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<b>let </b><font color="Maroon" title="c1">QO</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="oposet_1.html#V10" title="OPOSET_1:attr.10">QuasiOrdered</a>  <a href="qmax_1.html#L2" title="QMAX_1:struct.2">OrthoRelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">QO</font> is <a href="oposet_1.html#V6" title="OPOSET_1:attr.6">SubAntisymmetric</a> implies <font color="Maroon" title="c1">QO</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a> )</span><br/>

<b>assume </b><a NAME="E1:115"/><i><font color="Green" title="E60">A1</font></i>: 
<font color="Maroon" title="c1">QO</font> is <a href="oposet_1.html#V6" title="OPOSET_1:attr.6">SubAntisymmetric</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">QO</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a></span><br/>

<a NAME="E2:115"/><i><font color="Green" title="E61">A2</font></i>: 
( <font color="Maroon" title="c1">QO</font> is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; <font color="Maroon" title="c1">QO</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> )
 
<b>by </b><i><a class="ref" href="oposet_1.html#D22" target="_self" title="OPOSET_1:def.22">Def22</a></i>;<br/>
<a NAME="E3:115"/><b>then </b>
<font color="Maroon" title="c1">QO</font> is <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>
 
<b>by </b><i><a class="txt" href="oposet_1.html#E1:115"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="oposet_1.html#T39" target="_self" title="OPOSET_1:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E4:115"/>
<font color="Maroon" title="c1">QO</font> is <a href="oposet_1.html#V13" title="OPOSET_1:attr.13">PartialOrdered</a>
 <b>by </b><i><a class="txt" href="oposet_1.html#E2:115"><i><font color="Green" title="E61">A2</font></i></a>, <a class="ref" href="oposet_1.html#D25" target="_self" title="OPOSET_1:def.25">Def25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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