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<b>let </b><font color="Maroon">P</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3" target="_self">field</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<a NAME="E2:34"/><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" target="_self">dom</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:34"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2" target="_self">rng</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:34"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K1" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:34"/><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K2" target="_self">rng</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">R</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:34"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font></span>)</span> ) implies ( ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">P</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">P</font> ) &amp; ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">R</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:34"/><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" target="_self">dom</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">R</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">R</font></span>)</span> ) implies ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">dom</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" target="_self">rng</a> <font color="Maroon">P</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" target="_self">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" target="_self">rng</a> <font color="Maroon">R</font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E8:34"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3" target="_self">field</a> <font color="Maroon">P</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3" target="_self">field</a> <font color="Maroon">R</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E9:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K3" target="_self">field</a> <font color="Maroon">P</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K3" target="_self">field</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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