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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/> <a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Olive" title="b1">s</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> </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  <a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:38"/><span class="lab"><font color="Green" title="E28">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">  <a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_1.html#D16" title="FUNCT_1:def.16">FUNCT_1:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#NK1" title="DIST_1:NK.1">whole_event</a>  or  not <font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dist_1.html#NK1" title="DIST_1:NK.1">whole_event</a>  or <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">b</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:38"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:38"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c4">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">b</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">na</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c6">nb</font> = <font color="Maroon" title="c4">b</font> as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E3:38"><span class="lab"><font color="Green" title="E30">A3</font></span></a></span>;<br/>
<span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">na</font> = 
1 <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">S</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E2:38"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="ref" href="dist_1.html#D11" target="_self" title="DIST_1:def.11">Def11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">nb</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E3:38"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="ref" href="dist_1.html#D11" target="_self" title="DIST_1:def.11">Def11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:38"/>
<span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="dist_1.html#K5" title="DIST_1:func.5">FDprobSEQ</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">b</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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