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<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="E1:13"/><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>set </b><font color="Maroon">L</font> = <font color="Maroon">S</font>;<br/>
<a NAME="E2:13"/><i><font color="Green">E35</font></i>: 
<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/>
<a NAME="E3:13"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K1">id</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K1">id</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> =  <a href="pralg_3.html#K1">id</a> <font color="Maroon">A</font> as   <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">S</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/>
<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">S</font><b> such that </b><br/><a NAME="E6:13"/>
<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="E7:13"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">h'</font> being   <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">S</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/>
<b>let </b><font color="Maroon">h'</font> be    <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E8:13"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">h'</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pralg_3.html#K1">id</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E9:13"/><i><font color="Green">E59</font></i>: 
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font> is    <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:13"/><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pralg_3.html#K1">id</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="funct_3.html#T1">FUNCT_3:1</a></i>;<br/>
<b>thus </b><font color="Maroon">h'</font> = 
<font color="Maroon">h</font>
<b>by </b><i>, </i>
<br/>.= 
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font>
<b>by </b><i>, , </i>
;<br/>


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