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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="Red">::  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>  st <font color="Olive" title="b1">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  holds <br/>for <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>  st <font color="Olive" title="b2">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  holds <br/><font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Olive" title="b1">s</font></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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  implies for <font color="Olive" title="b1">t</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">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  holds <br/><font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c2">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t</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">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  holds <br/><font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font></span><br/>

<a NAME="E2:43"/>
for <font color="Olive" title="b1">t</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">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  holds <br/><font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  implies <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:43_1"/>
<font color="Maroon" title="c3">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font></span><br/>

<a NAME="E2:43_1"/><span class="kw">then </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">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="dist_1.html#T25" target="_self" title="DIST_1:th.25">Th25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:43_1"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:43"/>
for <font color="Olive" title="b1">t</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">t</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  holds <br/><font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">Finseq-EQclass</a> <font color="Maroon" title="c2">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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