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<span class="kw">let </span><font color="Maroon" title="c2">A</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a>  <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c2">A</font> &amp; <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">A</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  )</span><br/>

<a NAME="E1:43"/>
<a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">A</font> is  <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E2:43"/>
(  <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a>  <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c2">A</font> &amp; <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">A</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="integra8.html#E46"><span class="lab"><font color="Green" title="E41">Lm6</font></span></a>, <a class="ref" href="integra5.html#T10" onmouseover="rs('integra5/T10')" onmouseout="rh()">INTEGRA5:10</a>, <a class="ref" href="integra5.html#T11" onmouseover="rs('integra5/T11')" onmouseout="rh()">INTEGRA5:11</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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