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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">M</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  st  ex <font color="Olive" title="b4">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">S</font> st <br/>( <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b3">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b4">A</font> ) &amp; <font color="Olive" title="b3">f</font> <a href="mesfun6c.html#R2" title="MESFUN6C:pred.2">is_integrable_on</a> <font color="Olive" title="b2">M</font> &amp;  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Olive" title="b2">M</font>,<font color="Olive" title="b3">f</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Olive" title="b2">M</font>,<font color="Olive" title="b3">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Olive" title="b2">M</font>,<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Olive" title="b3">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c2">S</font><br/>  for <font color="Olive" title="b2">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  st  ex <font color="Olive" title="b3">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="b2">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b3">A</font> ) &amp; <font color="Olive" title="b2">f</font> <a href="mesfun6c.html#R2" title="MESFUN6C:pred.2">is_integrable_on</a> <font color="Olive" title="b1">M</font> &amp;  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Olive" title="b1">M</font>,<font color="Olive" title="b2">f</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Olive" title="b1">M</font>,<font color="Olive" title="b2">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Olive" title="b1">M</font>,<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Olive" title="b2">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</font> be   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  st  ex <font color="Olive" title="b2">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b1">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b2">A</font> ) &amp; <font color="Olive" title="b1">f</font> <a href="mesfun6c.html#R2" title="MESFUN6C:pred.2">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c4">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b1">A</font> ) &amp; <font color="Maroon" title="c4">f</font> <a href="mesfun6c.html#R2" title="MESFUN6C:pred.2">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:50"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
 ex <font color="Olive" title="b1">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c4">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b1">A</font> )
 <span class="kw">and </span><br/><a NAME="E2:50"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="mesfun6c.html#R2" title="MESFUN6C:pred.2">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">and </span><br/><a NAME="E3:50"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
 <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>)</span><br/>

<a NAME="E4:50"/><span class="lab"><font color="Green" title="E37">A4</font></span>: 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="mesfunc6.html#R3" title="MESFUNC6:pred.3">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="mesfun6c.html#T31" target="_self" title="MESFUN6C:th.31">Th31</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">a</font> =  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>);<br/>
<a NAME="E5:50"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="complex1.html#T47" title="COMPLEX1:th.47">COMPLEX1:47</a></span>;<br/>
<a NAME="E6:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A5</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">h</font> = <font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">b</font> = <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>;<br/>
<a NAME="E7:50"/><span class="lab"><font color="Green" title="E39">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/>
<a NAME="E8:50"/>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T65" title="COMPLEX1:th.65">COMPLEX1:65</a></span>;<br/>
<a NAME="E9:50"/><span class="kw">then </span>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T69" title="COMPLEX1:th.69">COMPLEX1:69</a></span>;<br/>
<a NAME="E10:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A7</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T65" title="COMPLEX1:th.65">COMPLEX1:65</a></span>;<br/>
<a NAME="E11:50"/><span class="lab"><font color="Green" title="E41">A8</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c4">f</font> <a href="valued_1.html#K51" title="VALUED_1:func.51">/"</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>
 
;<br/>
<a NAME="E12:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A9</font></span>: 
 <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#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T16" title="VALUED_1:th.16">VALUED_1:16</a></span>;<br/>
<a NAME="E13:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A10</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/>
<a NAME="E14:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A11</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c4">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/>
<a NAME="E15:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="ref" href="comseq_3.html#D3" title="COMSEQ_3:def.3">COMSEQ_3:def 3</a></span>;<br/>
<a NAME="E16:50"/><span class="lab"><font color="Green" title="E46">A13</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></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="E17:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A14</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:50_1"/><span class="lab"><font color="Green" title="E48">A15</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span><br/><a NAME="E2:50_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E16:50"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="txt" href="#E14:50"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/><a NAME="E3:50_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</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="E4:50_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E17:50"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E1:50_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/><a NAME="E5:50_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A16</font></span>: 
