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<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="qmax_1.html#NM1">Quantum_Mechanics</a>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></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">c<sub>6</sub></font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:35"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>7</sub></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">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></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">c<sub>6</sub></font></span>)</span> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">c<sub>6</sub></font>;<br/>

<a NAME="E2:35"/><i><font color="Green">E28</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></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">c<sub>6</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="qmax_1.html#E1:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<a NAME="E3:35"/><i><font color="Green">E29</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></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">c<sub>6</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="qmax_1.html#E1:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="eqrel_1.html#D5">EQREL_1:def 5</a></i>;<br/>
<b>assume </b><a NAME="E4:35"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> )
 ;<br/>

<a NAME="E5:35"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></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">c<sub>6</sub></font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></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">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="qmax_1.html#E2:35"><i><font color="Green">E28</font></i></a>, <a class="txt" href="qmax_1.html#E3:35"><i><font color="Green">E29</font></i></a>, <a class="ref" href="eqrel_1.html#T30">EQREL_1:30</a></i>;<br/>
<a NAME="E6:35"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="ref" href="qmax_1.html#D12" target="_self">Def12</a></i>;<br/>
<b>assume </b><a NAME="E7:35"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="qmax_1.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qmax_1.html#K3" target="_self">Sts</a> <font color="Maroon">c<sub>6</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="qmax_1.html#D10" target="_self">QMAX_1:def 10</a><br/>

<a NAME="E8:35"/>
( <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">c<sub>9</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <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"><font color="Maroon">c<sub>10</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> &amp; <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">c<sub>11</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <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"><font color="Maroon">c<sub>12</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="qmax_1.html#E6:35"><i><font color="Green">E30</font></i></a>, <a class="ref" href="qmax_1.html#T20" target="_self">Th20</a></i>;<br/>
<b>hence </b><a NAME="E9:35"/>
<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">c<sub>10</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <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">c<sub>12</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="qmax_1.html#E7:35"><i><font color="Green">E31</font></i></a>, <a class="ref" href="qmax_1.html#D10" target="_self">Def10</a></i>;<br/>


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