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<span class="kw">let </span><font color="Maroon" title="c1">Omega</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Sigma</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font><br/>  for <font color="Olive" title="b2">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b1">Sigma</font><br/>  for <font color="Olive" title="b3">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Olive" title="b1">Sigma</font>,<font color="Olive" title="b2">P</font>)<br/>  for <font color="Olive" title="b4">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Olive" title="b3">A</font> holds <br/><font color="Olive" title="b2">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Olive" title="b2">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font><br/>  for <font color="Olive" title="b2">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Maroon" title="c2">Sigma</font>,<font color="Olive" title="b1">P</font>)<br/>  for <font color="Olive" title="b3">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Olive" title="b2">A</font> holds <br/><font color="Olive" title="b1">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Olive" title="b1">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font>)<br/>  for <font color="Olive" title="b2">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font>); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font> holds <br/><font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">B</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font> implies <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">A</font> )</span><br/>









<span class="kw">assume </span><a NAME="E1:52"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c5">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">A</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c5">B</font> as    <a href="prob_4.html#M2" title="PROB_4:mode.2">thin</a> of <font color="Maroon" title="c3">P</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E3:52"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
<font color="Maroon" title="c5">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E4:52"/>
<font color="Maroon" title="c5">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E5:52"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c6">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T45" onmouseover="rs('xboole_1/T45')" onmouseout="rh()">XBOOLE_1:45</a></span>;<br/>
<a NAME="E6:52"/>
<font color="Maroon" title="c2">Sigma</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_4.html#T28" target="_self" onmouseover="rs('prob_4/T28')" onmouseout="rh()">Th28</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">B</font> = <font color="Maroon" title="c5">B</font> as    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52"><span class="lab"><font color="Green" title="E38">A2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">A</font> = <font color="Maroon" title="c4">A</font> as    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> (<font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font>) ;<br/>
<a NAME="E9:52"/>
<font color="Maroon" title="c7">B</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c6">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E40">A4</font></span>: <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">A</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">C</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:52"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="prob_1.html#D8" onmouseover="rs('prob_1/D8')" onmouseout="rh()">PROB_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_4.html#T40" target="_self" onmouseover="rs('prob_4/T40')" onmouseout="rh()">Th40</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">B</font>

;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">B</font> = <font color="Maroon" title="c7">B</font> as    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Maroon" title="c2">Sigma</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E12:52"/>
<span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:52"><span class="lab"><font color="Green" title="E40">A4</font></span></a>, <a class="ref" href="prob_4.html#T39" target="_self" onmouseover="rs('prob_4/T39')" onmouseout="rh()">Th39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:52"/>
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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