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<b>let </b><font color="Maroon">c<sub>1</sub></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>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="integra1.html#R3">is_integrable_on</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:28"/>
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T68">RFUNCT_1:68</a></i>;<br/>
<a NAME="E4:28"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T131">FUNCT_2:131</a></i>;<br/>
<a NAME="E5:28"/><i><font color="Green">E31</font></i>: 
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="rfunct_1.html#R3">is_bounded_on</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="integra4.html#E1:28"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rfunct_1.html#T99">RFUNCT_1:99</a></i>;<br/>
<a NAME="E6:28"/>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="seq_1.html#K13">(#)</a> <font color="Maroon">c<sub>2</sub></font> <a href="integra1.html#R3">is_integrable_on</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="integra4.html#E1:28"><i><font color="Green">E28</font></i></a>, <a class="txt" href="integra4.html#E2:28"><i><font color="Green">E29</font></i></a>, <a class="ref" href="integra2.html#T31">INTEGRA2:31</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="integra1.html#R3">is_integrable_on</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T38">RFUNCT_1:38</a></i>;<br/>
<a NAME="E8:28"/><b>then </b>
 <a href="rfunct_3.html#K19">max+</a> <span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="integra1.html#R3">is_integrable_on</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="integra4.html#E4:28"><i><font color="Green">E30</font></i></a>, <a class="txt" href="integra4.html#E5:28"><i><font color="Green">E31</font></i></a>, <a class="ref" href="integra4.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E9:28"/>
 <a href="rfunct_3.html#K20">max-</a> <font color="Maroon">c<sub>2</sub></font> <a href="integra1.html#R3">is_integrable_on</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="integra4.html#T21" target="_self">Th21</a></i>;<br/>


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