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<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="orders_1.html#NM2">Order</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>take </b><font color="Maroon">c<sub>3</sub></font> =  <a href="orders_2.html#G1" target="_self">RelStr</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> #);<br/>

<b>thus </b><a NAME="E3:4_1_1"/>
not the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a><br/>

<a NAME="E4:4_1_1"/><i><font color="Green">E4</font></i>: 
 <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T97">ORDERS_1:97</a></i>;<br/>
<b>hence </b><a NAME="E5:4_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R1">is_reflexive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="relat_2.html#D9">RELAT_2:def 9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_2.html#D4" target="_self">ORDERS_2:def 4</a><br/>

<b>thus </b><a NAME="E6:4_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R8">is_transitive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="orders_2.html#E4:4_1_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="relat_2.html#D16">RELAT_2:def 16</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_2.html#D5" target="_self">ORDERS_2:def 5</a><br/>

<b>thus </b><a NAME="E7:4_1_1"/>
the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R4">is_antisymmetric_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="orders_2.html#E4:4_1_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="relat_2.html#D12">RELAT_2:def 12</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_2.html#D6" target="_self">ORDERS_2:def 6</a><br/>

<b>thus </b><a NAME="E8:4_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="orders_2.html#V1" target="_self">strict</a>
 ;<br/>


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