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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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">E1</font>, <font color="Olive" title="b4">E2</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b4">E2</font></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>  holds <br/> <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Olive" title="b2">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Olive" title="b3">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b4">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b4">E2</font></span>)</span></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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">E1</font>, <font color="Olive" title="b3">E2</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>  st <font color="Olive" title="b1">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b3">E2</font></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>  holds <br/> <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Olive" title="b1">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Olive" title="b2">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b3">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b3">E2</font></span>)</span></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">E1</font>, <font color="Olive" title="b2">E2</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>  st <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b2">E2</font></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>  holds <br/> <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Olive" title="b1">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b2">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b2">E2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">E1</font>, <font color="Maroon" title="c5">E2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></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>  implies  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c5">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span> )</span><br/>









<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c5">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c6">XX</font> = <font color="Maroon" title="c1">X</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> <b>by </b><i><a class="ref" href="measure1.html#T21" title="MEASURE1:th.21">MEASURE1:21</a></i>;<br/>
<a NAME="E3:41"/><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c6">XX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> &amp;  <a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font> <a href="mesfunc1.html#R1" title="MESFUNC1:pred.1">is_measurable_on</a> <font color="Maroon" title="c6">XX</font> )
 
<b>by </b><i><a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a>, <a class="ref" href="mesfunc2.html#T32" title="MESFUNC2:th.32">MESFUNC2:32</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> implies  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> )</span><br/><b>assume </b><a NAME="E1:41_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font></span><br/><a NAME="E2:41_1"/><b>then </b><i><font color="Green" title="E29">A3</font></i>: 
<span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T12" title="FUNCT_1:th.12">FUNCT_1:12</a></i>;<br/><a NAME="E3:41_1"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#T48" title="FUNCT_3:th.48">FUNCT_3:48</a></i>;<br/><b>hence </b><a NAME="E4:41_1"/>
 <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="#E2:41_1"><i><font color="Green" title="E29">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E5:41"/><b>then </b><i><font color="Green" title="E29">A4</font></i>: 
 <a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font> is <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>
 
<b>by </b><i><a class="ref" href="supinf_2.html#T71" title="SUPINF_2:th.71">SUPINF_2:71</a></i>;<br/>
<a NAME="E6:41"/>
( <font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font> &amp; <font color="Maroon" title="c5">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span> <a href="prob_1.html#K7" title="PROB_1:func.7">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T51" title="XBOOLE_1:th.51">XBOOLE_1:51</a>, <a class="ref" href="xboole_1.html#T89" title="XBOOLE_1:th.89">XBOOLE_1:89</a></i>;<br/>
<a NAME="E7:41"/><b>then </b><i><font color="Green" title="E30">A5</font></i>: 
 <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c5">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:41"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="#E5:41"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="mesfunc5.html#T97" title="MESFUNC5:th.97">MESFUNC5:97</a></i>;<br/>
<i><font color="Green" title="E31">A6</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
<br/>.= 
<font color="Maroon" title="c1">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></i>
;<br/>
<i><font color="Green" title="E32">A7</font></i>:  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>
<br/>.= 
<font color="Maroon" title="c1">X</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> )</span><br/><b>assume </b><a NAME="E1:41_4"/><i><font color="Green" title="E33">A8</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font></span><br/><a NAME="E2:41_4"/><b>then </b><i><font color="Green" title="E34">A9</font></i>: 
( <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font> )
 <b>by </b><i><a class="txt" href="#E8:41"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:41_4"/><b>then </b><i><font color="Green" title="E35">A10</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><i><font color="Green" title="E36">A11</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> = 
<span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="#E1:41_4"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="#E3:41_4"><i><font color="Green" title="E35">A10</font></i></a>, <a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></i>
;<br/><a NAME="E5:41_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="#E8:41"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="#E9:41"><i><font color="Green" title="E32">A7</font></i></a>, <a class="txt" href="#E1:41_4"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/><b>hence </b><a NAME="E6:41_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="#E2:41_4"><i><font color="Green" title="E34">A9</font></i></a>, <a class="txt" href="#E4:41_4"><i><font color="Green" title="E36">A11</font></i></a>, <a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E11:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E8:41"><i><font color="Green" title="E31">A6</font></i></a>, <a class="txt" href="#E9:41"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="partfun1.html#T34" title="PARTFUN1:th.34">PARTFUN1:34</a></i>;<br/>
<a NAME="E12:41"/><b>then </b><i><font color="Green" title="E33">A12</font></i>: 
 <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:41"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="mesfunc7.html#T24" target="_self" title="MESFUNC7:th.24">Th24</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">F</font> = <font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font>;<br/>
<a NAME="E13:41"/><i><font color="Green" title="E34">A13</font></i>: 
<font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:41"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E14:41"/><b>then </b>
<font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/>
<a NAME="E15:41"/><b>then </b><i><font color="Green" title="E35">A14</font></i>: 
<span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span> <a href="mesfunc1.html#R1" title="MESFUNC1:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font>
 
<b>by </b><i><a class="ref" href="mesfunc2.html#T32" title="MESFUNC2:th.32">MESFUNC2:32</a>, <a class="ref" href="mesfunc5.html#T48" title="MESFUNC5:th.48">MESFUNC5:48</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span> implies  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c8">x</font> )</span><br/><b>assume </b><a NAME="E1:41_5"/><i><font color="Green" title="E36">A15</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c8">x</font></span><br/><a NAME="E2:41_5"/>
<font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c4">E1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T33" title="XBOOLE_1:th.33">XBOOLE_1:33</a></i>;<br/><a NAME="E3:41_5"/><b>then </b>
<span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="#E13:41"><i><font color="Green" title="E34">A13</font></i></a>, <a class="txt" href="#E1:41_5"><i><font color="Green" title="E36">A15</font></i></a>, <a class="ref" href="funct_3.html#T43" title="FUNCT_3:th.43">FUNCT_3:43</a></i>;<br/><b>hence </b><a NAME="E4:41_5"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="#E1:41_5"><i><font color="Green" title="E36">A15</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E17:41"/><b>then </b>
 <a href="mesfunc5.html#K6" title="MESFUNC5:func.6">integral+</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="#E13:41"><i><font color="Green" title="E34">A13</font></i></a>, <a class="txt" href="#E15:41"><i><font color="Green" title="E35">A14</font></i></a>, <a class="ref" href="mesfunc5.html#T93" title="MESFUNC5:th.93">MESFUNC5:93</a></i>;<br/>
<a NAME="E18:41"/><b>then </b>
 <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">E2</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c4">E1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a> 
 
<b>by </b><i><a class="txt" href="#E5:41"><i><font color="Green" title="E29">A4</font></i></a>, <a class="txt" href="#E13:41"><i><font color="Green" title="E34">A13</font></i></a>, <a class="txt" href="#E15:41"><i><font color="Green" title="E35">A14</font></i></a>, <a class="ref" href="mesfunc5.html#T21" title="MESFUNC5:th.21">MESFUNC5:21</a>, <a class="ref" href="mesfunc5.html#T94" title="MESFUNC5:th.94">MESFUNC5:94</a></i>;<br/>
<b>hence </b><a NAME="E19:41"/>
 <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> <font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> <font color="Maroon" title="c4">E1</font>,<font color="Maroon" title="c1">X</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c5">E2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">E1</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">E2</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:41"><i><font color="Green" title="E30">A5</font></i></a>, <a class="txt" href="#E12:41"><i><font color="Green" title="E33">A12</font></i></a>, <a class="ref" href="supinf_2.html#T18" title="SUPINF_2:th.18">SUPINF_2:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
