<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font> holds <br/> ( <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>  iff <font color="Olive" title="b2">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <font color="Olive" title="b1">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">t</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>  iff <font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font> )</span><br/>



<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font> implies <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></a><div class="add"><span class="kw">assume </span><a NAME="E1:15_1"/>
<font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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> </span><br/><a NAME="E2:15_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">t0</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c3">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t0</font> &amp; <font color="Maroon" title="c2">s</font>,<font color="Olive" title="b1">t0</font> <a href="dist_1.html#R1" title="DIST_1:pred.1">-are_prob_equivalent</a>  )
 ;<br/><span class="kw">hence </span><a NAME="E3:15_1"/>
<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> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="E2:15"/>
( <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>  iff <font color="Maroon" title="c3">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