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:50"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E13:50"><span class="lab"><font color="Green" title="E43">A10</font></span></a>, <a class="txt" href="#E1:50_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/><a NAME="E6:50_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/><a NAME="E7:50_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E16:50"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="txt" href="#E17:50"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E1:50_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/><a NAME="E8:50_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E17:50"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E1:50_1"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E9:50_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:50_1"><span class="lab"><font color="Green" title="E49">A16</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E19:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A17</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:50"><span class="lab"><font color="Green" title="E47">A14</font></span></a>, <a class="txt" href="#E14:50"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/>
<a NAME="E20:50"/><span class="lab"><font color="Green" title="E49">A18</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T67" title="COMPLEX1:th.67">COMPLEX1:67</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p0">(<span class="default"><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></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> <span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></span>)</span> implies <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><a NAME="E1:50_2"/><span class="lab"><font color="Green" title="E50">A19</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:50"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="valued_1.html#T17" title="VALUED_1:th.17">VALUED_1:17</a></span>;<br/><span class="kw">assume </span><a NAME="E2:50_2"/><span class="lab"><font color="Green" title="E51">A20</font></span>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p0">(<span class="default"><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></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> <span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E3:50_2"/><span class="kw">then </span>
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/><a NAME="E4:50_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A21</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50_2"><span class="lab"><font color="Green" title="E50">A19</font></span></a>, <a class="ref" href="complex1.html#T67" title="COMPLEX1:th.67">COMPLEX1:67</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:50_2_1"/>
( <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:50_2_1_1"/><span class="lab"><font color="Green" title="E53">A22</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:50_2_1_1"/><span class="lab"><font color="Green" title="E54">A23</font></span>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="comseq_3.html#D3" title="COMSEQ_3:def.3">COMSEQ_3:def 3</a></span>;<br/><a NAME="E3:50_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E14:50"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/><a NAME="E4:50_2_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/><a NAME="E5:50_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A24</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p0">(<span class="default"><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T65" title="COMPLEX1:th.65">COMPLEX1:65</a></span>;<br/><a NAME="E6:50_2_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/><a NAME="E7:50_2_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/><a NAME="E8:50_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A25</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T65" title="COMPLEX1:th.65">COMPLEX1:65</a></span>;<br/><a NAME="E9:50_2_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50_2_1_1"><span class="lab"><font color="Green" title="E53">A22</font></span></a>, <a class="ref" href="complex1.html#T47" title="COMPLEX1:th.47">COMPLEX1:47</a></span>;<br/><a NAME="E10:50_2_1_1"/><span class="kw">then </span>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></span>;<br/><a NAME="E11:50_2_1_1"/><span class="kw">then </span>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:50"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E20:50"><span class="lab"><font color="Green" title="E49">A18</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="txt" href="#E4:50_2"><span class="lab"><font color="Green" title="E52">A21</font></span></a>, <a class="txt" href="#E8:50_2_1_1"><span class="lab"><font color="Green" title="E56">A25</font></span></a>, <a class="txt" href="#E5:50_2_1_1"><span class="lab"><font color="Green" title="E55">A24</font></span></a>, <a class="ref" href="complex1.html#T54" title="COMPLEX1:th.54">COMPLEX1:54</a></span>;<br/><span class="kw">hence </span><a NAME="E12:50_2_1_1"/>
<span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="txt" href="#E2:50_2_1_1"><span class="lab"><font color="Green" title="E54">A23</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:50_2_1_2"/><span class="lab"><font color="Green" title="E53">A26</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:50_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E14:50"><span class="lab"><font color="Green" title="E44">A11</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/><a NAME="E3:50_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/><a NAME="E4:50_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A27</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p0">(<span class="default"><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T65" title="COMPLEX1:th.65">COMPLEX1:65</a></span>;<br/><a NAME="E5:50_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></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="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50_2_1_2"><span class="lab"><font color="Green" title="E53">A26</font></span></a>, <a class="ref" href="complex1.html#T5" title="COMPLEX1:th.5">COMPLEX1:5</a></span>;<br/><a NAME="E6:50_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A28</font></span>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50_2_1_2"><span class="lab"><font color="Green" title="E54">A27</font></span></a>, <a class="ref" href="complex1.html#T54" title="COMPLEX1:th.54">COMPLEX1:54</a>, <a class="ref" href="square_1.html#T17" title="SQUARE_1:th.17">SQUARE_1:17</a></span>;<br/><a NAME="E7:50_2_1_2"/>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="ref" href="comseq_3.html#D3" title="COMSEQ_3:def.3">COMSEQ_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E8:50_2_1_2"/>
