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<span class="kw">let </span><font color="Maroon" title="c6">Q</font> be   <a href="qmax_1.html#NM1" title="QMAX_1:NM.1">Quantum_Mechanics</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">C</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font></span>)</span>  st <font color="Olive" title="b1">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span> &amp; <font color="Olive" title="b2">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span> holds <br/>for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">q1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font>  st <font color="Olive" title="b3">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp; <font color="Olive" title="b4">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">B</font> &amp;  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b3">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">C</font> holds <br/> <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b4">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">C</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">B</font>, <font color="Maroon" title="c8">C</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span> &amp; <font color="Maroon" title="c8">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span> implies for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">q1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font>  st <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp; <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp;  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font> holds <br/> <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font> )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:58"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c7">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:58"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c8">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">q1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font>  st <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp; <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp;  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font> holds <br/> <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b2">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c9">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:58"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font>
 <span class="kw">and </span><br/><a NAME="E5:58"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
<font color="Maroon" title="c8">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<font color="Maroon" title="c9">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c10">p1</font>, <font color="Maroon" title="c11">q1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp; <font color="Maroon" title="c11">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp;  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font> implies  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:58"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
( <font color="Maroon" title="c10">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> &amp; <font color="Maroon" title="c11">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">B</font> )
 <span class="kw">and </span><br/><a NAME="E7:58"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
 <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font></span><br/>

<a NAME="E8:58"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font> &amp; <font color="Maroon" title="c7">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font></span>)</span>,<font color="Olive" title="b1">x</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="eqrel_1.html#D5" title="EQREL_1:def.5">EQREL_1:def 5</a></span>;<br/>
<a NAME="E9:58"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">p1</font>,<font color="Maroon" title="c11">q1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="ref" href="eqrel_1.html#T30" title="EQREL_1:th.30">EQREL_1:30</a></span>;<br/>
<a NAME="E10:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A7</font></span>: 
<font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a> <font color="Maroon" title="c11">q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#D12" target="_self" title="QMAX_1:def.12">Def12</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c12">E1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c11">q1</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  as    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T50" title="PROB_1:th.50">PROB_1:50</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">E</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  as    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T50" title="PROB_1:th.50">PROB_1:50</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c14">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K3" title="QMAX_1:func.3">Sts</a> <font color="Maroon" title="c6">Q</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span></span><br/><span class="kw">set </span><font color="Maroon" title="c15">r1</font> = <span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">E</font>;<br/><span class="kw">set </span><font color="Maroon" title="c16">r2</font> = <span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">q1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">E1</font>;<br/><a NAME="E3:58_1"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
( <span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a>  &amp; <span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E4:58_1"/><span class="lab"><font color="Green" title="E34">A9</font></span>: 
<span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">q1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">E</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#T16" target="_self" title="QMAX_1:th.16">Th16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">q1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">q1</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="ref" href="qmax_1.html#T20" target="_self" title="QMAX_1:th.20">Th20</a></span>
<br/>.= 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">q1</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">E1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#T16" target="_self" title="QMAX_1:th.16">Th16</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:58_1"/>
<span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c14">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E4:58_1"><span class="lab"><font color="Green" title="E34">A9</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E12:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A10</font></span>: 
 <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a>  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#T20" target="_self" title="QMAX_1:th.20">Th20</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">q</font> = <font color="Maroon" title="c9">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qmax_1.html#K5" title="QMAX_1:func.5">Prop</a> <font color="Maroon" title="c6">Q</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:58"><span class="lab"><font color="Green" title="E28">A3</font></span></a></span>;<br/>
<a NAME="E14:58"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font></span>)</span>,<font color="Maroon" title="c12">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E7:58"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="ref" href="eqrel_1.html#T27" title="EQREL_1:th.27">EQREL_1:27</a></span>;<br/>
<a NAME="E15:58"/><span class="kw">then </span>
 <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a> <font color="Maroon" title="c12">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#D12" target="_self" title="QMAX_1:def.12">Def12</a></span>;<br/>
<a NAME="E16:58"/><span class="kw">then </span>
<font color="Maroon" title="c12">q</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a>  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c10">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#T24" target="_self" title="QMAX_1:th.24">Th24</a></span>;<br/>
<a NAME="E17:58"/><span class="kw">then </span>
<font color="Maroon" title="c12">q</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a>  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:58"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="ref" href="qmax_1.html#T25" target="_self" title="QMAX_1:th.25">Th25</a></span>;<br/>
<a NAME="E18:58"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">q</font>,<span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qmax_1.html#D12" target="_self" title="QMAX_1:def.12">Def12</a></span>;<br/>
<a NAME="E19:58"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font></span>)</span>,<font color="Maroon" title="c12">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qmax_1.html#K9" title="QMAX_1:func.9">PropRel</a> <font color="Maroon" title="c6">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="eqrel_1.html#T12" title="EQREL_1:th.12">EQREL_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:58"/>
 <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c11">q1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:58"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="ref" href="eqrel_1.html#T27" title="EQREL_1:th.27">EQREL_1:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
