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<b>let </b><font color="Maroon">O</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:80"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">O</font> is <a href="necklace.html#V3">irreflexive</a> &amp; <font color="Maroon">O</font> is <a href="necklace.html#V2">asymmetric</a> )
 ;<br/>

<b>set </b><font color="Maroon">IntRel</font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font>;<br/>
<b>set </b><font color="Maroon">CO</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>;<br/>
<a NAME="E2:80"/><i><font color="Green">E23</font></i>: 
 <a href="relat_1.html#K3">field</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T19">RELSET_1:19</a></i>;<br/>
<a NAME="E3:80"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font> is <a href="relat_2.html#V5">asymmetric</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T15" target="_self">Th15</a>, <a class="ref" href="necklace.html#D5">NECKLACE:def 5</a></i>;<br/>
<a NAME="E4:80"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font> <a href="relat_2.html#R5">is_asymmetric_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T16" target="_self">Th16</a>, </i>;<br/>
<b>hence </b><a NAME="E5:80"/>
<font color="Maroon">O</font> is <a href="oposet_1.html#V8" target="_self">Asymmetric</a>
 <b>by </b><i/>;<br/>


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