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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#M1" title="HIDDEN:mode.1">set</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">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">C</font> being   <a href="prob_4.html#M2" title="PROB_4:mode.2">thin</a> of <font color="Olive" title="b2">P</font> holds  <span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">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">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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" 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="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">C</font> being   <a href="prob_4.html#M2" title="PROB_4:mode.2">thin</a> of <font color="Olive" title="b1">P</font> holds  <span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">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">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">C</font> being   <a href="prob_4.html#M2" title="PROB_4:mode.2">thin</a> of <font color="Maroon" title="c3">P</font> holds  <span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">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">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">C</font> be    <a href="prob_4.html#M2" title="PROB_4:mode.2">thin</a> of <font color="Maroon" title="c3">P</font>; <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="prob_4.html#K8" title="PROB_4:func.8">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">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>







<span class="kw">consider </span><font color="Maroon" title="c5">A</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E2:54"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c5">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font>
 <span class="kw">and </span><br/><a NAME="E3:54"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<font color="Maroon" title="c4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">A</font>
 <span class="kw">and </span><br/><a NAME="E4:54"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_4.html#D4" target="_self" title="PROB_4:def.4">Def4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">A</font> = <font color="Maroon" title="c5">A</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="#E2:54"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<a NAME="E6:54"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
<span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:54"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="prob_4.html#T40" target="_self" title="PROB_4:th.40">Th40</a></span>;<br/>
<a NAME="E7:54"/>
<font color="Maroon" title="c2">Sigma</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_4.html#K7" title="PROB_4:func.7">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#T29" target="_self" title="PROB_4:th.29">Th29</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">A</font> = <font color="Maroon" title="c6">A</font> as    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="prob_4.html#K7" title="PROB_4:func.7">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="#E2:54"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<a NAME="E9:54"/>
<span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">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">C</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">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">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="prob_1.html#T70" title="PROB_1:th.70">PROB_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:54"/>
<span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">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">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:54"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="prob_1.html#D13" title="PROB_1:def.13">PROB_1:def 13</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/>


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