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<span class="kw">let </span><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S1</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b2">S2</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b3">M1</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b1">S1</font><br/>  for <font color="Olive" title="b4">M2</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b2">S2</font><br/>  for <font color="Olive" title="b5">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<font color="Olive" title="b1">S1</font>,<font color="Olive" title="b2">S2</font>)</span>)</span><br/>  for <font color="Olive" title="b6">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b7">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b8">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">S1</font><br/>  for <font color="Olive" title="b9">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">S2</font> holds <br/> ( <font color="Olive" title="b3">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Olive" title="b5">E</font>,<font color="Olive" title="b7">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b8">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b3">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b5">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b8">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b7">y</font>)</span>)</span>) &amp; <font color="Olive" title="b4">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Olive" title="b5">E</font>,<font color="Olive" title="b6">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b9">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b4">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b5">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b9">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b6">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">S1</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S2</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b2">M1</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b3">M2</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b1">S2</font><br/>  for <font color="Olive" title="b4">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<font color="Maroon" title="c3">S1</font>,<font color="Olive" title="b1">S2</font>)</span>)</span><br/>  for <font color="Olive" title="b5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b6">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b7">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b8">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">S2</font> holds <br/> ( <font color="Olive" title="b2">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Olive" title="b4">E</font>,<font color="Olive" title="b6">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b7">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b2">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b4">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b7">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b6">y</font>)</span>)</span>) &amp; <font color="Olive" title="b3">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Olive" title="b4">E</font>,<font color="Olive" title="b5">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b8">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b3">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b4">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b8">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b5">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">S2</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">X2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M1</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b2">M2</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c4">S2</font><br/>  for <font color="Olive" title="b3">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<font color="Maroon" title="c3">S1</font>,<font color="Maroon" title="c4">S2</font>)</span>)</span><br/>  for <font color="Olive" title="b4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b5">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b6">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b7">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Olive" title="b1">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Olive" title="b3">E</font>,<font color="Olive" title="b5">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b6">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b1">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b3">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b6">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b5">y</font>)</span>)</span>) &amp; <font color="Olive" title="b2">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Olive" title="b3">E</font>,<font color="Olive" title="b4">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b7">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b2">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b3">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b7">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b4">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">M1</font> be   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c3">S1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M2</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c4">S2</font><br/>  for <font color="Olive" title="b2">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<font color="Maroon" title="c3">S1</font>,<font color="Maroon" title="c4">S2</font>)</span>)</span><br/>  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b4">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b5">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b6">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Olive" title="b2">E</font>,<font color="Olive" title="b4">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b5">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b2">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b5">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b4">y</font>)</span>)</span>) &amp; <font color="Olive" title="b1">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Olive" title="b2">E</font>,<font color="Olive" title="b3">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b6">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Olive" title="b1">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b2">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b6">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b3">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">M2</font> be   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c4">S2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<font color="Maroon" title="c3">S1</font>,<font color="Maroon" title="c4">S2</font>)</span>)</span><br/>  for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b4">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b5">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Olive" title="b1">E</font>,<font color="Olive" title="b3">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b4">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b1">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b4">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b3">y</font>)</span>)</span>) &amp; <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b5">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Olive" title="b1">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b5">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b2">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">E</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<font color="Maroon" title="c3">S1</font>,<font color="Maroon" title="c4">S2</font>)</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font><br/>  for <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b3">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b4">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Olive" title="b2">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b3">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b3">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b2">y</font>)</span>)</span>) &amp; <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Olive" title="b1">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b4">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b4">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b1">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><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">X1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font><br/>  for <font color="Olive" title="b2">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b3">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Olive" title="b1">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b2">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b2">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Olive" title="b1">y</font>)</span>)</span>) &amp; <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b3">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b3">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">U</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font><br/>  for <font color="Olive" title="b2">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b1">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span>) &amp; <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b2">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c10">U</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c3">S1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font> holds <br/> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span>) &amp; <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Olive" title="b1">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Olive" title="b1">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">V</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c4">S2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span>) &amp; <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>) )</span><br/>



















<a NAME="E1:95"/>
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> holds  <span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span>,<font color="Maroon" title="c1">X1</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="95_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span>,<font color="Maroon" title="c1">X1</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font></span><br/>

