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<span class="kw">let </span><font color="Maroon" title="c1">b</font>, <font color="Maroon" title="c2">a</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font>, <font color="Olive" title="b4">F</font>, <font color="Olive" title="b5">G</font> being  <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>   st <font color="Maroon" title="c1">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b2">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Olive" title="b3">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Olive" title="b2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Olive" title="b3">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">f</font> &amp; <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">g</font> &amp; <font color="Olive" title="b4">F</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b5">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b1">X</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b5">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b3">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font>, <font color="Olive" title="b3">F</font>, <font color="Olive" title="b4">G</font> being  <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>   st <font color="Maroon" title="c1">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Olive" title="b1">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Olive" title="b2">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Olive" title="b1">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Olive" title="b2">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font> &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b3">F</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">X</font> &amp; <font color="Olive" title="b4">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Olive" title="b2">g</font>,<font color="Maroon" title="c3">X</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b4">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b2">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font>, <font color="Maroon" title="c6">F</font>, <font color="Maroon" title="c7">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> &amp; <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c4">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Maroon" title="c5">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Maroon" title="c5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font> &amp; <font color="Maroon" title="c6">F</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c7">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:23"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c1">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">and </span><br/><a NAME="E2:23"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">and </span><br/><a NAME="E3:23"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 <span class="kw">and </span><br/><a NAME="E4:23"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
<font color="Maroon" title="c5">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 <span class="kw">and </span><br/><a NAME="E5:23"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 <span class="kw">and </span><br/><a NAME="E6:23"/><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<font color="Maroon" title="c5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> or  not <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font> or  not <font color="Maroon" title="c6">F</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font> or  not <font color="Maroon" title="c7">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">I</font> = <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E7:23"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">and </span><br/><a NAME="E8:23"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font>
 <span class="kw">and </span><br/><a NAME="E9:23"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">X</font>
 <span class="kw">and </span><br/><a NAME="E10:23"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
<font color="Maroon" title="c7">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span></span><br/>

<a NAME="E11:23"/><span class="lab"><font color="Green" title="E26">A11</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="integra7.html#T11" target="_self" title="INTEGRA7:th.11">Th11</a></span>;<br/>
<a NAME="E12:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A12</font></span>: 
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E13:23"/><span class="lab"><font color="Green" title="E28">A13</font></span>: 
<font color="Maroon" title="c7">G</font> <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="integra7.html#E13"><span class="lab"><font color="Green" title="E10">Lm1</font></span></a></span>;<br/>
<a NAME="E14:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A14</font></span>: 
<font color="Maroon" title="c7">G</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font> is  <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fdiff_1.html#T33" title="FDIFF_1:th.33">FDIFF_1:33</a></span>;<br/>
<a NAME="E15:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A15</font></span>: 
<font color="Maroon" title="c7">G</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="fcont_1.html#T17" title="FCONT_1:th.17">FCONT_1:17</a>, <a class="ref" href="integra5.html#T10" title="INTEGRA5:th.10">INTEGRA5:10</a></span>;<br/>
<a NAME="E16:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A16</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span></span>)</span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="rfunct_1.html#T101" title="RFUNCT_1:th.101">RFUNCT_1:101</a></span>;<br/>
