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<span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="dist_1.html#K7" title="DIST_1:func.7">distribution_family</a> <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"> ( ( 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> holds <br/> ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> iff <font color="Olive" title="b1">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  ) ) &amp; ( 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> holds <br/> ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> iff <font color="Olive" title="b1">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  ) ) implies <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:44_1_2"/><span class="lab"><font color="Green" title="E33">A4</font></span>: 
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> holds <br/> ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> iff <font color="Olive" title="b1">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"> (  ex <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 <br/>( ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> implies <font color="Olive" title="b1">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  ) implies ( <font color="Olive" title="b1">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a>  &amp; not <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> ) ) or <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:44_1_2"/><span class="lab"><font color="Green" title="E34">A5</font></span>: 
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> holds <br/> ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> iff <font color="Olive" title="b1">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"> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font></span><br/>

<a NAME="E3:44_1_2"/><span class="lab"><font color="Green" title="E35">A6</font></span>: 
for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">s</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> implies <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:44_1_2_1"/><span class="lab"><font color="Green" title="E36">A7</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</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="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  ;<br/>
<a NAME="E3:44_1_2_1"/>
<font color="Maroon" title="c5">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44_1_2"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="txt" href="#E1:44_1_2_1"><span class="lab"><font color="Green" title="E36">A7</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:44_1_2_1"/>
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1_2"><span class="lab"><font color="Green" title="E33">A4</font></span></a></span>; <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>
<a NAME="E4:44_1_2"/>
for <font color="Olive" title="b1">s</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">s</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> implies <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:44_1_2_2"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</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="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">s</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">S</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  ;<br/>
<a NAME="E3:44_1_2_2"/>
<font color="Maroon" title="c5">s</font> <a href="dist_1.html#R2" title="DIST_1:pred.2">is_uniformly_distributed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44_1_2"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="txt" href="#E1:44_1_2_2"><span class="lab"><font color="Green" title="E36">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:44_1_2_2"/>
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44_1_2"><span class="lab"><font color="Green" title="E34">A5</font></span></a></span>; <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="E5:44_1_2"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:44_1_2"><span class="lab"><font color="Green" title="E35">A6</font></span></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></span>; <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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