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

<b>set </b><font color="Maroon">Cs</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1">Constants</a> <font color="Maroon">OU0</font>,<font color="Olive">s2</font></span>)</span> where <font color="Olive">s2</font> is   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S1</font> : <font color="Olive">s2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font> </span>}</span> ;<br/>
<a NAME="E1:16_1_1"/>
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1">Constants</a> <font color="Maroon">OU0</font>,<font color="Olive">s2</font></span>)</span> where <font color="Olive">s2</font> is   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S1</font> : <font color="Olive">s2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font> </span>}</span>  holds <br/><font color="Olive">X</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">OU0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:16_1_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1">Constants</a> <font color="Maroon">OU0</font>,<font color="Olive">s2</font></span>)</span> where <font color="Olive">s2</font> is   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S1</font> : <font color="Olive">s2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font> </span>}</span> 
 ;<br/>

<b>consider </b><font color="Maroon">s2</font> being   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S1</font><b> such that </b><br/><a NAME="E3:16_1_1_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="msualg_2.html#K1">Constants</a> <font color="Maroon">OU0</font>,<font color="Maroon">s2</font> &amp; <font color="Maroon">s2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font> )
 <b>by </b><i/>;<br/>
<a NAME="E4:16_1_1_1"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">OU0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s2</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">OU0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 
<b>by </b><i>, <a class="ref" href="osalg_1.html#D19">OSALG_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E5:16_1_1_1"/>
<font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">OU0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:16_1_1"/>
 <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1">Constants</a> <font color="Maroon">OU0</font>,<font color="Olive">s2</font></span>)</span> where <font color="Olive">s2</font> is   <a href="osalg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S1</font> : <font color="Olive">s2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">s</font> </span>}</span>  is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">OU0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T94">ZFMISC_1:94</a></i>;<br/>


</div>
