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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</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="E1:26"/><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/>

<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as  <a href="waybel_0.html#V22">directed-sups-preserving</a> <a href="waybel_1.html#V6">projection</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> <b>by </b><i>, , </i>;<br/>
<a NAME="E3:26"/><i><font color="Green">E32</font></i>: 
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">g</font> is  <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</a>
 
<b>by </b><i><a class="ref" href="waybel15.html#T17">WAYBEL15:17</a></i>;<br/>
<a NAME="E4:26"/>
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> #)
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:26"/>
<font color="Maroon">S</font> is <a href="waybel_3.html#V3">continuous</a>
 <b>by </b><i>, <a class="ref" href="yellow12.html#T15">YELLOW12:15</a></i>;<br/>


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