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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> , <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="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<a NAME="E1:6"/><i><font color="Green">E15</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/>
<b>assume </b><a NAME="E2:6"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">B</font>,<font color="Maroon">C</font> )
 ;<br/>

<a NAME="E3:6"/><b>then </b>
(  ex <font color="Olive">f'</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Olive">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">f'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> ) &amp;  ex <font color="Olive">g'</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Olive">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">g'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> ) )
 
<b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<a NAME="E4:6"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> )
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">A</font>,<font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>


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