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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:18_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:18_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a> </span>)</span>
 <b>and </b><br/><a NAME="E3:18_1_1_1"/><i><font color="Green">E14</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a> 
 ;<br/><a NAME="E4:18_1_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a> </span>)</span>
 <b>by </b><i><a class="txt" href="dickson.html#E3:18_1_1_1"><i><font color="Green">E14</font></i></a></i>;<br/><a NAME="E5:18_1_1_1"/><b>then </b>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E6:18_1_1_1"/><b>then </b>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#D7">RELAT_1:def 7</a></i>;<br/><a NAME="E7:18_1_1_1"/><b>then </b>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K4">~</a> </span>)</span>
 ;<br/><b>hence </b><a NAME="E8:18_1_1_1"/>
not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a> 
 ;<br/></div><b>end;</b></div>
<a NAME="E2:18_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a>  <a href="relat_2.html#R5">is_asymmetric_in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_2.html#D5">RELAT_2:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:18_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K3" target="_self">\~</a>  is <a href="relat_2.html#V5">asymmetric</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D13">RELAT_2:def 13</a></i>;<br/>


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