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<span class="kw">let </span><font color="Maroon" title="c1">O</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="qmax_1.html#L2" title="QMAX_1:struct.2">OrthoRelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">O</font> is  <a href="oposet_1.html#V8" title="OPOSET_1:attr.8">StrictPartialOrdered</a>  implies <font color="Maroon" title="c1">O</font> is  <a href="necklace.html#V3" title="NECKLACE:attr.3">irreflexive</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:60"/>
<font color="Maroon" title="c1">O</font> is  <a href="oposet_1.html#V8" title="OPOSET_1:attr.8">StrictPartialOrdered</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">O</font> is  <a href="necklace.html#V3" title="NECKLACE:attr.3">irreflexive</a> </span><br/>

<a NAME="E2:60"/><span class="kw">then </span>
( <font color="Maroon" title="c1">O</font> is  <a href="necklace.html#V2" title="NECKLACE:attr.2">asymmetric</a>  &amp; <font color="Maroon" title="c1">O</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oposet_1.html#D16" target="_self" title="OPOSET_1:def.16">Def28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:60"/>
<font color="Maroon" title="c1">O</font> is  <a href="necklace.html#V3" title="NECKLACE:attr.3">irreflexive</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="oposet_1.html#T10" target="_self" title="OPOSET_1:th.10">Th36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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