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<div><span class="kw">theorem </span><a NAME="T53"><span class="comment"><font color="firebrick">:: RPR_1:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">E</font> being   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#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B1</font>, <font color="Olive" title="b4">B2</font>, <font color="Olive" title="b5">B3</font> being   <a href="rpr_1.html#NM1" title="RPR_1:NM.1">Event</a> of <font color="Olive" title="b1">E</font>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">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="b3">B1</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>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b4">B2</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>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b5">B3</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">B1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b4">B2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b5">B3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b3">B1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b4">B2</font> &amp; <font color="Olive" title="b3">B1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b5">B3</font> &amp; <font color="Olive" title="b4">B2</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b5">B3</font> holds <br/> <a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Olive" title="b3">B1</font>,<font color="Olive" title="b2">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B1</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b3">B1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B1</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b3">B1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b4">B2</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b4">B2</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K2" title="RPR_1:func.2">prob</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b5">B3</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b5">B3</font></span>)</span></span>)</span></span>)</span></div></div>
