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

<b>thus </b><a NAME="E1:160_1_1"/>
<font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> is <a href="classes1.html#V1">subset-closed</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a><br/>

<b>assume </b><a NAME="E1:160_1_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 ;<br/>

<b>then consider </b><font color="Maroon">a1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font>, <font color="Maroon">a2</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E3:160_1_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T23" target="_self">Th23</a></i>;<br/>
<b>assume </b><a NAME="E4:160_1_1_1"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E5:160_1_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:160_1_1_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T23" target="_self">Th23</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="cohsp_1.html#D1" target="_self">COHSP_1:def 1</a><br/>

<b>assume </b><a NAME="E2:160_1_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 ;<br/>

<b>set </b><font color="Maroon">A1</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon">A2</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:160_1_1_2"/>
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E3:160_1_1_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><b>assume </b><a NAME="E4:160_1_1_2"/>
<font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">b</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E6:160_1_1_2"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><a NAME="E7:160_1_1_2"/>
<font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E8:160_1_1_2"/><b>then </b>
 <a href="funct_5.html#K1">proj1</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E9:160_1_1_2"/>
<font color="Maroon">a1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font>
 <b>by </b><i>, , <a class="ref" href="funct_5.html#T6">FUNCT_5:6</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:160_1_1"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span>  <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font>
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:160_1_1_3"/>
<font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">a</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E3:160_1_1_3"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><b>assume </b><a NAME="E4:160_1_1_3"/>
<font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">b</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E6:160_1_1_3"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><a NAME="E7:160_1_1_3"/>
<font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 <b>by </b><i>, , <a class="ref" href="cohsp_1.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E8:160_1_1_3"/><b>then </b>
 <a href="funct_5.html#K2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">C2</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E9:160_1_1_3"/>
<font color="Maroon">a1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C2</font>
 <b>by </b><i>, <a class="ref" href="cohsp_1.html#T24" target="_self">Th24</a>, <a class="ref" href="funct_5.html#T6">FUNCT_5:6</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:160_1_1"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span>  <a href="hidden.html#R2">in</a> <font color="Maroon">C2</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:160_1_1"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="160_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:160_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">A</font>
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:160_1_1_4"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<a NAME="E4:160_1_1_4"/>
<font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 
<b>by </b><i>, <a class="ref" href="cohsp_1.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E5:160_1_1_4"/><b>then </b>
( <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Maroon">a</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span>  &amp;  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T24" target="_self">Th24</a>, </i>;<br/>
<a NAME="E6:160_1_1_4"/><b>then </b><i><font color="Green">E62</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Maroon">a</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span>  &amp;  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T24" target="_self">Th24</a>, <a class="ref" href="zfmisc_1.html#T92">ZFMISC_1:92</a></i>;<br/>
<a NAME="E7:160_1_1_4"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Maroon">a</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<b>hence </b><a NAME="E8:160_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="funct_5.html#K1">proj1</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> </span>)</span>,<span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3">{<span class="default"> <span class="p4">(<span class="default"><a href="funct_5.html#K2">proj2</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font> : <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> </span>}</span> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#D17" target="_self">Def17</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:160_1_1"/>
 <a href="tarski.html#K3">union</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K17" target="_self">[*]</a> <font color="Maroon">C2</font>
 <b>by </b><i>, , <a class="ref" href="cohsp_1.html#T23" target="_self">Th23</a></i>;<br/>


</div>
