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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Olive" title="b2">q</font> holds <br/> <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b2">q</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a>  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Olive" title="b1">p</font></span><br/><b>let </b><font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c8">q</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Maroon" title="c8">q</font> implies  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c8">q</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a>  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c7">p</font> )</span><br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c7">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Maroon" title="c8">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c8">q</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a>  <a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c7">p</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">E</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</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#M2" title="PROB_1:mode.2">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>  <b>by </b><i><a class="ref" href="prob_1.html#T50" title="PROB_1:th.50">PROB_1:50</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">E1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">q</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#M2" title="PROB_1:mode.2">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>  <b>by </b><i><a class="ref" href="prob_1.html#T50" title="PROB_1:th.50">PROB_1:50</a></i>;<br/>
<b>let </b><font color="Maroon" title="c11">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>; <i><font color="Red">:: according to </font></i><a class="ref" href="qmax_1.html#D10" target="_self" title="QMAX_1:def.10">QMAX_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><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="c8">q</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c8">q</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="c7">p</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c7">p</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c12">p1</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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">E</font>;<br/>
<b>set </b><font color="Maroon" title="c13">p2</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="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">E1</font>;<br/>
<a NAME="E4:33"/><i><font color="Green" title="E24">A2</font></i>: 
( <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="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">q</font> <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> 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="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">E1</font></span>)</span> &amp; <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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <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> 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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">E</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="qmax_1.html#T16" target="_self" title="QMAX_1:th.16">Th16</a></i>;<br/>
<a NAME="E5:33"/><i><font color="Green" title="E25">A3</font></i>: 
(  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">E</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">E</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp;  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K4" title="QMAX_1:func.4">Meas</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">E1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">E1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 )
 
;<br/>
<a NAME="E6:33"/>
<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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">p</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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"><font color="Maroon" title="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">q</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="qmax_1.html#E1:33"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="qmax_1.html#D10" target="_self" title="QMAX_1:def.10">Def10</a></i>;<br/>
<a NAME="E7:33"/><b>then </b><i><font color="Green" title="E26">A4</font></i>: 
<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="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">E1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">E</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1
 
<b>by </b><i><a class="txt" href="qmax_1.html#E4:33"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="qmax_1.html#E5:33"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="xreal_1.html#T26" title="XREAL_1:th.26">XREAL_1:26</a></i>;<br/>
<a NAME="E8:33"/>
( <span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c8">q</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="c8">q</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="c8">q</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="c8">q</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>  &amp; <span class="p1">(<span class="default"><a href="qmax_1.html#K8" title="QMAX_1:func.8">'not'</a> <font color="Maroon" title="c7">p</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="c7">p</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="c7">p</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="c7">p</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>  )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<b>hence </b><a NAME="E9:33"/>
<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="c8">q</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c8">q</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="c7">p</font></span>)</span> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c11">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c7">p</font></span>)</span> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="qmax_1.html#E7:33"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
