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<b>let </b><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <a href="integra1.html#V1" title="INTEGRA1:attr.1">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>   st <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Olive" title="b1">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Olive" title="b1">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Olive" title="b1">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Olive" title="b1">A</font> holds <br/><span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Olive" title="b1">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c1">f</font>,<font color="Olive" title="b1">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be  <a href="integra1.html#V1" title="INTEGRA1:attr.1">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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> implies <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> )</span><br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E20">A1</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> or  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> or  not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> or  not <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> or  not <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> or  not <font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> or <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> )</span><br/>

<b>assume </b><a NAME="E2:37"/><i><font color="Green" title="E21">A2</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">A</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> or  not <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> or  not <font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> or <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> )</span><br/>

<a NAME="E3:37"/><b>then </b><i><font color="Green" title="E22">A3</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> )
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T100" title="RFUNCT_1:th.100">RFUNCT_1:100</a></i>;<br/>
<b>assume </b><a NAME="E4:37"/>
( <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">A</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span><br/>

<a NAME="E5:37"/><b>then </b><i><font color="Green" title="E23">A4</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="integra1.html#V4" title="INTEGRA1:attr.4">integrable</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="integra1.html#V4" title="INTEGRA1:attr.4">integrable</a> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font> is <a href="integra1.html#V4" title="INTEGRA1:attr.4">integrable</a> )
 
<b>by </b><i><a class="ref" href="integra5.html#D2" title="INTEGRA5:def.2">INTEGRA5:def 2</a></i>;<br/>
<a NAME="E6:37"/><b>then </b><i><font color="Green" title="E24">A5</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> is <a href="integra1.html#V4" title="INTEGRA1:attr.4">integrable</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> is <a href="integra1.html#V4" title="INTEGRA1:attr.4">integrable</a> )
 
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E2:37"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="integra1.html#T59" title="INTEGRA1:th.59">INTEGRA1:59</a></i>;<br/>
<span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> = 
 <a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T22" title="RFUNCT_1:th.22">RFUNCT_1:22</a></i>
<br/>.= 
 <a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="integra5.html#T5" title="INTEGRA5:th.5">INTEGRA5:5</a></i>
<br/>.= 
 <a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T23" title="RFUNCT_1:th.23">RFUNCT_1:23</a></i>
<br/>.= 
 <a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#T23" title="RFUNCT_1:th.23">RFUNCT_1:23</a></i>
<br/>.= 
 <a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="integra5.html#T5" title="INTEGRA5:th.5">INTEGRA5:5</a></i>
<br/>.= 
 <a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="integra5.html#T5" title="INTEGRA5:th.5">INTEGRA5:5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E3:37"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="#E6:37"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="integra1.html#T59" title="INTEGRA1:th.59">INTEGRA1:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E2:37"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="#E5:37"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="integra1.html#T59" title="INTEGRA1:th.59">INTEGRA1:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="integra1.html#K13" title="INTEGRA1:func.13">integral</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">g</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="integra5.html#K1" title="INTEGRA5:func.1">||</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="#E2:37"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="#E5:37"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="integra1.html#T59" title="INTEGRA1:th.59">INTEGRA1:59</a></i>
;<br/>
<b>hence </b><a NAME="E8:37"/>
<span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c2">g</font></span>)</span>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c3">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
