<?xml version="1.0"?>
<div class="add">

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



<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V3" target="_self">symmetric</a>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="relat_2.html#V3" target="_self">symmetric</a>
 ;<br/>

<a NAME="E3:19"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R3" target="_self">is_symmetric_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="relat_2.html#E1:19"><i><font color="Green">E21</font></i></a>, <a class="ref" href="relat_2.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E4:19"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R3" target="_self">is_symmetric_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="relat_2.html#E2:19"><i><font color="Green">E22</font></i></a>, <a class="ref" href="relat_2.html#D11" target="_self">Def11</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:19_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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E2:19_1"/><i><font color="Green">E25</font></i>: 
<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>4</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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_1"/><i><font color="Green">E27</font></i>: 
<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>4</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>
 ;<br/><a NAME="E2:19_1_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>1</sub></font> &amp; <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>1</sub></font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><a NAME="E3:19_1_1"/><b>then </b>
<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>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>
 <b>by </b><i><a class="txt" href="relat_2.html#E3:19"><i><font color="Green">E23</font></i></a>, <a class="txt" href="relat_2.html#E1:19_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E4:19_1_1"/>
<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>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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:19_1_2"/><i><font color="Green">E27</font></i>: 
<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>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:19_1_2"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> &amp; <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>2</sub></font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><a NAME="E3:19_1_2"/><b>then </b>
<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>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="relat_2.html#E4:19"><i><font color="Green">E24</font></i></a>, <a class="txt" href="relat_2.html#E1:19_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E4:19_1_2"/>
<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>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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:19_1"/>
<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>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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="relat_2.html#E2:19_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="relat_2.html#E3:19_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:19"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R3" target="_self">is_symmetric_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="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E7:19"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_2.html#V3" target="_self">symmetric</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D11" target="_self">Def11</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:19_2"/><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T34">RELAT_1:34</a></i>;<br/><b>assume </b><a NAME="E2:19_2"/><i><font color="Green">E26</font></i>: 
( <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="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</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="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <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>4</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="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/><a NAME="E3:19_2"/><b>then </b><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="relat_2.html#E1:19_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:19_2"/><i><font color="Green">E28</font></i>: 
( <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>1</sub></font> &amp; <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>2</sub></font> )
 <b>by </b><i><a class="txt" href="relat_2.html#E1:19_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="relat_2.html#E2:19_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:19_2"/><i><font color="Green">E29</font></i>: 
( <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>4</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> &amp; <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>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="relat_2.html#E2:19_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:19_2"/><b>then </b><i><font color="Green">E30</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>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>
 <b>by </b><i><a class="txt" href="relat_2.html#E3:19"><i><font color="Green">E23</font></i></a>, <a class="txt" href="relat_2.html#E3:19_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="relat_2.html#E4:19_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E7:19_2"/>
<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>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="relat_2.html#E4:19"><i><font color="Green">E24</font></i></a>, <a class="txt" href="relat_2.html#E3:19_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="relat_2.html#E4:19_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="relat_2.html#E5:19_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/><b>hence </b><a NAME="E8:19_2"/>
<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>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="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="relat_2.html#E6:19_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div>
<a NAME="E9:19"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R3" target="_self">is_symmetric_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="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E10:19"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_2.html#V3" target="_self">symmetric</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D11" target="_self">Def11</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:19_3"/>
( <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="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</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="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E2:19_3"/><i><font color="Green">E25</font></i>: 
<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>4</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="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E3:19_3"/><i><font color="Green">E26</font></i>: 
( <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>4</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> &amp; 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>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="relat_2.html#E2:19_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:19_3"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>1</sub></font> &amp; <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>1</sub></font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><a NAME="E5:19_3"/><b>then </b><i><font color="Green">E27</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>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>
 <b>by </b><i><a class="txt" href="relat_2.html#E3:19"><i><font color="Green">E23</font></i></a>, <a class="txt" href="relat_2.html#E3:19_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E6:19_3"/><i><font color="Green">E28</font></i>: 
(  not <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>2</sub></font> or  not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> or  not <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>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="relat_2.html#E4:19"><i><font color="Green">E24</font></i></a>, <a class="txt" href="relat_2.html#E3:19_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E7:19_3"/>
( (  not <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>2</sub></font> or  not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> ) implies  not <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>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</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="E8:19_3"/>
<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>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="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="relat_2.html#E5:19_3"><i><font color="Green">E27</font></i></a>, <a class="txt" href="relat_2.html#E6:19_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<a NAME="E12:19"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R3" target="_self">is_symmetric_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="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_2.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E13:19"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">c<sub>2</sub></font> is <a href="relat_2.html#V3" target="_self">symmetric</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D11" target="_self">Def11</a></i>;<br/>


</div>
