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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V24">up-complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/>



<b>given </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">S</font><b> such that </b><a NAME="E1:24"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">f</font> <a href="yellow16.html#R1" target="_self">is_a_retraction_of</a> <font color="Maroon">L</font>,<font color="Maroon">S</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D3" target="_self">YELLOW16:def 3</a><br/>

<a NAME="E2:24"/>
<font color="Maroon">S</font> is  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4">full</a> <a href="waybel_0.html#V4">directed-sups-inheriting</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:24"/>
<font color="Maroon">S</font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i/>;<br/>


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