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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:24"/>
<font color="Maroon">A1</font> is <a href="prob_1.html#V3">non-decreasing</a>
 ;<br/>

<a NAME="E2:24"/><b>then </b>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="prob_3.html#K2">Partial_Union</a> <font color="Maroon">A1</font></span>)</span> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> <a href="prob_1.html#K1">.</a> <font color="Olive">n</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:24"/>
 <a href="prob_3.html#K2">Partial_Union</a> <font color="Maroon">A1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">A1</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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