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<b>let </b><font color="Maroon">Omega</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Sigma</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">Omega</font>;<br/><b>let </b><font color="Maroon">ASeq</font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Sigma</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font>;<br/>







<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font> = <span class="p1">(<span class="default"><font color="Maroon">ASeq</font> <a href="prob_2.html#K1" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="prob_1.html#K6">/\</a> <font color="Maroon">B</font>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E2:5"/><i><font color="Green">E37</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>) ) )
 <b>from </b><i><a class="ref" href="funct_1.html#S4">FUNCT_1:sch 4</a>();<br/></i>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:5_1"/>
<span class="p1">(<span class="default"><font color="Maroon">ASeq</font> <a href="prob_2.html#K1" target="_self">.</a> <font color="Maroon">m</font></span>)</span> <a href="prob_1.html#K6">/\</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Omega</font>
 ;<br/><b>hence </b><a NAME="E2:5_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Omega</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E4:5"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Omega</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">Omega</font> <b>by </b><i>, <a class="ref" href="funct_2.html#T5">FUNCT_2:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><a NAME="E1:5_2"/>
<span class="p1">(<span class="default"><font color="Maroon">ASeq</font> <a href="prob_2.html#K1" target="_self">.</a> <font color="Maroon">m</font></span>)</span> <a href="prob_1.html#K6">/\</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 <b>by </b><i><a class="ref" href="prob_1.html#D10">PROB_1:def 10</a></i>;<br/><b>hence </b><a NAME="E2:5_2"/>
<font color="Maroon">f</font> <a href="prob_1.html#K1">.</a> <font color="Maroon">m</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Sigma</font> <b>by </b><i><a class="ref" href="prob_1.html#D9">PROB_1:def 9</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E8:5"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="prob_2.html#K1" target="_self">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">ASeq</font> <a href="prob_2.html#K1" target="_self">.</a> <font color="Olive">n</font></span>)</span> <a href="prob_1.html#K6">/\</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/>


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