<a NAME="E17:23"/><span class="lab"><font color="Green" title="E32">A17</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="ref" href="integra7.html#T11" target="_self" title="INTEGRA7:th.11">Th11</a></span>;<br/>
<a NAME="E18:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A18</font></span>: 
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E19:23"/><span class="lab"><font color="Green" title="E34">A19</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="integra7.html#E13"><span class="lab"><font color="Green" title="E10">Lm1</font></span></a></span>;<br/>
<a NAME="E20:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A20</font></span>: 
<font color="Maroon" title="c3">X</font> is   <a href="rcomp_1.html#V3" title="RCOMP_1:attr.3">open</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fdiff_1.html#T15" title="FDIFF_1:th.15">FDIFF_1:15</a>, <a class="ref" href="fdiff_1.html#T17" title="FDIFF_1:th.17">FDIFF_1:17</a></span>;<br/>
<a NAME="E21:23"/><span class="lab"><font color="Green" title="E36">A21</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font> is  <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:23"><span class="lab"><font color="Green" title="E34">A19</font></span></a>, <a class="ref" href="fdiff_1.html#T33" title="FDIFF_1:th.33">FDIFF_1:33</a></span>;<br/>
<a NAME="E22:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A22</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E18:23"><span class="lab"><font color="Green" title="E33">A18</font></span></a>, <a class="ref" href="fcont_1.html#T17" title="FCONT_1:th.17">FCONT_1:17</a>, <a class="ref" href="integra5.html#T10" title="INTEGRA5:th.10">INTEGRA5:10</a></span>;<br/>
<a NAME="E23:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A23</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span></span>)</span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="ref" href="rfunct_1.html#T101" title="RFUNCT_1:th.101">RFUNCT_1:101</a></span>;<br/>
<a NAME="E24:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A24</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span></span>)</span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E31">A16</font></span></a>, <a class="ref" href="rfunct_1.html#T100" title="RFUNCT_1:th.100">RFUNCT_1:100</a></span>;<br/>
<a NAME="E25:23"/>
<font color="Maroon" title="c6">F</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E21:23"><span class="lab"><font color="Green" title="E36">A21</font></span></a>, <a class="ref" href="fcont_1.html#T17" title="FCONT_1:th.17">FCONT_1:17</a></span>;<br/>
<a NAME="E26:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A25</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:23"><span class="lab"><font color="Green" title="E33">A18</font></span></a>, <a class="ref" href="integra5.html#T17" title="INTEGRA5:th.17">INTEGRA5:17</a></span>;<br/>
<a NAME="E27:23"/>
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E28:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A26</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E6:23"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E18:23"><span class="lab"><font color="Green" title="E33">A18</font></span></a>, <a class="txt" href="#E26:23"><span class="lab"><font color="Green" title="E40">A25</font></span></a>, <a class="txt" href="#E22:23"><span class="lab"><font color="Green" title="E37">A22</font></span></a>, <a class="ref" href="integra6.html#T14" title="INTEGRA6:th.14">INTEGRA6:14</a></span>;<br/>
<a NAME="E29:23"/>
( <font color="Maroon" title="c6">F</font> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c7">G</font> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:23"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E10:23"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="txt" href="integra7.html#E13"><span class="lab"><font color="Green" title="E10">Lm1</font></span></a></span>;<br/>
<a NAME="E30:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:23"><span class="lab"><font color="Green" title="E34">A19</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="ref" href="fdiff_2.html#T20" title="FDIFF_2:th.20">FDIFF_2:20</a></span>;<br/>
<a NAME="E31:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T61" title="RFUNCT_1:th.61">RFUNCT_1:61</a></span>;<br/>
<a NAME="E32:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</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="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T61" title="RFUNCT_1:th.61">RFUNCT_1:61</a></span>;<br/>
<a NAME="E33:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A27</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="fdiff_1.html#K2" title="FDIFF_1:func.2">`|</a> <font color="Maroon" title="c3">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfunct_1.html#T60" title="RFUNCT_1:th.60">RFUNCT_1:60</a></span>;<br/>
<a NAME="E34:23"/>
<font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font> <a href="fdiff_1.html#R2" title="FDIFF_1:pred.2">is_differentiable_on</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:23"><span class="lab"><font color="Green" title="E34">A19</font></span></a>, <a class="txt" href="#E13:23"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E20:23"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="ref" href="fdiff_2.html#T20" title="FDIFF_2:th.20">FDIFF_2:20</a></span>;<br/>
<a NAME="E35:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A28</font></span>: 
<font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:23"><span class="lab"><font color="Green" title="E42">A27</font></span></a>, <a class="txt" href="integra7.html#E13"><span class="lab"><font color="Green" title="E10">Lm1</font></span></a></span>;<br/>
<a NAME="E36:23"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="xxreal_0.html#D9" title="XXREAL_0:def.9">XXREAL_0:def 9</a></span>;<br/>
