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<b>let </b><font color="Maroon">Q</font> be   <a href="qmax_1.html#NM1">Quantum_Mechanics</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font></span>)</span>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font></span>)</span> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K9">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font></span>)</span> )
 ;<br/>

<b>let </b><font color="Maroon">p1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font>;<br/><b>let </b><font color="Maroon">q1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font>;<br/>



<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:38"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font></span>)</span>,<font color="Maroon">x</font> )
 <b>by </b><i>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:38"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font></span>)</span>,<font color="Maroon">y</font> )
 <b>by </b><i>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">Q</font> <b>by </b><i><a class="ref" href="qmax_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>assume </b><a NAME="E7:38"/>
( <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp;  <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> )
 ;<br/>

<a NAME="E8:38"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">q1</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font></span>)</span>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font> )
 
<b>by </b><i>, <a class="ref" href="qmax_1.html#D1" target="_self">Def1</a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a>, <a class="ref" href="eqrel_1.html#T30">EQREL_1:30</a></i>;<br/>
<a NAME="E9:38"/><b>then </b><i><font color="Green">E48</font></i>: 
( <font color="Maroon">p1</font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">q1</font> &amp;  <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">q</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E10:38"/><b>then </b><i><font color="Green">E49</font></i>: 
( <font color="Maroon">p1</font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">q1</font> &amp; <font color="Maroon">q</font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a>  <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font> )
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qmax_1.html#K3" target="_self">Sts</a> <font color="Maroon">Q</font>;<br/><b>reconsider </b><font color="Maroon">E</font> = <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> <a href="subset_1.html#K3">`</a>  as    <a href="prob_1.html#M2">Event</a> of  <a href="prob_1.html#K14">Borel_Sets</a>  <b>by </b><i><a class="ref" href="prob_1.html#T50">PROB_1:50</a></i>;<br/><b>reconsider </b><font color="Maroon">E1</font> = <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> <a href="subset_1.html#K3">`</a>  as    <a href="prob_1.html#M2">Event</a> of  <a href="prob_1.html#K14">Borel_Sets</a>  <b>by </b><i><a class="ref" href="prob_1.html#T50">PROB_1:50</a></i>;<br/><b>set </b><font color="Maroon">r1</font> = <span class="p1">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">E</font>;<br/><b>set </b><font color="Maroon">r2</font> = <span class="p1">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">E1</font>;<br/><i><font color="Green">E50</font></i>: 1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p3">(<span class="default"><font color="Maroon">p1</font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">E</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p2">(<span class="default"><font color="Maroon">p1</font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p2">(<span class="default"><font color="Maroon">q1</font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span>
<b>by </b><i>, </i>
<br/>.= 
1 <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p3">(<span class="default"><font color="Maroon">q1</font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">E1</font></span>)</span>
<b>by </b><i/>
;<br/><a NAME="E4:38_1"/>
( <span class="p1">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font></span>)</span> <a href="qmax_1.html#K6" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="qmax_1.html#K6" target="_self">`1</a>  &amp; <span class="p1">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font></span>)</span> <a href="qmax_1.html#K7" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> <a href="subset_1.html#K3">`</a>  &amp; <span class="p1">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font></span>)</span> <a href="qmax_1.html#K6" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q1</font> <a href="qmax_1.html#K6" target="_self">`1</a>  &amp; <span class="p1">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font></span>)</span> <a href="qmax_1.html#K7" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q1</font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> <a href="subset_1.html#K3">`</a>  )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:38_1"/>
<span class="p1">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font></span>)</span> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font></span>)</span> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qmax_1.html#K4" target="_self">Meas</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font></span>)</span> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font></span>)</span> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="qmax_1.html#E3:38"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E12:38"/><b>then </b>
 <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">p1</font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a>  <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E13:38"/><b>then </b>
<font color="Maroon">q</font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a>  <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font>
 
<b>by </b><i><a class="txt" href="qmax_1.html#E1:38"><i><font color="Green">E34</font></i></a>, </i>;<br/>
<a NAME="E14:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">q</font>,<span class="p2">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font></span>)</span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font>
 
<b>by </b><i/>;<br/>
<a NAME="E15:38"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font></span>)</span>,<font color="Maroon">q</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K9" target="_self">PropRel</a> <font color="Maroon">Q</font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T12">EQREL_1:12</a></i>;<br/>
<b>hence </b><a NAME="E16:38"/>
 <a href="qmax_1.html#K8" target="_self">'not'</a> <font color="Maroon">q1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="qmax_1.html#D1" target="_self">Def1</a>, <a class="ref" href="eqrel_1.html#T27">EQREL_1:27</a></i>;<br/>


</div>
