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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>



<b>assume </b><a NAME="E1:16"/>
<font color="Maroon" title="c3">f</font> <a href="yellow16.html#R1" title="YELLOW16:pred.1">is_a_retraction_of</a> <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font>
 ;<br/>

<a NAME="E2:16"/><b>then </b>
( <font color="Maroon" title="c3">f</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="yellow_9.html#K1" title="YELLOW_9:func.1">incl</a> <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c3">f</font> is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c1">S</font> is    <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">T</font> )
 
<b>by </b><i><a class="ref" href="yellow16.html#D1" target="_self" title="YELLOW16:def.1">Def1</a>, <a class="ref" href="yellow16.html#T10" target="_self" title="YELLOW16:th.10">Th10</a></i>;<br/>
<b>hence </b><a NAME="E3:16"/>
<font color="Maroon" title="c3">f</font> is  <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="yellow16.html#T9" target="_self" title="YELLOW16:th.9">Th9</a></i>;<br/>


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