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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">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Z</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">Y'</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Z'</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">Z</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X'</font>,<font color="Maroon">Y'</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">Z'</font>;<br/>















<a NAME="E1:63"/>
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X'</font>,<font color="Maroon">Y'</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
;<br/>
<a NAME="E2:63"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_4.html#K3" target="_self">|:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="funct_4.html#K3" target="_self">:|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">X'</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Y</font>,<font color="Maroon">Y'</font></span><a href="zfmisc_1.html#K2">:]</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:63"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_4.html#K3" target="_self">|:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="funct_4.html#K3" target="_self">:|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Z</font>,<font color="Maroon">Z'</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E4:63"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="funct_4.html#K3" target="_self">|:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="funct_4.html#K3" target="_self">:|</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Z</font>,<font color="Maroon">Z'</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E5:63"/>
<span class="p1"><a href="funct_4.html#K3" target="_self">|:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="funct_4.html#K3" target="_self">:|</a></span> is   <a href="partfun1.html#NM1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">X'</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Y</font>,<font color="Maroon">Y'</font></span><a href="zfmisc_1.html#K2">:]</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">Z</font>,<font color="Maroon">Z'</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="funct_4.html#T1" target="_self">Th1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>


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