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<div><span class="kw">theorem </span><a NAME="T65"><span class="comment"><font color="firebrick">:: PROB_3:65</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">FSeq</font> being    <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Olive" title="b2">Sigma</font> holds <br/> ( <font color="Olive" title="b3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" title="PROB_3:func.5">Union</a> <font color="Olive" title="b4">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="prob_3.html#K9" title="PROB_3:func.9">*</a> <font color="Olive" title="b4">FSeq</font></span>)</span> &amp; ( <font color="Olive" title="b4">FSeq</font> is  <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>  implies <font color="Olive" title="b3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" title="PROB_3:func.5">Union</a> <font color="Olive" title="b4">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="prob_3.html#K9" title="PROB_3:func.9">*</a> <font color="Olive" title="b4">FSeq</font></span>)</span> ) )</div></div>
