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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="oposet_1.html#L1" title="OPOSET_1:struct.1">OrthoRelStr</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">IntRel</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font>;<br/>
<b>set </b><font color="Maroon" title="c3">CO</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>;<br/>
<b>assume </b><a NAME="E1:112"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V17" title="OPOSET_1:attr.17">StrictPartialOrdered</a>
 ;<br/>

<a NAME="E2:112"/><b>then </b>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V8" title="OPOSET_1:attr.8">Asymmetric</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#D28" target="_self" title="OPOSET_1:def.28">Def28</a></i>;<br/>
<a NAME="E3:112"/><b>then </b>
<font color="Maroon" title="c1">O</font> is <a href="necklace.html#V2" title="NECKLACE:attr.2">asymmetric</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T30" target="_self" title="OPOSET_1:th.30">Th30</a></i>;<br/>
<a NAME="E4:112"/><b>then </b>
<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#T37" target="_self" title="OPOSET_1:th.37">Th37</a></i>;<br/>
<a NAME="E5:112"/><b>then </b><i><font color="Green" title="E60">A1</font></i>: 
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="oposet_1.html#D11" target="_self" title="OPOSET_1:def.11">Def11</a></i>;<br/>
<a NAME="E6:112"/>
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T19" title="RELSET_1:th.19">RELSET_1:19</a></i>;<br/>
<a NAME="E7:112"/><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> <a href="relat_2.html#R2" title="RELAT_2:pred.2">is_irreflexive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E5:112"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="oposet_1.html#T16" target="_self" title="OPOSET_1:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E8:112"/>
<font color="Maroon" title="c1">O</font> is <a href="necklace.html#V3" title="NECKLACE:attr.3">irreflexive</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D12" target="_self" title="OPOSET_1:def.12">Def12</a></i>;<br/>


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