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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="Red">::  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#K7" title="NUMBERS:func.7">ExtREAL</a> <br/> for <font color="Olive" title="b4">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b3">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Olive" title="b2">M</font> holds <br/>( <font color="Olive" title="b4">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Olive" title="b3">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Olive" title="b2">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Olive" title="b2">M</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Olive" title="b4">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b3">f</font></span>)</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="Red">::  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#K7" title="NUMBERS:func.7">ExtREAL</a> <br/> for <font color="Olive" title="b3">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b2">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Olive" title="b1">M</font> holds <br/>( <font color="Olive" title="b3">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Olive" title="b2">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Olive" title="b1">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Olive" title="b1">M</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b2">f</font></span>)</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="Red">::  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#K7" title="NUMBERS:func.7">ExtREAL</a> <br/> for <font color="Olive" title="b2">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> holds <br/>( <font color="Olive" title="b2">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Olive" title="b1">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Olive" title="b2">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">f</font></span>)</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#K7" title="NUMBERS:func.7">ExtREAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">c</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> holds <br/>( <font color="Olive" title="b1">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">c</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> implies ( <font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span> ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:147"/><span class="lab"><font color="Green" title="E126">A1</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span> )</span><br/>

<a NAME="E2:147"/><span class="lab"><font color="Green" title="E127">A2</font></span>: 
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="mesfunc5.html#D17" target="_self" title="MESFUNC5:def.17">Def17</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">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="E4:147"/><span class="lab"><font color="Green" title="E128">A3</font></span>: 
<font color="Maroon" title="c6">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="E5:147"/><span class="lab"><font color="Green" title="E129">A4</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="mesfunc1.html#R1" title="MESFUNC1:pred.1">is_measurable_on</a> <font color="Maroon" title="c6">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="mesfunc5.html#D17" target="_self" title="MESFUNC5:def.17">Def17</a></span>;<br/>
<a NAME="E6:147"/><span class="lab"><font color="Green" title="E130">A5</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc1.html#R1" title="MESFUNC1:pred.1">is_measurable_on</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="ref" href="mesfunc5.html#T55" target="_self" title="MESFUNC5:th.55">Th55</a></span>;<br/>
<a NAME="E7:147"/><span class="lab"><font color="Green" title="E131">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="ref" href="mesfunc2.html#D3" title="MESFUNC2:def.3">MESFUNC2:def 3</a></span>;<br/>
<a NAME="E8:147"/><span class="lab"><font color="Green" title="E132">A7</font></span>: 
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="mesfunc5.html#D17" target="_self" title="MESFUNC5:def.17">Def17</a></span>;<br/>
<a NAME="E9:147"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="mesfunc5.html#T102" target="_self" title="MESFUNC5:th.102">Th102</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">I2</font> =  <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:147"><span class="lab"><font color="Green" title="E132">A7</font></span></a>, <a class="ref" href="xxreal_0.html#T14" title="XXREAL_0:th.14">XXREAL_0:14</a></span>;<br/>
<a NAME="E11:147"/><span class="lab"><font color="Green" title="E133">A8</font></span>: 
 <a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="mesfunc5.html#E35"><span class="lab"><font color="Green" title="E26">Lm1</font></span></a></span>;<br/>
<a NAME="E12:147"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147"><span class="lab"><font color="Green" title="E126">A1</font></span></a>, <a class="ref" href="mesfunc5.html#T102" target="_self" title="MESFUNC5:th.102">Th102</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">I1</font> =  <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:147"><span class="lab"><font color="Green" title="E127">A2</font></span></a>, <a class="ref" href="xxreal_0.html#T14" title="XXREAL_0:th.14">XXREAL_0:14</a></span>;<br/>
<a NAME="E14:147"/><span class="lab"><font color="Green" title="E134">A9</font></span>: 
 <a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="mesfunc5.html#E35"><span class="lab"><font color="Green" title="E26">Lm1</font></span></a></span>;<br/>
<a NAME="E15:147"/><span class="lab"><font color="Green" title="E135">A10</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="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="ref" href="mesfunc1.html#D6" title="MESFUNC1:def.6">MESFUNC1:def 6</a></span>;<br/>
<a NAME="E16:147"/><span class="lab"><font color="Green" title="E136">A11</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="ref" href="mesfunc2.html#D2" title="MESFUNC2:def.2">MESFUNC2:def 2</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="147_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="E1:147_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">c</font> or <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="147_1_1"><span class="kw">suppose </span></a><a NAME="E1:147_1_1"/><span class="lab"><font color="Green" title="E137">A12</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:147_1_1"/>
