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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>, <font color="Olive" title="b2">t</font>, <font color="Olive" title="b3">u</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a>  &amp; <font color="Olive" title="b2">t</font>,<font color="Olive" title="b3">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a>  holds <br/><font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">t</font>, <font color="Maroon" title="c4">u</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"> ( <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a>  &amp; <font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c4">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a>  implies <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c4">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a> 
 <span class="kw">and </span><br/><a NAME="E2:13"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon" title="c3">t</font>,<font color="Maroon" title="c4">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c4">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">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#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c2">s</font>) <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="Maroon" title="c5">x</font>,<font color="Maroon" title="c4">u</font>)</span><br/><span class="kw">thus </span> <a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c2">s</font>) = 
 <a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c3">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="dist_1.html#D4" target="_self" title="DIST_1:def.4">Def4</a></span>
<br/>.= 
 <a href="dist_1.html#K3" title="DIST_1:func.3">FDprobability</a> (<font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c4">u</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="dist_1.html#D4" target="_self" title="DIST_1:def.4">Def4</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>
<span class="kw">hence </span><a NAME="E4:13"/>
<font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c4">u</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="dist_1.html#D4" target="_self" title="DIST_1:def.4">Def4</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/>


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