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

<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> <a href="waybel22.html#R1" target="_self">is_FreeGen_set_of</a> <font color="Maroon">S</font>
 ;<br/>

<b>consider </b><font color="Maroon">T</font> being  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="orders_2.html#NM1">Poset</a>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>;<br/>
<b>consider </b><font color="Maroon">h</font> being    <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font><b> such that </b><br/><a NAME="E5:12"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">h</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:12"/>
for <font color="Olive">h'</font> being   <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>  st <font color="Olive">h'</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> holds <br/><font color="Olive">h'</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">h</font>
 <b>by </b><i>, </i>;<br/>
<a NAME="E7:12"/><i><font color="Green">E37</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E8:12"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font></span>)</span> <a href="subset_1.html#K8">/\</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<b>hence </b><a NAME="E9:12"/>
<font color="Maroon">A</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>
 <b>by </b><i>, </i>;<br/>


</div>
