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<b>consider </b><font color="Maroon" title="c2">X</font> being  <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/>
<b>consider </b><font color="Maroon" title="c3">M</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>;<br/>
<b>take </b><font color="Maroon" title="c4">N</font> =  <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c3">M</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c4">N</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="waybel_0.html#V7" title="WAYBEL_0:attr.7">directed</a> )</span><br/>

<b>thus </b><a NAME="E3:23_1_1"/>
not <font color="Maroon" title="c4">N</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="waybel_0.html#V7" title="WAYBEL_0:attr.7">directed</a> )</span><br/>

<a NAME="E4:23_1_1"/>
( the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">N</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">N</font> &amp; the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">N</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">N</font> &amp; the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">N</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">N</font> )
 
<b>by </b><i><a class="ref" href="orders_2.html#D4" title="ORDERS_2:def.4">ORDERS_2:def 4</a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a>, <a class="ref" href="orders_2.html#D6" title="ORDERS_2:def.6">ORDERS_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:23_1_1"/>
( <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> &amp; <font color="Maroon" title="c4">N</font> is <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> )
 <b>by </b><i><a class="ref" href="orders_2.html#D4" title="ORDERS_2:def.4">ORDERS_2:def 4</a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a>, <a class="ref" href="orders_2.html#D6" title="ORDERS_2:def.6">ORDERS_2:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">N</font> is <a href="waybel_0.html#V7" title="WAYBEL_0:attr.7">directed</a></span><br/>

<a NAME="E6:23_1_1"/><i><font color="Green" title="E10">A1</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">N</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">X</font> #)
 
;<br/>
<a NAME="E7:23_1_1"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">N</font>
 
;<br/>
<b>hence </b><a NAME="E8:23_1_1"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c4">N</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 <b>by </b><i><a class="txt" href="waybel_0.html#E6:23_1_1"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="waybel_0.html#T3" target="_self" title="WAYBEL_0:th.3">Th3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D6" target="_self" title="WAYBEL_0:def.6">WAYBEL_0:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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