<font color="Maroon" title="c5">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">I1</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 ;<br/><a NAME="E3:147_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E138">A13</font></span>: 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extreal1.html#T13" title="EXTREAL1:th.13">EXTREAL1:13</a></span>;<br/><a NAME="E4:147_1_1"/><span class="lab"><font color="Green" title="E139">A14</font></span>: 
 <a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T32" target="_self" title="MESFUNC5:th.32">Th32</a></span>;<br/><a NAME="E5:147_1_1"/>
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E14:147"><span class="lab"><font color="Green" title="E134">A9</font></span></a>, <a class="txt" href="#E16:147"><span class="lab"><font color="Green" title="E136">A11</font></span></a>, <a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T27" title="MESFUNC2:th.27">MESFUNC2:27</a></span>;<br/><a NAME="E6:147_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E140">A15</font></span>: 
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147_1_1"><span class="lab"><font color="Green" title="E139">A14</font></span></a>, <a class="txt" href="#E3:147_1_1"><span class="lab"><font color="Green" title="E138">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a></span>;<br/><a NAME="E7:147_1_1"/>
<font color="Maroon" title="c5">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">I2</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 ;<br/><a NAME="E8:147_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extreal1.html#T13" title="EXTREAL1:th.13">EXTREAL1:13</a></span>;<br/><a NAME="E9:147_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E141">A16</font></span>: 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a></span>;<br/><a NAME="E10:147_1_1"/><span class="lab"><font color="Green" title="E142">A17</font></span>: 
 <a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T32" target="_self" title="MESFUNC5:th.32">Th32</a></span>;<br/><a NAME="E11:147_1_1"/>
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E11:147"><span class="lab"><font color="Green" title="E133">A8</font></span></a>, <a class="txt" href="#E7:147"><span class="lab"><font color="Green" title="E131">A6</font></span></a>, <a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T28" title="MESFUNC2:th.28">MESFUNC2:28</a></span>;<br/><span class="kw">hence </span><a NAME="E12:147_1_1"/>
<font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:147"><span class="lab"><font color="Green" title="E130">A5</font></span></a>, <a class="txt" href="#E15:147"><span class="lab"><font color="Green" title="E135">A10</font></span></a>, <a class="txt" href="#E10:147_1_1"><span class="lab"><font color="Green" title="E142">A17</font></span></a>, <a class="txt" href="#E6:147_1_1"><span class="lab"><font color="Green" title="E140">A15</font></span></a>, <a class="txt" href="#E9:147_1_1"><span class="lab"><font color="Green" title="E141">A16</font></span></a>, <a class="ref" href="mesfunc5.html#D17" target="_self" title="MESFUNC5:def.17">Def17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span></span><br/><span class="kw">thus </span> <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T32" target="_self" title="MESFUNC5:th.32">Th32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p3">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T32" target="_self" title="MESFUNC5:th.32">Th32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p3">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E14:147"><span class="lab"><font color="Green" title="E134">A9</font></span></a>, <a class="txt" href="#E16:147"><span class="lab"><font color="Green" title="E136">A11</font></span></a>, <a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T27" title="MESFUNC2:th.27">MESFUNC2:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E11:147"><span class="lab"><font color="Green" title="E133">A8</font></span></a>, <a class="txt" href="#E7:147"><span class="lab"><font color="Green" title="E131">A6</font></span></a>, <a class="txt" href="#E1:147_1_1"><span class="lab"><font color="Green" title="E137">A12</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T28" title="MESFUNC2:th.28">MESFUNC2:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T112" title="XXREAL_3:th.112">XXREAL_3:112</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="147_1_2"><span class="kw">suppose </span></a><a NAME="E1:147_1_2"/><span class="lab"><font color="Green" title="E137">A18</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font> &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:147_1_2"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">a</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E4:147_1_2"/><span class="lab"><font color="Green" title="E138">A19</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">and </span><br/><a NAME="E5:147_1_2"/><span class="lab"><font color="Green" title="E139">A20</font></span>: 
<font color="Maroon" title="c9">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:147_1_2"><span class="lab"><font color="Green" title="E137">A18</font></span></a></span>;<br/><a NAME="E6:147_1_2"/><span class="lab"><font color="Green" title="E140">A21</font></span>: 
 <a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c9">a</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147_1_2"><span class="lab"><font color="Green" title="E138">A19</font></span></a>, <a class="txt" href="#E5:147_1_2"><span class="lab"><font color="Green" title="E139">A20</font></span></a>, <a class="ref" href="mesfunc5.html#T33" target="_self" title="MESFUNC5:th.33">Th33</a></span>;<br/><a NAME="E7:147_1_2"/><span class="lab"><font color="Green" title="E141">A22</font></span>: 
 <a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c9">a</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147_1_2"><span class="lab"><font color="Green" title="E138">A19</font></span></a>, <a class="txt" href="#E5:147_1_2"><span class="lab"><font color="Green" title="E139">A20</font></span></a>, <a class="ref" href="mesfunc5.html#T33" target="_self" title="MESFUNC5:th.33">Th33</a></span>;<br/><a NAME="E8:147_1_2"/>
