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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><b>that </b><br/><a NAME="E1:12"/>
<font color="Maroon" title="c3">f</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</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="c1">S</font>
 <b>and </b><br/><a NAME="E2:12"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <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>
 <b>and </b><br/><a NAME="E3:12"/><i><font color="Green" title="E11">A2</font></i>: 
<font color="Maroon" title="c1">S</font> is  <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="waybel_0.html#V4" title="WAYBEL_0:attr.4">directed-sups-inheriting</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">T</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D1" target="_self" title="YELLOW16:def.1">YELLOW16:def 1</a><br/>

<a NAME="E4:12"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="txt" href="yellow16.html#E3:12"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a></i>;<br/>
<b>hence </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> = 
<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="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_9.html#D1" title="YELLOW_9:def.1">YELLOW_9:def 1</a></i>
<br/>.= 
 <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c1">S</font>
<b>by </b><i><a class="txt" href="yellow16.html#E2:12"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="relat_1.html#T94" title="RELAT_1:th.94">RELAT_1:94</a></i>
;<br/><br/>


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