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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: DIST_2:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</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">D</font> being   <a href="dist_2.html#NM2" title="DIST_2:NM.2">EqSampleSpaces</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">s</font> being    <a href="dist_2.html#M1" title="DIST_2:mode.1">Element</a> of <font color="Olive" title="b2">D</font><br/>  for <font color="Olive" title="b4">judgefunc</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">S</font>,<a href="margrel1.html#K5" title="MARGREL1:func.5">BOOLEAN</a>  ex <font color="Olive" title="b5">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><a href="dist_1.html#K9" title="DIST_1:func.9">freqSEQ</a> <font color="Olive" title="b3">s</font></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_2.html#K3" title="DIST_2:func.3">trueEVENT</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">judgefunc</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Olive" title="b1">S</font></span>)</span></span>)</span> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="dist_2.html#K3" title="DIST_2:func.3">trueEVENT</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">judgefunc</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">s</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K16" title="RVSUM_1:func.16">Sum</a> <span class="p1">(<span class="default"><a href="dist_2.html#K5" title="DIST_2:func.5">extract</a> (<span class="p2">(<span class="default"><a href="dist_1.html#K9" title="DIST_1:func.9">freqSEQ</a> <font color="Olive" title="b3">s</font></span>)</span>,<font color="Olive" title="b5">A</font>)</span>)</span> )</div></div>