<font color="Maroon" title="c9">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">I2</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 ;<br/><a NAME="E9:147_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E142">A23</font></span>: 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extreal1.html#T13" title="EXTREAL1:th.13">EXTREAL1:13</a></span>;<br/><a NAME="E10:147_1_2"/>
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E11:147"><span class="lab"><font color="Green" title="E133">A8</font></span></a>, <a class="txt" href="#E7:147"><span class="lab"><font color="Green" title="E131">A6</font></span></a>, <a class="txt" href="#E5:147_1_2"><span class="lab"><font color="Green" title="E139">A20</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T28" title="MESFUNC2:th.28">MESFUNC2:28</a></span>;<br/><a NAME="E11:147_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E143">A24</font></span>: 
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:147_1_2"><span class="lab"><font color="Green" title="E140">A21</font></span></a>, <a class="txt" href="#E9:147_1_2"><span class="lab"><font color="Green" title="E142">A23</font></span></a>, <a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a></span>;<br/><a NAME="E12:147_1_2"/>
<font color="Maroon" title="c9">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c8">I1</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 ;<br/><a NAME="E13:147_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extreal1.html#T13" title="EXTREAL1:th.13">EXTREAL1:13</a></span>;<br/><a NAME="E14:147_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E144">A25</font></span>: 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a></span>;<br/><a NAME="E15:147_1_2"/>
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E14:147"><span class="lab"><font color="Green" title="E134">A9</font></span></a>, <a class="txt" href="#E16:147"><span class="lab"><font color="Green" title="E136">A11</font></span></a>, <a class="txt" href="#E5:147_1_2"><span class="lab"><font color="Green" title="E139">A20</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T27" title="MESFUNC2:th.27">MESFUNC2:27</a></span>;<br/><span class="kw">hence </span><a NAME="E16:147_1_2"/>
<font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:147"><span class="lab"><font color="Green" title="E130">A5</font></span></a>, <a class="txt" href="#E15:147"><span class="lab"><font color="Green" title="E135">A10</font></span></a>, <a class="txt" href="#E7:147_1_2"><span class="lab"><font color="Green" title="E141">A22</font></span></a>, <a class="txt" href="#E11:147_1_2"><span class="lab"><font color="Green" title="E143">A24</font></span></a>, <a class="txt" href="#E14:147_1_2"><span class="lab"><font color="Green" title="E144">A25</font></span></a>, <a class="ref" href="mesfunc5.html#D17" target="_self" title="MESFUNC5:def.17">Def17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span></span><br/><a NAME="E17:147_1_2"/><span class="lab"><font color="Green" title="E145">A26</font></span>: 
 <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="supinf_2.html#T3" title="SUPINF_2:th.3">SUPINF_2:3</a></span>;<br/><span class="kw">thus </span> <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">a</font> <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">(#)</a> <span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147"><span class="lab"><font color="Green" title="E128">A3</font></span></a>, <a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E11:147"><span class="lab"><font color="Green" title="E133">A8</font></span></a>, <a class="txt" href="#E7:147"><span class="lab"><font color="Green" title="E131">A6</font></span></a>, <a class="txt" href="#E5:147_1_2"><span class="lab"><font color="Green" title="E139">A20</font></span></a>, <a class="txt" href="#E6:147_1_2"><span class="lab"><font color="Green" title="E140">A21</font></span></a>, <a class="txt" href="#E7:147_1_2"><span class="lab"><font color="Green" title="E141">A22</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T28" title="MESFUNC2:th.28">MESFUNC2:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:147"><span class="lab"><font color="Green" title="E129">A4</font></span></a>, <a class="txt" href="#E14:147"><span class="lab"><font color="Green" title="E134">A9</font></span></a>, <a class="txt" href="#E16:147"><span class="lab"><font color="Green" title="E136">A11</font></span></a>, <a class="txt" href="#E5:147_1_2"><span class="lab"><font color="Green" title="E139">A20</font></span></a>, <a class="ref" href="mesfunc5.html#T92" target="_self" title="MESFUNC5:th.92">Th92</a>, <a class="ref" href="mesfunc2.html#T27" title="MESFUNC2:th.27">MESFUNC2:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p2">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p3">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T112" title="XXREAL_3:th.112">XXREAL_3:112</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p4">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p3">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p4">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T27" title="XXREAL_3:th.27">XXREAL_3:27</a></span>
<br/>.= 
 <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p4">(<span class="default"><a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <span class="p3">(<span class="default"><a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p4">(<span class="default"><a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Maroon" title="c4">f</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T103" title="XXREAL_3:th.103">XXREAL_3:103</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:147_1_2"><span class="lab"><font color="Green" title="E138">A19</font></span></a>, <a class="txt" href="#E17:147_1_2"><span class="lab"><font color="Green" title="E145">A26</font></span></a>, <a class="ref" href="xxreal_3.html#T103" title="XXREAL_3:th.103">XXREAL_3:103</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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