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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</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>  st <font color="Olive" title="b1">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b2">q</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Olive" title="b3">r</font> holds <br/><font color="Olive" title="b1">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Olive" title="b3">r</font></span><br/><b>let </b><font color="Maroon" title="c7">p</font>, <font color="Maroon" title="c8">q</font>, <font color="Maroon" title="c9">r</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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="c9">r</font> implies <font color="Maroon" title="c7">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Maroon" title="c9">r</font> )</span><br/>







<b>assume </b><a NAME="E1:27"/><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="c9">r</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">p</font> <a href="qmax_1.html#R3" title="QMAX_1:pred.3">|-</a> <font color="Maroon" title="c9">r</font></span><br/>

<b>let </b><font color="Maroon" title="c10">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="c7">p</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c10">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="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="c9">r</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c10">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="c9">r</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span></span><br/>

<a NAME="E2:27"/>
( <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="c10">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="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="c10">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">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="c10">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">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="c9">r</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c10">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="c9">r</font> <a href="qmax_1.html#K7" title="QMAX_1:func.7">`2</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="#E1:27"><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="E3:27"/>
<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="c10">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="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="c9">r</font> <a href="qmax_1.html#K6" title="QMAX_1:func.6">`1</a> </span>)</span>,<font color="Maroon" title="c10">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="c9">r</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#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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