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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">P</font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">Sigma</font>;<br/>







<a NAME="E1:37"/><i><font color="Green">E36</font></i>: 
 <a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font> is <a href="prob_1.html#V3">non-decreasing</a>
 
<b>by </b><i/>;<br/>
<a NAME="E2:37"/><b>then </b>
<font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="ref" href="prob_2.html#T20">PROB_2:20</a></i>;<br/>
<a NAME="E3:37"/><b>then </b>
<font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span> is <a href="seq_2.html#V3">bounded</a>
 
<b>by </b><i><a class="ref" href="seq_2.html#T27">SEQ_2:27</a></i>;<br/>
<a NAME="E4:37"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span> is <a href="seq_2.html#V1">bounded_above</a>
 
<b>by </b><i><a class="ref" href="seq_2.html#D5">SEQ_2:def 5</a></i>;<br/>
<a NAME="E5:37"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span> is <a href="seqm_3.html#V3">non-decreasing</a>
 
<b>by </b><i/>;<br/>
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> = 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <span class="p2">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="prob_2.html#T20">PROB_2:20</a></i>
<br/>.= 
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <font color="Maroon">ASeq</font></span>)</span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E7:37"/>
( <font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rinfsup1.html#K1">sup</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <font color="Maroon">ASeq</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="prob_2.html#T20">PROB_2:20</a>, , , <a class="ref" href="rinfsup1.html#T24">RINFSUP1:24</a></i>;<br/>


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