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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>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/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>assume </b><a NAME="E1:111"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V17" target="_self">StrictPartialOrdered</a>
 ;<br/>

<a NAME="E2:111"/><b>then </b>
<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="ref" href="oposet_1.html#D28" target="_self">Def28</a></i>;<br/>
<a NAME="E3:111"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="necklace.html#V2">asymmetric</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E4:111"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> is <a href="oposet_1.html#V5" target="_self">SubIrreFlexive</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E5:111"/><b>then </b><i><font color="Green">E60</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="ref" href="oposet_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E6:111"/>
 <a href="relat_1.html#K3">field</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T19">RELSET_1:19</a></i>;<br/>
<a NAME="E7:111"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R2">is_irreflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E5:111"><i><font color="Green">E60</font></i></a>, <a class="ref" href="oposet_1.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E8:111"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="necklace.html#V3">irreflexive</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D12" target="_self">Def12</a></i>;<br/>


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