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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:24"/>
( <font color="Maroon">f</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( <font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">0</span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E3:24"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font></span>)</span> <a href="rfunct_1.html#K4">^</a>  <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:24"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K4">^</a> </span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">X</font> <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T62">RFUNCT_1:62</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon">f</font> <a href="rfunct_1.html#K4">^</a>  <a href="fcont_1.html#R2" target="_self">is_continuous_on</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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