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



<b>assume </b><a NAME="E1:15"/>
( <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> &amp;  ex <font color="Olive">g</font> being <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> st <font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">S</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D2" target="_self">YELLOW16:def 2</a><br/>

<b>hence </b><a NAME="E2:15"/>
 <a href="relat_1.html#K2">rng</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>
 <b>by </b><i/>;<br/>


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