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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#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">  <a href="dist_1.html#K10" title="DIST_1:func.10">uniform_distribution</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K8" title="DIST_1:func.8">distribution</a> (<span class="p1">(<span class="default"><a href="dist_1.html#K11" title="DIST_1:func.11">Uniform_FDprobSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span>,<font color="Maroon" title="c1">S</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">p</font> =  <a href="dist_1.html#K11" title="DIST_1:func.11">Uniform_FDprobSEQ</a> <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">s</font> =  <a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:48"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
 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> is  <a href="dist_1.html#V1" title="DIST_1:attr.1">uniformly_distributed</a>  holds <br/><font color="Olive" title="b1">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> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="48_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">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="c4">t</font> is  <a href="dist_1.html#V1" title="DIST_1:attr.1">uniformly_distributed</a>  implies <font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:48_1"/>
<font color="Maroon" title="c4">t</font> is  <a href="dist_1.html#V1" title="DIST_1:attr.1">uniformly_distributed</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"> <font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span></span><br/>

<a NAME="E2:48_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c4">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="ref" href="dist_1.html#T23" target="_self" onmouseover="rs('dist_1/T23')" onmouseout="rh()">Th21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:48_1"/>
<font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</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"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:48"/>
( (  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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span> holds <br/><font color="Olive" title="b1">t</font> is  <a href="dist_1.html#V1" title="DIST_1:attr.1">uniformly_distributed</a>  ) &amp;  <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="dist_1.html#K6" title="DIST_1:func.6">distribution_family</a> <font color="Maroon" title="c1">S</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dist_1.html#D6" target="_self" onmouseover="rs('dist_1/D6')" onmouseout="rh()">Def6</a>, <a class="txt" href="dist_1.html#E37"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/>
<a NAME="E3:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A2</font></span>: 
 <a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K10" title="DIST_1:func.10">uniform_distribution</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="ref" href="dist_1.html#D12" target="_self" onmouseover="rs('dist_1/D12')" onmouseout="rh()">Def12</a></span>;<br/>
<a NAME="E4:48"/>
<span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K11" title="DIST_1:func.11">Uniform_FDprobSEQ</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dist_1.html#T12" target="_self" onmouseover="rs('dist_1/T12')" onmouseout="rh()">Th10</a></span>;<br/>
<a NAME="E5:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="dist_1.html#K8" title="DIST_1:func.8">distribution</a> (<span class="p2">(<span class="default"><a href="dist_1.html#K11" title="DIST_1:func.11">Uniform_FDprobSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span>,<font color="Maroon" title="c1">S</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">Finseq-EQclass</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <font color="Maroon" title="c1">S</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="dist_1.html#T20" target="_self" onmouseover="rs('dist_1/T20')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E6:48"/>
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="dist_1.html#K7" title="DIST_1:func.7">GenProbSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K6" title="DIST_1:func.6">distribution_family</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:48"/>
 <a href="dist_1.html#K10" title="DIST_1:func.10">uniform_distribution</a> <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dist_1.html#K8" title="DIST_1:func.8">distribution</a> (<span class="p1">(<span class="default"><a href="dist_1.html#K11" title="DIST_1:func.11">Uniform_FDprobSEQ</a> <font color="Maroon" title="c1">S</font></span>)</span>,<font color="Maroon" title="c1">S</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="funct_1.html#D4" onmouseover="rs('funct_1/D4')" onmouseout="rh()">FUNCT_1:def 4</a></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"> verum</span><br/>


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