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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: PROB_2:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Omega</font> being   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> <br/>  for <font color="Olive" title="b2">Sigma</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">Omega</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="Olive" title="b2">Sigma</font><br/>  for <font color="Olive" title="b4">A</font>, <font color="Olive" title="b5">B</font>, <font color="Olive" title="b6">C</font> being    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Olive" title="b2">Sigma</font>  st <font color="Olive" title="b6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">B</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">B</font> &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">C</font> holds <br/><font color="Olive" title="b3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">P</font> <a href="prob_2.html#K3" title="PROB_2:func.3">.|.</a> <font color="Olive" title="b5">B</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">A</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">B</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">P</font> <a href="prob_2.html#K3" title="PROB_2:func.3">.|.</a> <font color="Olive" title="b6">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">A</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">C</font></span>)</span></span>)</span></div></div>
