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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#M1">Element</a> of  <a href="qmax_1.html#K5" target="_self">Prop</a> <font color="Maroon">c<sub>6</sub></font>;<br/>





<b>thus </b><a NAME="E1:26"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>8</sub></font> implies for <font color="Olive">b<sub>1</sub></font> being   <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> holds <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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="qmax_1.html#R4" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:26_1"/><b>then </b><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="qmax_1.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="qmax_1.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="qmax_1.html#D11" target="_self">Def11</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>9</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>;<br/>

<a NAME="E3:26_1"/>
( <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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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#E2:26_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="qmax_1.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E4:26_1"/>
<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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:26"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <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> holds <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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="qmax_1.html#K7" target="_self">`2</a> </span>)</span>
 ;<br/>

<b>thus </b><a NAME="E3:26"/>
<font color="Maroon">c<sub>7</sub></font> <a href="qmax_1.html#R3" target="_self">|-</a> <font color="Maroon">c<sub>8</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="qmax_1.html#D11" target="_self">QMAX_1:def 11</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</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/>

<b>thus </b><a NAME="E1:26_2"/>
<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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</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#E2:26"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>9</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/>

<b>thus </b><a NAME="E4:26"/>
<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>8</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</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>7</sub></font> <a href="qmax_1.html#K6" target="_self">`1</a> </span>)</span>,<font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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#E2:26"><i><font color="Green">E17</font></i></a></i>;<br/>


</div>
