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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">O</font> be   <a href="orders_1.html#NM2">Order</a> of <font color="Maroon">X</font>;<br/>



<a NAME="E1:63"/>
 <a href="relat_1.html#K3">field</a> <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:63"/><b>then </b>
( <font color="Maroon">O</font> <a href="relat_2.html#R1">is_reflexive_in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">O</font> <a href="relat_2.html#R4">is_antisymmetric_in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">O</font> <a href="relat_2.html#R8">is_transitive_in</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="relat_2.html#D9">RELAT_2:def 9</a>, <a class="ref" href="relat_2.html#D12">RELAT_2:def 12</a>, <a class="ref" href="relat_2.html#D16">RELAT_2:def 16</a></i>;<br/>
<b>hence </b><a NAME="E3:63"/>
<font color="Maroon">O</font> <a href="orders_1.html#R2" target="_self">partially_orders</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="orders_1.html#D1" target="_self">Def1</a></i>;<br/>


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