<?xml version="1.0"?>
<div class="add">

<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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">O</font> is  <a href="oposet_1.html#V16" title="OPOSET_1:attr.16">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">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">assume </span><a NAME="E1:115"/>
<font color="Maroon" title="c1">O</font> is  <a href="oposet_1.html#V16" title="OPOSET_1:attr.16">StrictPartialOrdered</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E2:115"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A1</font></span>: 
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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oposet_1.html#D11" target="_self" title="OPOSET_1:def.11">Def11</a></span>;<br/>
<a NAME="E3:115"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T19" title="RELSET_1:th.19">RELSET_1:19</a></span>;<br/>
<a NAME="E4:115"/><span class="kw">then </span>
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="ref" href="oposet_1.html#T16" target="_self" title="OPOSET_1:th.16">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:115"/>
<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#D12" target="_self" title="OPOSET_1:def.12">Def12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
