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<b>let </b><font color="Maroon">V</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:4"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font>
 ;<br/>

<b>consider </b><font color="Maroon">f1</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:4"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> )
 <b>by </b><i><a class="ref" href="partfun1.html#D5">PARTFUN1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">g</font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i>, <a class="ref" href="grfunc_1.html#T6">GRFUNC_1:6</a></i>;<br/>
<a NAME="E5:4"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g'</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g'</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f1</font> )
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T25">RELAT_1:25</a></i>;<br/>
<a NAME="E6:4"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E7:4"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K4">PFuncs</a> <font color="Maroon">V</font>,<font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="partfun1.html#D5">PARTFUN1:def 5</a></i>;<br/>


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