<span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E2:50_2"><span class="lab"><font color="Green" title="E51">A20</font></span></a>, <a class="txt" href="#E6:50_2_1_2"><span class="lab"><font color="Green" title="E55">A28</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E22:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A29</font></span>: 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc6.html#T58" title="MESFUNC6:th.58">MESFUNC6:58</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">F</font> =  <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">b1</font> = <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  ;<br/>
<a NAME="E24:50"/><span class="lab"><font color="Green" title="E51">A30</font></span>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></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="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T40" title="COMPLEX1:th.40">COMPLEX1:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E26:50"/><span class="lab"><font color="Green" title="E52">A31</font></span>: 
<font color="Maroon" title="c10">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="E27:50"/><span class="lab"><font color="Green" title="E53">A32</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c10">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E34">A1</font></span></a></span>;<br/>
<a NAME="E28:50"/><span class="lab"><font color="Green" title="E54">A33</font></span>: 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c10">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:50"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E27:50"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="ref" href="mesfun6c.html#T30" target="_self" title="MESFUN6C:th.30">Th30</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E55">A34</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="50_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> implies <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><a NAME="E1:50_3"/><span class="lab"><font color="Green" title="E56">A35</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:50"><span class="lab"><font color="Green" title="E41">A8</font></span></a>, <a class="ref" href="valued_1.html#T17" title="VALUED_1:th.17">VALUED_1:17</a></span>;<br/><span class="kw">assume </span><a NAME="E2:50_3"/><span class="lab"><font color="Green" title="E57">A36</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><a NAME="E3:50_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A37</font></span>: 
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>;<br/><a NAME="E4:50_3"/><span class="lab"><font color="Green" title="E59">A38</font></span>: 
<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</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#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E16:50"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="txt" href="#E2:50_3"><span class="lab"><font color="Green" title="E57">A36</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:50_3_1"/>
( <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:50_3_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:50_3_1_1"/><span class="kw">then </span>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T47" title="COMPLEX1:th.47">COMPLEX1:47</a></span>;<br/><span class="kw">hence </span><a NAME="E3:50_3_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50_3"><span class="lab"><font color="Green" title="E59">A38</font></span></a>, <a class="txt" href="#E3:50_3"><span class="lab"><font color="Green" title="E58">A37</font></span></a>, <a class="txt" href="#E1:50_3"><span class="lab"><font color="Green" title="E56">A35</font></span></a>, <a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="50_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:50_3_1_2"/><span class="lab"><font color="Green" title="E60">A39</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:50_3_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></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="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T5" title="COMPLEX1:th.5">COMPLEX1:5</a></span>;<br/><a NAME="E3:50_3_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50_3_1_2"><span class="lab"><font color="Green" title="E60">A39</font></span></a>, <a class="ref" href="square_1.html#T17" title="SQUARE_1:th.17">SQUARE_1:17</a></span>;<br/><span class="kw">hence </span><a NAME="E4:50_3_1_2"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E2:50_3"><span class="lab"><font color="Green" title="E57">A36</font></span></a>, <a class="txt" href="#E4:50_3"><span class="lab"><font color="Green" title="E59">A38</font></span></a>, <a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E30:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A40</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E16:50"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/>
<a NAME="E31:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A41</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="mesfun6c.html#R2" title="MESFUN6C:pred.2">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="mesfun6c.html#T40" target="_self" title="MESFUN6C:th.40">Th40</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">R1</font>, <font color="Maroon" title="c12">I1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E33:50"/><span class="lab"><font color="Green" title="E58">A42</font></span>: 
<font color="Maroon" title="c11">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)
 <span class="kw">and </span><br/><a NAME="E34:50"/>
<font color="Maroon" title="c12">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="comseq_3.html#K6" title="COMSEQ_3:func.6">Im</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)
 <span class="kw">and </span><br/><a NAME="E35:50"/><span class="lab"><font color="Green" title="E59">A43</font></span>: 
 <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">I1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:50"><span class="lab"><font color="Green" title="E48">A17</font></span></a>, <a class="ref" href="mesfun6c.html#D3" target="_self" title="MESFUN6C:def.3">Def5</a></span>;<br/>
<a NAME="E36:50"/><span class="lab"><font color="Green" title="E60">A44</font></span>: 
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">b1</font> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T40" title="COMPLEX1:th.40">COMPLEX1:40</a></span>;<br/>
<a NAME="E37:50"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T13" title="COMPLEX1:th.13">COMPLEX1:13</a></span>;<br/>
<a NAME="E38:50"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p2"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:50"><span class="lab"><font color="Green" title="E51">A30</font></span></a>, <a class="txt" href="#E36:50"><span class="lab"><font color="Green" title="E60">A44</font></span></a>, <a class="ref" href="complex1.html#T68" title="COMPLEX1:th.68">COMPLEX1:68</a></span>;<br/>
