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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: TOPRNS_1:37</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">seq</font>, <font color="Olive" title="b3">seq9</font> being   <a href="toprns_1.html#NM1" title="TOPRNS_1:NM.1">Real_Sequence</a> of <font color="Olive" title="b1">N</font>  st <font color="Olive" title="b2">seq</font> is  <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>  &amp; <font color="Olive" title="b3">seq9</font> is  <a href="toprns_1.html#V3" title="TOPRNS_1:attr.3">convergent</a>  holds <br/> <a href="toprns_1.html#K6" title="TOPRNS_1:func.6">lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">seq</font> <a href="toprns_1.html#K1" title="TOPRNS_1:func.1">+</a> <font color="Olive" title="b3">seq9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="toprns_1.html#K6" title="TOPRNS_1:func.6">lim</a> <font color="Olive" title="b2">seq</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="toprns_1.html#K6" title="TOPRNS_1:func.6">lim</a> <font color="Olive" title="b3">seq9</font></span>)</span></div></div>
