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<b>let </b><font color="Maroon">O</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:72"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">O</font> is <a href="orders_2.html#V2">reflexive</a> &amp; <font color="Maroon">O</font> is <a href="oposet_1.html#V6" target="_self">SubSymmetric</a> )
 ;<br/>

<b>set </b><font color="Maroon">IntRel</font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font>;<br/>
<b>set </b><font color="Maroon">CO</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>;<br/>
<a NAME="E2:72"/><i><font color="Green">E23</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T12" target="_self">Th12</a>, <a class="ref" href="orders_2.html#D4">ORDERS_2:def 4</a></i>;<br/>
<a NAME="E3:72"/><i><font color="Green">E24</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font> is <a href="relat_2.html#V3">symmetric</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T12" target="_self">Th12</a>, </i>;<br/>
<a NAME="E4:72"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K3">field</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:72"/><b>then </b>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">O</font> <a href="relat_2.html#R3">is_symmetric_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T13" target="_self">Th13</a>, </i>;<br/>
<b>hence </b><a NAME="E6:72"/>
<font color="Maroon">O</font> is <a href="necklace.html#V1">symmetric</a>
 <b>by </b><i><a class="ref" href="necklace.html#D4">NECKLACE:def 4</a></i>;<br/>


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