" title="b1">S</font> <a href="dualsp01.html#K10" title="DUALSP01:func.10">-</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <font color="Olive" title="b1">S</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b2">x</font> )</div></div>
