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<span class="kw">set </span><font color="Maroon" title="c3">IT</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #);<br/>
<a NAME="E1:45_1_1"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #) <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 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="poset_1.html#E36"><span class="lab"><font color="Green" title="E33">LemConRelat02</font></span></a></span>;<br/>
<a NAME="E2:45_1_1"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #) <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 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="poset_1.html#E37"><span class="lab"><font color="Green" title="E34">LemConRelat03</font></span></a></span>;<br/>
<a NAME="E3:45_1_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #) <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 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="poset_1.html#E38"><span class="lab"><font color="Green" title="E35">LemConRelat04</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:45_1_1"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="poset_1.html#K4" title="POSET_1:func.4">ConFuncs</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span>,<span class="p1">(<span class="default"><a href="poset_1.html#K5" title="POSET_1:func.5">ConRelat</a> <font color="Maroon" title="c1">P</font>,<font color="Maroon" title="c2">Q</font></span>)</span> #) is  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45_1_1"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:45_1_1"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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