<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">x0</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c3">f2</font> be   <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> ;<br/>





<b>assume </b><a NAME="E1:11"/>
( <font color="Maroon" title="c2">f1</font> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font> &amp; <font color="Maroon" title="c2">f1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">x0</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">f2</font> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font> )
 ;<br/>

<a NAME="E2:11"/><b>then </b>
( <font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a>  <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font> &amp; <font color="Maroon" title="c3">f2</font> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font> )
 
<b>by </b><i><a class="ref" href="fcont_1.html#T10" target="_self" title="FCONT_1:th.10">Th10</a></i>;<br/>
<a NAME="E3:11"/><b>then </b>
<font color="Maroon" title="c3">f2</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfunct_1.html#K4" title="RFUNCT_1:func.4">^</a> </span>)</span> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font>
 
<b>by </b><i><a class="ref" href="fcont_1.html#T7" target="_self" title="FCONT_1:th.7">Th7</a></i>;<br/>
<b>hence </b><a NAME="E4:11"/>
<font color="Maroon" title="c3">f2</font> <a href="rfunct_1.html#K2" title="RFUNCT_1:func.2">/</a> <font color="Maroon" title="c2">f1</font> <a href="fcont_1.html#R1" title="FCONT_1:pred.1">is_continuous_in</a> <font color="Maroon" title="c1">x0</font>
 <b>by </b><i><a class="ref" href="rfunct_1.html#T47" title="RFUNCT_1:th.47">RFUNCT_1:47</a></i>;<br/>


</div>
