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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: RANDOM_3:18</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">s</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">S</font>  ex <font color="Olive" title="b3">G</font> being   <a href="random_3.html#NM1" title="RANDOM_3:NM.1">random_variable</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">s</font></span>)</span></span>)</span>, <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Olive" title="b1">S</font> st <br/>( <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> &amp; (  for <font color="Olive" title="b4">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">S</font> holds <br/><span class="p1">(<span class="default"><a href="random_3.html#K2" title="RANDOM_3:func.2">probability</a> (<font color="Olive" title="b3">G</font>,<span class="p2">(<span class="default"><a href="random_1.html#K2" title="RANDOM_1:func.2">Trivial-Probability</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">s</font></span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Olive" title="b4">x</font>,<font color="Olive" title="b2">s</font>) ) )</div></div>