<a NAME="E1:95_1"/><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<font color="Maroon" title="c2">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c2">X2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D3" onmouseover="rs('subset_1/D3')" onmouseout="rh()">SUBSET_1:def 3</a></span>;<br/>
<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font> = 
<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c9">y</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc9.html#D7" onmouseover="rs('mesfunc9/D7')" onmouseout="rh()">MESFUNC9:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span>,<font color="Maroon" title="c1">X1</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="measur11.html#T34" target="_self" onmouseover="rs('measur11/T34')" onmouseout="rh()">Th28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<span class="p4"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<span class="p5">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c2">X2</font></span>)</span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span>,<font color="Maroon" title="c9">y</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c1">X1</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_1"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="measur11.html#T27" target="_self" onmouseover="rs('measur11/T27')" onmouseout="rh()">Th21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:95_1"/>
<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span>,<font color="Maroon" title="c1">X1</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_1"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="measur11.html#T22" target="_self" onmouseover="rs('measur11/T22')" onmouseout="rh()">Th16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:95"/><span class="kw">then </span>
 <a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span>,<font color="Maroon" title="c1">X1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D8" onmouseover="rs('funct_2/D8')" onmouseout="rh()">FUNCT_2:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:95"/>
<font color="Maroon" title="c5">M1</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K10" title="MEASUR11:func.10">Measurable-Y-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c9">y</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c10">U</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c5">M1</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K6" title="MESFUNC9:func.6">ProjMap2</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c10">U</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c9">y</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc9.html#T14" onmouseover="rs('mesfunc9/T14')" onmouseout="rh()">MESFUNC9:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>)</span><br/>

<a NAME="E4:95"/>
 for <font color="Olive" title="b1">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font> holds  <span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span>,<font color="Maroon" title="c2">X2</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">y</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="95_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">y</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X2</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span>,<font color="Maroon" title="c2">X2</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font></span><br/>

<a NAME="E1:95_2"/><span class="lab"><font color="Green" title="E65">A3</font></span>: 
<font color="Maroon" title="c1">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D3" onmouseover="rs('subset_1/D3')" onmouseout="rh()">SUBSET_1:def 3</a></span>;<br/>
<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font> = 
<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c12">y</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc9.html#D6" onmouseover="rs('mesfunc9/D6')" onmouseout="rh()">MESFUNC9:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>,<font color="Maroon" title="c2">X2</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="measur11.html#T34" target="_self" onmouseover="rs('measur11/T34')" onmouseout="rh()">Th28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<span class="p4"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p5">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X1</font></span>)</span>,<font color="Maroon" title="c11">V</font></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span>,<font color="Maroon" title="c8">x</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c2">X2</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_2"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="ref" href="measur11.html#T27" target="_self" onmouseover="rs('measur11/T27')" onmouseout="rh()">Th21</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:95_2"/>
<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span>,<font color="Maroon" title="c2">X2</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c12">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95_2"><span class="lab"><font color="Green" title="E65">A3</font></span></a>, <a class="ref" href="measur11.html#T22" target="_self" onmouseover="rs('measur11/T22')" onmouseout="rh()">Th16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E5:95"/><span class="kw">then </span>
 <a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p1">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span>,<font color="Maroon" title="c2">X2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D8" onmouseover="rs('funct_2/D8')" onmouseout="rh()">FUNCT_2:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:95"/>
<font color="Maroon" title="c6">M2</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K9" title="MEASUR11:func.9">Measurable-X-section</a> (<font color="Maroon" title="c7">E</font>,<font color="Maroon" title="c8">x</font>)</span>)</span> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c11">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<font color="Maroon" title="c6">M2</font>,<span class="p1">(<span class="default"><a href="mesfunc9.html#K5" title="MESFUNC9:func.5">ProjMap1</a> (<span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c7">E</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p4"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c11">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>,<span class="p3"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X1</font>,<font color="Maroon" title="c2">X2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span>,<font color="Maroon" title="c8">x</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc9.html#T14" onmouseover="rs('mesfunc9/T14')" onmouseout="rh()">MESFUNC9:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
