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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <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>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:12"/>
<font color="Maroon">c<sub>3</sub></font> is  <a href="waybel_0.html#V22">directed-sups-preserving</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:12"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:12"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D1" target="_self">YELLOW16:def 1</a><br/>

<a NAME="E4:12"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="yellow16.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a></i>;<br/>
<b>hence </b><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="yellow_9.html#K1">incl</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_9.html#D1">YELLOW_9:def 1</a></i>
<br/>.= 
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="yellow16.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="relat_1.html#T94">RELAT_1:94</a></i>
;<br/><br/>


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