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<b>let </b><font color="Maroon">c<sub>1</sub></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="E1:70"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V5" target="_self">SubIrreFlexive</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V9" target="_self">SubTransitive</a> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E2:70"/><i><font color="Green">E41</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V2">irreflexive</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:70"><i><font color="Green">E40</font></i></a>, <a class="ref" href="oposet_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E3:70"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V8">transitive</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:70"><i><font color="Green">E40</font></i></a>, <a class="ref" href="oposet_1.html#D19" target="_self">Def19</a></i>;<br/>
<a NAME="E4:70"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V5">asymmetric</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E2:70"><i><font color="Green">E41</font></i></a>, <a class="ref" href="relat_2.html#T25">RELAT_2:25</a></i>;<br/>
<b>hence </b><a NAME="E5:70"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="necklace.html#V2">asymmetric</a>
 <b>by </b><i><a class="ref" href="necklace.html#D5">NECKLACE:def 5</a></i>;<br/>


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