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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="relset_1.html#NM3">Relation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:14"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="relat_2.html#V5">asymmetric</a> &amp;  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:14"/><b>then </b><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R5">is_asymmetric_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D13">RELAT_2:def 13</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D5">RELAT_2:def 5</a><br/>

<b>assume </b><a NAME="E3:14"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E4:14"/><i><font color="Green">E14</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E5:14"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/>
<b>hence </b><a NAME="E6:14"/>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="oposet_1.html#E2:14"><i><font color="Green">E13</font></i></a>, <a class="txt" href="oposet_1.html#E4:14"><i><font color="Green">E14</font></i></a>, <a class="ref" href="relat_2.html#D5">RELAT_2:def 5</a></i>;<br/>


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