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<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>let </b><font color="Maroon">T</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">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>





<b>assume </b><a NAME="E1:13"/><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">T</font>,<font color="Maroon">S</font>
 ;<br/>

<b>hence </b><a NAME="E2:13"/>
<font color="Maroon">f</font> is  <a href="waybel_0.html#V22">directed-sups-preserving</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">S</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D2" target="_self">YELLOW16:def 2</a><br/>

<a NAME="E3:13"/>
<font color="Maroon">S</font> is  <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">T</font>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">g</font> =  <a href="yellow_9.html#K1">incl</a> <font color="Maroon">S</font>,<font color="Maroon">T</font> as  <a href="waybel_0.html#V22">directed-sups-preserving</a> <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="waybel21.html#T10">WAYBEL21:10</a></i>;<br/>
<b>take </b>
<font color="Maroon">g</font>
;<br/>

<b>thus </b><a NAME="E5:13"/>
<font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font>
 <b>by </b><i>, </i>;<br/>


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