<a NAME="E37:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A29</font></span>: 
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T36" title="XXREAL_0:th.36">XXREAL_0:36</a></span>;<br/>
<a NAME="E38:23"/>
( <font color="Maroon" title="c1">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font> &amp; <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="integra5.html#D4" title="INTEGRA5:def.4">INTEGRA5:def 4</a>, <a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></span>;<br/>
<a NAME="E39:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A30</font></span>: 
( <font color="Maroon" title="c1">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:23"><span class="lab"><font color="Green" title="E44">A29</font></span></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></span>;<br/>
<a NAME="E40:23"/>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">F</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:23"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="txt" href="#E17:23"><span class="lab"><font color="Green" title="E32">A17</font></span></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>;<br/>
<a NAME="E41:23"/><span class="kw">then </span>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/>
<a NAME="E42:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A31</font></span>: 
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E43:23"/>
<font color="Maroon" title="c7">G</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> is  <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E14:23"><span class="lab"><font color="Green" title="E29">A14</font></span></a>, <a class="ref" href="fcont_1.html#T17" title="FCONT_1:th.17">FCONT_1:17</a></span>;<br/>
<a NAME="E44:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A32</font></span>: 
<font color="Maroon" title="c7">G</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="integra5.html#T17" title="INTEGRA5:th.17">INTEGRA5:17</a></span>;<br/>
<a NAME="E45:23"/>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="txt" href="#E11:23"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></span>;<br/>
<a NAME="E46:23"/><span class="kw">then </span>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/>
<a NAME="E47:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A33</font></span>: 
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E48:23"/>
<span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E7:23"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E49:23"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A34</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E5:23"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E12:23"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="txt" href="#E44:23"><span class="lab"><font color="Green" title="E47">A32</font></span></a>, <a class="txt" href="#E15:23"><span class="lab"><font color="Green" title="E30">A15</font></span></a>, <a class="ref" href="integra6.html#T14" title="INTEGRA6:th.14">INTEGRA6:14</a></span>;<br/>
<a NAME="E50:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="integra5.html#R1" title="INTEGRA5:pred.1">is_integrable_on</a> <span class="p1"><a href="integra5.html#K3" title="INTEGRA5:func.3">['</a><span class="default"><font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span><a href="integra5.html#K3" title="INTEGRA5:func.3">']</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:23"><span class="lab"><font color="Green" title="E48">A33</font></span></a>, <a class="txt" href="#E42:23"><span class="lab"><font color="Green" title="E46">A31</font></span></a>, <a class="txt" href="#E28:23"><span class="lab"><font color="Green" title="E41">A26</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E31">A16</font></span></a>, <a class="txt" href="#E23:23"><span class="lab"><font color="Green" title="E38">A23</font></span></a>, <a class="ref" href="integra6.html#T11" title="INTEGRA6:th.11">INTEGRA6:11</a></span>;<br/>
<a NAME="E51:23"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></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"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E24:23"><span class="lab"><font color="Green" title="E39">A24</font></span></a>, <a class="txt" href="#E35:23"><span class="lab"><font color="Green" title="E43">A28</font></span></a>, <a class="ref" href="integra7.html#T18" target="_self" title="INTEGRA7:th.18">Th18</a></span>;<br/>
<a NAME="E52:23"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:23"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E47:23"><span class="lab"><font color="Green" title="E48">A33</font></span></a>, <a class="txt" href="#E42:23"><span class="lab"><font color="Green" title="E46">A31</font></span></a>, <a class="txt" href="#E49:23"><span class="lab"><font color="Green" title="E49">A34</font></span></a>, <a class="txt" href="#E28:23"><span class="lab"><font color="Green" title="E41">A26</font></span></a>, <a class="txt" href="#E16:23"><span class="lab"><font color="Green" title="E31">A16</font></span></a>, <a class="txt" href="#E23:23"><span class="lab"><font color="Green" title="E38">A23</font></span></a>, <a class="txt" href="#E39:23"><span class="lab"><font color="Green" title="E45">A30</font></span></a>, <a class="ref" href="integra6.html#T24" title="INTEGRA6:th.24">INTEGRA6:24</a>, <a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E53:23"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">G</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c7">G</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="integra5.html#K4" title="INTEGRA5:func.4">integral</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T5" title="VALUED_1:th.5">VALUED_1:5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
