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<div class="add">

<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">ASeq</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">Omega</font>;<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/>





<a NAME="E1:48"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">ASeq</font> is    <a href="prob_1.html#M1" target="_self">SetSequence</a> of <font color="Maroon">Sigma</font> implies 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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:48_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">ASeq</font> is    <a href="prob_1.html#M1" target="_self">SetSequence</a> of <font color="Maroon">Sigma</font>
 ;<br/>

<a NAME="E2:48_1"/>
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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E1:48_1_1"/>
<font color="Maroon">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:48_1_1"/>
<font color="Maroon">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:48_1"/>
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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:48"/>
( ( 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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font> ) implies 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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:48_2"/><i><font color="Green">E35</font></i>: 
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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font>
 ;<br/>

<a NAME="E2:48_2"/>
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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E1:48_2_1"/>
<font color="Maroon">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:48_2_1"/>
<font color="Maroon">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:48_2"/>
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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:48"/>
( <font color="Maroon">ASeq</font> is    <a href="prob_1.html#M1" target="_self">SetSequence</a> of <font color="Maroon">Sigma</font> iff 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">ASeq</font> <a href="prob_1.html#K1" target="_self">.</a> <font color="Olive">n</font> is    <a href="prob_1.html#M2" target="_self">Event</a> of <font color="Maroon">Sigma</font> )
 <b>by </b><i>, </i>;<br/>


</div>
