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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><a NAME="E1:25"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="yellow16.html#R1" target="_self">is_a_retraction_of</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></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#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="yellow16.html#E1:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="yellow16.html#T14" target="_self">Th14</a>, <a class="ref" href="yellow16.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E3:25"/>
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>4</sub></font> is <a href="lattice3.html#V3">complete</a> )
 
<b>by </b><i><a class="txt" href="yellow16.html#E1:25"><i><font color="Green">E22</font></i></a>, <a class="ref" href="yellow16.html#T15" target="_self">Th15</a>, <a class="ref" href="yellow_2.html#T37">YELLOW_2:37</a></i>;<br/>
<b>hence </b><a NAME="E4:25"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="lattice3.html#V3">complete</a>
 <b>by </b><i><a class="ref" href="yellow_0.html#T3">YELLOW_0:3</a></i>;<br/>


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