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<span class="kw">let </span><font color="Maroon" title="c1">E</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="rpr_1.html#NM1" title="RPR_1:NM.1">Event</a> of <font color="Maroon" title="c1">E</font>  st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b2">B</font> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font> holds <br/> <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Olive" title="b1">A</font>,<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="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b2">B</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="rpr_1.html#NM1" title="RPR_1:NM.1">Event</a> of <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> implies  <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:38"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">and </span><br/><a NAME="E2:38"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span></span><br/>

<a NAME="E3:38"/>
 <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <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="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="rpr_1.html#T36" target="_self" title="RPR_1:th.36">Th66</a></span>;<br/>
<a NAME="E4:38"/><span class="kw">then </span>
 <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <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"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="rpr_1.html#T24" target="_self" title="RPR_1:th.24">Th50</a></span>;<br/>
<a NAME="E5:38"/><span class="kw">then </span>
 <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <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"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T120" title="XCMPLX_1:th.120">XCMPLX_1:120</a></span>;<br/>
<a NAME="E6:38"/><span class="kw">then </span>
 <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <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">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:38"/>
 <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">B</font></span>)</span>
 ; <a class="txt" 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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