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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="measure1.html#M3">sigma_Measure</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="numbers.html#K6">ExtREAL</a> , <font color="Maroon">g</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="numbers.html#K6">ExtREAL</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:95"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">f</font> <a href="mesfunc2.html#R2">is_simple_func_in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">g</font> <a href="mesfunc2.html#R2">is_simple_func_in</a> <font color="Maroon">S</font> )
 <b>and </b><br/><a NAME="E2:95"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f</font> is <a href="supinf_2.html#V6">nonnegative</a> &amp; <font color="Maroon">g</font> is <a href="supinf_2.html#V6">nonnegative</a> )
 ;<br/>

<a NAME="E3:95"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font> <a href="mesfunc2.html#R2">is_simple_func_in</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="mesfunc5.html#T22" target="_self">Th22</a>, <a class="ref" href="mesfunc5.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E4:95"/>
( <font color="Maroon">f</font> is <a href="mesfunc5.html#V3" target="_self">without-infty</a> &amp; <font color="Maroon">g</font> is <a href="mesfunc5.html#V3" target="_self">without-infty</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:95"/><b>then </b>
( not  <a href="supinf_1.html#K2">-infty</a>  <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> &amp; not  <a href="supinf_1.html#K2">-infty</a>  <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:95"/><b>then </b><i><font color="Green">E39</font></i>: 
( <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">g</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="funct_1.html#T142">FUNCT_1:142</a></i>;<br/>
<a NAME="E7:95"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E8:95"/><i><font color="Green">E41</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>;<br/>

<a NAME="E9:95"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="mesfunc5.html#T24" target="_self">Th24</a>, </i>;<br/>
<a NAME="E10:95"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="mesfunc2.html#R2">is_simple_func_in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="mesfunc2.html#R2">is_simple_func_in</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="mesfunc5.html#T22" target="_self">Th22</a>, <a class="txt" href="mesfunc5.html#E14:95"><i><font color="Green">E44</font></i></a></i>;<br/>
<a NAME="E11:95"/>
( <font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> is <a href="supinf_2.html#V6">nonnegative</a> &amp; <font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> is <a href="supinf_2.html#V6">nonnegative</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E12:95"/><b>then </b><i><font color="Green">E43</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> implies 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Olive">x</font> ) &amp; ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> implies 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Olive">x</font> ) )
 
<b>by </b><i><a class="ref" href="supinf_2.html#T70">SUPINF_2:70</a></i>;<br/>
<a NAME="E13:95"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/>
<a NAME="E14:95"/><b>then </b><i><font color="Green">E44</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:95_1"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1"><b>suppose </b></a><a NAME="E1:95_1_1"/><i><font color="Green">E47</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:95_1_1"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="mesfunc5.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E3:95_1_1"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_1.html#T68">FUNCT_1:68</a></i>;<br/><a NAME="E4:95_1_1"/><b>then </b>
(  <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, <a class="ref" href="mesfunc5.html#T21" target="_self">Th21</a></i>;<br/><b>hence </b><a NAME="E5:95_1_1"/>
 <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_2"><b>suppose </b></a><a NAME="E1:95_1_2"/><i><font color="Green">E95</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:95_1_2"/><b>then </b><i><font color="Green">E98</font></i>: 
 <a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="txt" href="mesfunc5.html#E1:95_1_2"><i><font color="Green">E95</font></i></a>, , <a class="ref" href="mesfunc4.html#T5">MESFUNC4:5</a></i>;<br/><i><font color="Green">E99</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T139">FUNCT_1:139</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i/>
;<br/><span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T139">FUNCT_1:139</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i/>
;<br/><a NAME="E5:95_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p4">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K1">+infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p5">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default"><a href="supinf_1.html#K2">-infty</a> </span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="mesfunc5.html#E6:95_1_2"><i><font color="Green">E100</font></i></a>, <a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>;<br/><a NAME="E6:95_1_2"/><b>then </b><i><font color="Green">E100</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>;<br/><a NAME="E7:95_1_2"/>
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Olive">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>

<b>assume </b><a NAME="E1:95_1_2_3"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E8:95_1_2"><i><font color="Green">E102</font></i></a>, <a class="txt" href="mesfunc5.html#E1:95_1_2_3"><i><font color="Green">E101</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E8:95_1_2"><i><font color="Green">E102</font></i></a>, <a class="txt" href="mesfunc5.html#E1:95_1_2_3"><i><font color="Green">E101</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>
<b>hence </b><a NAME="E3:95_1_2_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K13">+</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#K4">.</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E8:95_1_2"><i><font color="Green">E102</font></i></a>, <a class="txt" href="mesfunc5.html#E1:95_1_2_3"><i><font color="Green">E101</font></i></a>, <a class="ref" href="mesfunc1.html#D3">MESFUNC1:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:95_1_2"/><b>then </b><i><font color="Green">E102</font></i>: 
 <a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:95_1_2"><i><font color="Green">E99</font></i></a>, , <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/><a NAME="E9:95_1_2"/><i><font color="Green">E103</font></i>: 
 <a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="txt" href="mesfunc5.html#E2:95_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="mesfunc5.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E10:95_1_2"/>
 <a href="mesfunc3.html#K1">integral</a> <font color="Maroon">X</font>,<font color="Maroon">S</font>,<font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="txt" href="mesfunc5.html#E2:95_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="mesfunc5.html#T21" target="_self">Th21</a></i>;<br/><b>hence </b><a NAME="E11:95_1_2"/>
 <a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="mesfunc5.html#K5" target="_self">integral'</a> <font color="Maroon">M</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="partfun1.html#K2">|</a> <span class="p3">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E8:95_1_2"><i><font color="Green">E102</font></i></a>, <a class="txt" href="mesfunc5.html#E9:95_1_2"><i><font color="Green">E103</font></i></a>, <a class="txt" href="mesfunc5.html#E2:95_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="mesfunc5.html#T21" target="_self">Th21</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
