<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="mssubfam.html#NM1">MSSubsetFamily</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D5">PBOOLE:def 5</a><br/>







<b>assume </b><a NAME="E1:61"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:61"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Olive">b<sub>1</sub></font> holds  <a href="setfam_1.html#K5">union</a> <font color="Olive">b<sub>2</sub></font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Olive">b<sub>1</sub></font>
 
;<br/>
<a NAME="E3:61"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> is   <a href="setfam_1.html#NM1">Subset-Family</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="mssubfam.html#E1:61"><i><font color="Green">E12</font></i></a>, <a class="ref" href="mssubfam.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E4:61"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="mssubfam.html#E2:61"><i><font color="Green">E13</font></i></a></i>;<br/>
<a NAME="E5:61"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 
;<br/>
<b>hence </b><a NAME="E6:61"/>
<span class="p1">(<span class="default"><a href="mboolean.html#K2">union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="mssubfam.html#E1:61"><i><font color="Green">E12</font></i></a>, <a class="ref" href="mboolean.html#D2">MBOOLEAN:def 2</a></i>;<br/>


</div>
