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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>





<b>assume </b><a NAME="E1:19"/>
<font color="Maroon">x</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">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font></span>)</span>
 ;<br/>

<a NAME="E2:19"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:19"/><b>then </b><i><font color="Green">E19</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:19"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font></span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font> &amp; <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:19"/><i><font color="Green">E27</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font></span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">R</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">R</font> )
 
<b>by </b><i><a class="txt" href="wellord1.html#E1"><i><font color="Green">Lemma17</font></i></a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a>, <a class="ref" href="relat_1.html#T99">RELAT_1:99</a>, <a class="ref" href="relat_1.html#T119">RELAT_1:119</a></i>;<br/>
<a NAME="E6:19"/><b>then </b>
( ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="relat_1.html#K8">|</a> <font color="Maroon">R</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> ) )
 
<b>by </b><i><a class="txt" href="wellord1.html#E3:19"><i><font color="Green">E19</font></i></a>, <a class="txt" href="wellord1.html#E4:19"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:19"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">R</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="txt" href="wellord1.html#E3"><i><font color="Green">Lemma21</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:19"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="txt" href="wellord1.html#E3:19"><i><font color="Green">E19</font></i></a>, <a class="txt" href="wellord1.html#E4:19"><i><font color="Green">E20</font></i></a>, <a class="txt" href="wellord1.html#E3"><i><font color="Green">Lemma21</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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