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





<b>assume </b><a NAME="E1:23"/><i><font color="Green">E29</font></i>: 
<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>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D2" target="_self">YELLOW16:def 2</a><br/>

<b>given </b><font color="Maroon">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><b> such that </b><a NAME="E2:23"/><i><font color="Green">E32</font></i>: 
<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>
 ;<br/>

<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as  <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/>;<br/>
<b>consider </b><font color="Maroon">h</font> being  <a href="waybel_1.html#V6">projection</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">T</font>,<font color="Maroon">T</font><b> such that </b><br/><a NAME="E5:23"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">h</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:23"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">h</font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">h</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">h</font></span>)</span>
 <b>and </b><br/><a NAME="E7:23"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">S</font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">h</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">h</font> = <font color="Maroon">h</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">T</font>,<font color="Maroon">T</font> <b>by </b><i>, <a class="ref" href="waybel20.html#T29">WAYBEL20:29</a></i>;<br/>
<b>take </b>
<font color="Maroon">h</font>
;<br/>

<b>reconsider </b><font color="Maroon">R</font> =  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">h</font> as  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a> ;<br/>
<a NAME="E10:23"/>
<font color="Maroon">h</font> <a href="funct_2.html#R1">=</a>  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">h</font>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T32">WAYBEL_1:32</a></i>;<br/>
<a NAME="E11:23"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">h</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">R</font>
 
<b>by </b><i><a class="ref" href="waybel20.html#T22">WAYBEL20:22</a></i>;<br/>
<a NAME="E12:23"/>
<font color="Maroon">R</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/>;<br/>
<b>hence </b><a NAME="E13:23"/>
<font color="Maroon">h</font> <a href="yellow16.html#R1" target="_self">is_a_retraction_of</a> <font color="Maroon">T</font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">h</font>
 <b>by </b><i>, , </i>;<br/>

<b>thus </b><a NAME="E14:23"/>
<font color="Maroon">S</font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">h</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i/>;<br/>


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