<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T56"><span class="comment"><font color="firebrick">:: LIMFUNC2:56</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x0</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b2">f</font> <a href="limfunc2.html#R4" title="LIMFUNC2:pred.4">is_right_convergent_in</a> <font color="Olive" title="b1">x0</font> &amp; <font color="Olive" title="b2">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="limfunc2.html#K2" title="LIMFUNC2:func.2">lim_right</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">x0</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/>( <font color="Olive" title="b2">f</font> <a href="rfunct_1.html#K6" title="RFUNCT_1:func.6">^</a>  <a href="limfunc2.html#R4" title="LIMFUNC2:pred.4">is_right_convergent_in</a> <font color="Olive" title="b1">x0</font> &amp;  <a href="limfunc2.html#K2" title="LIMFUNC2:func.2">lim_right</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="rfunct_1.html#K6" title="RFUNCT_1:func.6">^</a></span>)</span>,<font color="Olive" title="b1">x0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="limfunc2.html#K2" title="LIMFUNC2:func.2">lim_right</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">x0</font>)</span>)</span> <a href="xcmplx_0.html#K5" title="XCMPLX_0:func.5">"</a>  )</div></div>
