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<b>let </b><font color="Maroon" title="c1">O</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E41">A1</font></i>: 
<font color="Maroon" title="c1">O</font> is <a href="necklace.html#V2" title="NECKLACE:attr.2">asymmetric</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c2">R</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font>;<br/>
<a NAME="E2:72"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font> is <a href="relat_2.html#V5" title="RELAT_2:attr.5">asymmetric</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:72"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="necklace.html#D5" title="NECKLACE:def.5">NECKLACE:def 5</a></i>;<br/>
<a NAME="E3:72"/><b>then </b>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font> is <a href="relat_2.html#V2" title="RELAT_2:attr.2">irreflexive</a>
 
<b>by </b><i><a class="ref" href="relat_2.html#T26" title="RELAT_2:th.26">RELAT_2:26</a></i>;<br/>
<b>hence </b><a NAME="E4:72"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V5" title="OPOSET_1:attr.5">SubIrreFlexive</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D11" target="_self" title="OPOSET_1:def.11">Def11</a></i>;<br/>


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