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<b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>

<b>assume </b><a NAME="E1:52"/>
( <font color="Maroon">R</font> <a href="relat_2.html#R1">is_reflexive_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="relat_2.html#R8">is_transitive_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="relat_2.html#R4">is_antisymmetric_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> )
 ; <i><font color="Red">:: according to </font></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#D14">RELAT_2:def 14</a>,<a class="ref" href="relat_2.html#D16">RELAT_2:def 16</a>,<a class="ref" href="orders_1.html#D5" target="_self">ORDERS_1:def 5</a><br/>

<b>hence </b><a NAME="E2:52"/>
( <font color="Maroon">R</font> <a href="relat_2.html#R1">is_reflexive_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="relat_2.html#R8">is_transitive_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="relat_2.html#R4">is_antisymmetric_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D8" target="_self">ORDERS_1:def 8</a><br/>


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