<a NAME="E39:50"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p4"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:50"><span class="lab"><font color="Green" title="E40">A7</font></span></a>, <a class="txt" href="#E20:50"><span class="lab"><font color="Green" title="E49">A18</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="complex1.html#T65" title="COMPLEX1:th.65">COMPLEX1:65</a></span>;<br/>
<a NAME="E40:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A45</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T58" title="XCMPLX_1:th.58">XCMPLX_1:58</a></span>;<br/>
<a NAME="E41:50"/>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">R1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">I1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T12" title="COMPLEX1:th.12">COMPLEX1:12</a></span>;<br/>
<a NAME="E42:50"/><span class="kw">then </span>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">R1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E40:50"><span class="lab"><font color="Green" title="E61">A45</font></span></a>, <a class="txt" href="#E30:50"><span class="lab"><font color="Green" title="E56">A40</font></span></a>, <a class="txt" href="#E19:50"><span class="lab"><font color="Green" title="E48">A17</font></span></a>, <a class="txt" href="#E35:50"><span class="lab"><font color="Green" title="E59">A43</font></span></a>, <a class="ref" href="mesfun6c.html#T40" target="_self" title="MESFUN6C:th.40">Th40</a></span>;<br/>
<a NAME="E43:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A46</font></span>: 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p0"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p5">(<span class="default"><span class="p0"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:50"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="complex1.html#D1" title="COMPLEX1:def.1">COMPLEX1:def 1</a></span>;<br/>
<a NAME="E44:50"/>
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c10">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:50"><span class="lab"><font color="Green" title="E53">A32</font></span></a>, <a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E16:50"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="txt" href="#E29:50"><span class="lab"><font color="Green" title="E55">A34</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</a></span>;<br/>
<a NAME="E45:50"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p3"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p4">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c10">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:50"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E42">A9</font></span></a>, <a class="txt" href="#E16:50"><span class="lab"><font color="Green" title="E46">A13</font></span></a>, <a class="ref" href="mesfun6c.html#T17" target="_self" title="MESFUN6C:th.17">Th17</a></span>;<br/>
<a NAME="E46:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A47</font></span>: 
 <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c10">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:50"><span class="lab"><font color="Green" title="E48">A17</font></span></a>, <a class="ref" href="mesfun6c.html#D1" target="_self" title="MESFUN6C:def.1">Def3</a></span>;<br/>
<a NAME="E47:50"/>
 <a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p5"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p0">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="mesfunc6.html#R3" title="MESFUNC6:pred.3">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:50"><span class="lab"><font color="Green" title="E48">A17</font></span></a>, <a class="txt" href="#E31:50"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="ref" href="mesfun6c.html#D2" target="_self" title="MESFUN6C:def.2">Def4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font><span class="kw"> such that </span><br/><a NAME="E49:50"/><span class="lab"><font color="Green" title="E64">A48</font></span>: 
<font color="Maroon" title="c13">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p0">(<span class="default"><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></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> <span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E50:50"/><span class="lab"><font color="Green" title="E65">A49</font></span>: 
 <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K5" title="COMSEQ_3:func.5">Re</a> <span class="p3">(<span class="default"><span class="p4"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span></span>)</span> <a href="complex1.html#K15" title="COMPLEX1:func.15">*'</a></span>)</span> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <span class="p0">(<span class="default"><span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c13">E</font></span>)</span>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c13">E</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="txt" href="#E26:50"><span class="lab"><font color="Green" title="E52">A31</font></span></a>, <a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E28:50"><span class="lab"><font color="Green" title="E54">A33</font></span></a>, <a class="txt" href="#E46:50"><span class="lab"><font color="Green" title="E63">A47</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E22:50"><span class="lab"><font color="Green" title="E50">A29</font></span></a>, <a class="ref" href="mesfun6c.html#T42" target="_self" title="MESFUN6C:th.42">Th42</a></span>;<br/>
<a NAME="E51:50"/>
<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c13">E</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E49:50"><span class="lab"><font color="Green" title="E64">A48</font></span></a>, <a class="ref" href="relat_1.html#T68" title="RELAT_1:th.68">RELAT_1:68</a></span>;<br/>
<span class="kw">hence </span><a NAME="E52:50"/>
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font>)</span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Maroon" title="c3">M</font>,<span class="p1"><a href="valued_1.html#K55" title="VALUED_1:func.55">|.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="valued_1.html#K55" title="VALUED_1:func.55">.|</a></span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E39">A6</font></span></a>, <a class="txt" href="#E43:50"><span class="lab"><font color="Green" title="E62">A46</font></span></a>, <a class="txt" href="#E15:50"><span class="lab"><font color="Green" title="E45">A12</font></span></a>, <a class="txt" href="#E49:50"><span class="lab"><font color="Green" title="E64">A48</font></span></a>, <a class="txt" href="#E50:50"><span class="lab"><font color="Green" title="E65">A49</font></span></a>, <a class="ref" href="relat_1.html#T68" title="RELAT_1:th.68">RELAT_1:68</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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