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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>;<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>;<br/>





<b>thus </b><a NAME="E1:26"/>
( <font color="Maroon" title="c7">p</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a> <font color="Maroon" title="c8">q</font> implies for <font color="Olive" title="b1">s</font> being   <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> holds  <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="Olive" title="b1">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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> <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="Olive" title="b1">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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> )
 <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" title="c7">p</font> <a href="qmax_1.html#R4" title="QMAX_1:pred.4">&lt;==&gt;</a> <font color="Maroon" title="c8">q</font>
 ;<br/>

<a NAME="E2:26_1"/><b>then </b><i><font color="Green" title="E17">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> &amp; <font color="Maroon" title="c8">q</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Maroon" title="c7">p</font> )
 
<b>by </b><i><a class="ref" href="qmax_1.html#D11" target="_self" title="QMAX_1:def.11">Def11</a></i>;<br/>
<b>let </b><font color="Maroon" title="c9">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>;<br/>

<a NAME="E3:26_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"><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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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> &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="c8">q</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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="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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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> )
 
<b>by </b><i><a class="txt" href="qmax_1.html#E2:26_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="qmax_1.html#D10" target="_self" title="QMAX_1:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E4:26_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"><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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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> <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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>


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

<b>assume </b><a NAME="E2:26"/><i><font color="Green" title="E17">A2</font></i>: 
for <font color="Olive" title="b1">s</font> being   <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> holds  <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="Olive" title="b1">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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> <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="Olive" title="b1">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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>
 ;<br/>

<b>thus </b><a NAME="E3:26"/>
<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>
  <i><font color="Red">:: according to </font></i><a class="ref" href="qmax_1.html#D11" target="_self" title="QMAX_1:def.11">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" title="c9">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><br/>

<b>thus </b><a NAME="E1:26_2"/>
<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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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#E2:26"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>


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

<b>let </b><font color="Maroon" title="c9">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><br/>

<b>thus </b><a NAME="E4:26"/>
<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="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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="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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c9">s</font></span>)</span> <a href="prob_1.html#K10" title="PROB_1:func.10">.</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>
 <b>by </b><i><a class="txt" href="qmax_1.html#E2:26"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/>


</div>
