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<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>let </b><font color="Maroon">A</font> be  <a href="integra1.html#V1">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> , <font color="Maroon">B</font> be  <a href="integra1.html#V1">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:21"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">f</font> <a href="fcont_1.html#R2">is_continuous_on</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E3:21"/>
<font color="Maroon">f</font> <a href="fcont_1.html#R2">is_continuous_on</a> <font color="Maroon">B</font>
 
<b>by </b><i>, , <a class="ref" href="fcont_1.html#T17">FCONT_1:17</a></i>;<br/>
<b>hence </b><a NAME="E4:21"/>
<font color="Maroon">f</font> <a href="integra5.html#R1" target="_self">is_integrable_on</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/>


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