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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#L1" target="_self">OrthoRelStr</a> ;<br/>

<b>assume </b><a NAME="E1:109"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="necklace.html#V3">irreflexive</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V16" target="_self">SubStrictPartialOrdered</a> )
 ;<br/>

<a NAME="E2:109"/><b>then </b><i><font color="Green">E60</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="necklace.html#V2">asymmetric</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V9" target="_self">SubTransitive</a> )
 
<b>by </b><i><a class="ref" href="oposet_1.html#D27" target="_self">Def27</a></i>;<br/>
<a NAME="E3:109"/><b>then </b><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V8" target="_self">Asymmetric</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:109"><i><font color="Green">E59</font></i></a>, <a class="ref" href="oposet_1.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E4:109"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="orders_2.html#V3">transitive</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:109"><i><font color="Green">E59</font></i></a>, <a class="txt" href="oposet_1.html#E2:109"><i><font color="Green">E60</font></i></a>, <a class="ref" href="oposet_1.html#T41" target="_self">Th41</a></i>;<br/>
<b>hence </b><a NAME="E5:109"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V17" target="_self">StrictPartialOrdered</a>
 <b>by </b><i><a class="txt" href="oposet_1.html#E3:109"><i><font color="Green">E61</font></i></a>, <a class="ref" href="oposet_1.html#D28" target="_self">Def28</a></i>;<br/>


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