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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 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><br/> for <font color="Olive" title="b2">p</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><br/> for <font color="Olive" title="b3">E</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>   st <font color="Olive" title="b3">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">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>  holds <br/><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="Olive" title="b2">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="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">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="Olive" title="b2">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="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">E</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</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><br/> for <font color="Olive" title="b2">E</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>   st <font color="Olive" title="b2">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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>  holds <br/><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="Olive" title="b1">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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="Olive" title="b1">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">E</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">p</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">E</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>   st <font color="Olive" title="b1">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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>  holds <br/><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">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c8">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">E</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">E</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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>  implies <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">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c8">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">E</font></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:36"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c9">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><font color="Maroon" title="c8">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c8">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">E</font></span>)</span></span><br/>

<a NAME="E2:36"/>
(  <a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <a href="prob_1.html#K13" title="PROB_1:func.13">Borel_Sets</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp; <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c9">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">E</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D11" title="PROB_1:def.11">PROB_1:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:36"/>
<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">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c8">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c7">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">E</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="prob_1.html#T68" title="PROB_1:th.68">PROB_1:68</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
