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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">A</font>, <font color="Olive" title="b3">B</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Olive" title="b1">Sigma</font><br/> for <font color="Olive" title="b4">P</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b1">Sigma</font>  st <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">B</font> holds <br/><font color="Olive" title="b4">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">A</font></span>)</span></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">A</font>, <font color="Olive" title="b2">B</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Maroon" title="c2">Sigma</font><br/> for <font color="Olive" title="b3">P</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font>  st <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/><font color="Olive" title="b3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</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">P</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> holds <br/><font color="Olive" title="b1">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font></span>)</span> <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="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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"> ( <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font> implies <font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span> )</span><br/>









<span class="kw">assume </span><a NAME="E1:83"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 ; <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="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span></span><br/>

<a NAME="E2:83"/>
<font color="Maroon" title="c3">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="prob_1.html#K7" title="PROB_1:func.7">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D13" target="_self" title="PROB_1:def.13">Def13</a></span>
<br/>.= 
<font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:83"/>
<font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</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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