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<b>set </b><font color="Maroon">R</font> = the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font>;<br/>
<a NAME="E1:6_1_1"/><i><font color="Green">E18</font></i>: 
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:6_1_1"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K3">field</a> the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T98">ORDERS_1:98</a></i>;<br/>
<a NAME="E3:6_1_1"/>
 <a href="relset_1.html#K4">dom</a> the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="orders_1.html#T98">ORDERS_1:98</a></i>;<br/>
<b>hence </b><a NAME="E4:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> is <a href="partfun1.html#V1">total</a>
 <b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>

<a NAME="E5:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> is <a href="relat_2.html#V1">reflexive</a>
 <b>by </b><i>, <a class="ref" href="relat_2.html#D9">RELAT_2:def 9</a></i>;<br/>

<a NAME="E7:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="relat_2.html#R4">is_antisymmetric_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> is <a href="relat_2.html#V4">antisymmetric</a>
 <b>by </b><i>, <a class="ref" href="relat_2.html#D12">RELAT_2:def 12</a></i>;<br/>

<a NAME="E9:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="relat_2.html#R8">is_transitive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E10:6_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> is <a href="relat_2.html#V8">transitive</a>
 <b>by </b><i>, <a class="ref" href="relat_2.html#D16">RELAT_2:def 16</a></i>;<br/>


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