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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</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">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">E1</font>, <font color="Olive" title="b4">E2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st <font color="Olive" title="b3">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b4">E2</font> holds <br/>( <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="Olive" title="b3">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Olive" title="b3">E1</font>,<font color="Olive" title="b1">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Olive" title="b4">E2</font>,<font color="Olive" title="b1">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b2">y</font></span>)</span> &amp; <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="Olive" title="b3">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Olive" title="b3">E1</font>,<font color="Olive" title="b2">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Olive" title="b4">E2</font>,<font color="Olive" title="b2">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">x</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <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">E1</font>, <font color="Olive" title="b2">E2</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st <font color="Olive" title="b1">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">E2</font> holds <br/>( <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="Olive" title="b1">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Olive" title="b1">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Olive" title="b2">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> &amp; <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="Olive" title="b1">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Olive" title="b1">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Olive" title="b2">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">E1</font>, <font color="Maroon" title="c6">E2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</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="c5">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c6">E2</font> implies ( <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> &amp; <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:46"/>
<font color="Maroon" title="c5">E1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c6">E2</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> &amp; <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> )</span><br/>

<a NAME="E2:46"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A1</font></span>: 
(  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>) <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>) &amp;  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>) <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measur11.html#T35" target="_self" onmouseover="rs('measur11/T35')" onmouseout="rh()">Th29</a></span>;<br/>
<span class="lab"><font color="Green" title="E34">A2</font></span>: <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">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"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></span>)</span>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">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="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="measur11.html#T26" target="_self" onmouseover="rs('measur11/T26')" onmouseout="rh()">Th20</a></span>
;<br/>
<span class="kw">thus </span><a NAME="E4:46"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</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"> <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="46_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:46_2_1"/>
(  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> or ( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> ) or ( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp;  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:46_2_1_1"/><span class="lab"><font color="Green" title="E35">B1</font></span>: 
 not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_2_1_1"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><a NAME="E3:46_2_1_1"/><span class="kw">then </span>
( <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E1:46_2_1_1"><span class="lab"><font color="Green" title="E35">B1</font></span></a>, <a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:46_2_1_1"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:46_2_1_2"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</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"> <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:46_2_1_2_1"/>
( ( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>) &amp;  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>) ) or (  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>) &amp; <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>) ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E1:46_2_1_2"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="xboole_0.html#T5" onmouseover="rs('xboole_0/T5')" onmouseout="rh()">XBOOLE_0:5</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:46_2_1_2_1_1"/>
( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>) &amp;  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_2_1_2_1_1"/><span class="kw">then </span>
( <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:46_2_1_2_1_1"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_2_1_2"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="xxreal_3.html#T4" onmouseover="rs('xxreal_3/T4')" onmouseout="rh()">XXREAL_3:4</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:46_2_1_2_1_2"/>
(  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>) &amp; <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_2_1_2_1_2"/><span class="kw">then </span>
( <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:46_2_1_2_1_2"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_2_1_2"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="xxreal_3.html#T4" onmouseover="rs('xxreal_3/T4')" onmouseout="rh()">XXREAL_3:4</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:46_2_1_3"/><span class="lab"><font color="Green" title="E35">A5</font></span>: 
( <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp;  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</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"> <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_2_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A6</font></span>: 
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><a NAME="E3:46_2_1_3"/>
(  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>) &amp;  not <font color="Maroon" title="c4">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_2_1_3"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E4:46_2_1_3"/><span class="kw">then </span>
( <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_2_1_3"><span class="lab"><font color="Green" title="E35">A5</font></span></a>, <a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:46_2_1_3"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K7" title="MEASUR11:func.7">X-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c3">x</font>)</span>)</span>,<font color="Maroon" title="c2">Y</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c4">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_2_1_3"><span class="lab"><font color="Green" title="E36">A6</font></span></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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>

<span class="lab"><font color="Green" title="E35">C2</font></span>: <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">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"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></span>)</span>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">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="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="measur11.html#T26" target="_self" onmouseover="rs('measur11/T26')" onmouseout="rh()">Th20</a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:46_4"/>
(  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> or ( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> ) or ( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp;  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4_1"><span class="kw">suppose </span></a><a NAME="E1:46_4_1"/><span class="lab"><font color="Green" title="E36">B1</font></span>: 
 not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_4_1"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</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#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span></span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><a NAME="E3:46_4_1"/><span class="kw">then </span>
( <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46"><span class="lab"><font color="Green" title="E35">C2</font></span></a>, <a class="txt" href="#E1:46_4_1"><span class="lab"><font color="Green" title="E36">B1</font></span></a>, <a class="ref" href="funct_1.html#D2" onmouseover="rs('funct_1/D2')" onmouseout="rh()">FUNCT_1:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E4:46_4_1"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4_2"><span class="kw">suppose </span></a><a NAME="E1:46_4_2"/><span class="lab"><font color="Green" title="E36">C3</font></span>: 
( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</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"> <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">C4</font></span>: 
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46"><span class="lab"><font color="Green" title="E35">C2</font></span></a>, <a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:46_4_2_1"/>
( ( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>) &amp;  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>) ) or (  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>) &amp; <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>) ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E1:46_4_2"><span class="lab"><font color="Green" title="E36">C3</font></span></a>, <a class="ref" href="xboole_0.html#T5" onmouseover="rs('xboole_0/T5')" onmouseout="rh()">XBOOLE_0:5</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:46_4_2_1_1"/>
( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>) &amp;  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_4_2_1_1"/><span class="kw">then </span>
( <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:46_4_2_1_1"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_4_2"><span class="lab"><font color="Green" title="E37">C4</font></span></a>, <a class="ref" href="xxreal_3.html#T4" onmouseover="rs('xxreal_3/T4')" onmouseout="rh()">XXREAL_3:4</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:46_4_2_1_2"/>
(  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>) &amp; <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_4_2_1_2"/><span class="kw">then </span>
( <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:46_4_2_1_2"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_4_2"><span class="lab"><font color="Green" title="E37">C4</font></span></a>, <a class="ref" href="xxreal_3.html#T4" onmouseover="rs('xxreal_3/T4')" onmouseout="rh()">XXREAL_3:4</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="46_4_3"><span class="kw">suppose </span></a><a NAME="E1:46_4_3"/><span class="lab"><font color="Green" title="E36">C5</font></span>: 
( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp;  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</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"> <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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span></span><br/><div class="add"><a NAME="E2:46_4_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">C6</font></span>: 
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:46"><span class="lab"><font color="Green" title="E35">C2</font></span></a>, <a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><a NAME="E3:46_4_3"/>
(  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>) &amp;  not <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_4_3"><span class="lab"><font color="Green" title="E36">C5</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/><a NAME="E4:46_4_3"/><span class="kw">then </span>
( <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> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <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> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:46_4_3"><span class="lab"><font color="Green" title="E36">C5</font></span></a>, <a class="ref" href="funct_3.html#D3" onmouseover="rs('funct_3/D3')" onmouseout="rh()">FUNCT_3:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:46_4_3"/>
<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="c5">E1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c6">E2</font></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">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>)</span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</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="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c5">E1</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xxreal_3.html#K9" title="XXREAL_3:func.9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measur11.html#K1" title="MEASUR11:func.1">chi</a> (<span class="p3">(<span class="default"><a href="measur11.html#K8" title="MEASUR11:func.8">Y-section</a> (<font color="Maroon" title="c6">E2</font>,<font color="Maroon" title="c4">y</font>)</span>)</span>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_4_3"><span class="lab"><font color="Green" title="E37">C6</font></span></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></div><span class="kw">end;</span></div>

</div>
