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

<b>let </b><font color="Maroon">S</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="yellow_1.html#K6">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span>;<br/>





<b>set </b><font color="Maroon">f</font> =  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">F</font>;<br/>
<a NAME="E1:10"/>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="yellow_1.html#K6">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span>
 
;<br/>
<a NAME="E2:10"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T28">YELLOW_1:28</a></i>;<br/>
<b>then consider </b><font color="Maroon">f'</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E4:10"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">F</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f'</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<b>thus </b><a NAME="E5:10"/>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">F</font> is   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>


</div>
