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<b>consider </b><font color="Maroon">X</font> being  <a href="lattice3.html#V1">with_suprema</a> <a href="orders_2.html#NM1">Poset</a>;<br/>
<b>consider </b><font color="Maroon">M</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>;<br/>
<b>take </b><font color="Maroon">N</font> =  <a href="waybel_0.html#G1" target="_self">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">X</font>,<font color="Maroon">M</font> #);<br/>

<b>thus </b><a NAME="E3:23_1_1"/>
not <font color="Maroon">N</font> is <a href="struct_0.html#V3">empty</a>
 ;<br/>

<a NAME="E4:23_1_1"/>
( the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> <a href="relat_2.html#R8">is_transitive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> &amp; the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> <a href="relat_2.html#R4">is_antisymmetric_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> )
 
<b>by </b><i><a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a>, <a class="ref" href="orders_2.html#D5">ORDERS_2:def 5</a>, <a class="ref" href="orders_2.html#D6">ORDERS_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:23_1_1"/>
( <font color="Maroon">N</font> is <a href="orders_2.html#V2">reflexive</a> &amp; <font color="Maroon">N</font> is <a href="orders_2.html#V3">transitive</a> &amp; <font color="Maroon">N</font> is <a href="orders_2.html#V4">antisymmetric</a> )
 <b>by </b><i><a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a>, <a class="ref" href="orders_2.html#D5">ORDERS_2:def 5</a>, <a class="ref" href="orders_2.html#D6">ORDERS_2:def 6</a></i>;<br/>

<a NAME="E6:23_1_1"/><i><font color="Green">E28</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</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">X</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">X</font> #)
 
;<br/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X</font> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>
<br/>.= 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font>
<b>by </b><i><a class="ref" href="pre_topc.html#T12">PRE_TOPC:12</a></i>
;<br/>
<b>hence </b><a NAME="E8:23_1_1"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> is <a href="waybel_0.html#V1" target="_self">directed</a>
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D6" target="_self">WAYBEL_0:def 6</a><br/>


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