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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   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#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font><br/>  for <font color="Olive" title="b2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">s</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">s</font>)</span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>)</span>)</span></span><br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:10_1"/>
(  not <font color="Maroon" title="c2">s</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or <font color="Maroon" title="c2">s</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_1_1"/>
 not <font color="Maroon" title="c2">s</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>)</span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:10_1_1"/>
 <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_1.html#T87" title="XCMPLX_1:th.87">XCMPLX_1:87</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_1_2"/>
<font color="Maroon" title="c2">s</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>)</span>)</span></span><br/><div class="add"><a NAME="E2:10_1_2"/><span class="kw">then </span>
 <a href="dist_1.html#K1" title="DIST_1:func.1">event_pick</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T137" title="RELAT_1:th.137">RELAT_1:137</a></span>;<br/><a NAME="E3:10_1_2"/><span class="kw">then </span>
 <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><span class="kw">hence </span><a NAME="E4:10_1_2"/>
 <a href="dist_1.html#K2" title="DIST_1:func.2">frequency</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">s</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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