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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="oposet_1.html#V11" target="_self">QuasiOrdered</a>  <a href="oposet_1.html#L1" target="_self">OrthoRelStr</a> ;<br/>

<b>assume </b><a NAME="E1:115"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V7" target="_self">SubAntisymmetric</a>
 ;<br/>

<a NAME="E2:115"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V2">reflexive</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V3">transitive</a> )
 
<b>by </b><i><a class="ref" href="oposet_1.html#D22" target="_self">Def22</a></i>;<br/>
<a NAME="E3:115"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V4">antisymmetric</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:115"><i><font color="Green">E60</font></i></a>, <a class="ref" href="oposet_1.html#T39" target="_self">Th39</a></i>;<br/>
<b>hence </b><a NAME="E4:115"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V14" target="_self">PartialOrdered</a>
 <b>by </b><i><a class="txt" href="oposet_1.html#E2:115"><i><font color="Green">E61</font></i></a>, <a class="ref" href="oposet_1.html#D25" target="_self">Def25</a></i>;<br/>


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