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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:61"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R1">is_reflexive_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R8">is_transitive_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R4">is_antisymmetric_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">c<sub>2</sub></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/>

<b>hence </b><a NAME="E2:61"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a>  <a href="relat_2.html#R1">is_reflexive_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a>  <a href="relat_2.html#R8">is_transitive_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a>  <a href="relat_2.html#R4">is_antisymmetric_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a>  <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="orders_1.html#E154"><i><font color="Green">Lemma32</font></i></a>, <a class="txt" href="orders_1.html#E155"><i><font color="Green">Lemma33</font></i></a>, <a class="txt" href="orders_1.html#E156"><i><font color="Green">Lemma34</font></i></a>, <a class="txt" href="orders_1.html#E157"><i><font color="Green">Lemma35</font></i></a></i>; <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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