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<b>let </b><font color="Maroon">V</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>







<b>assume </b><a NAME="E1:9"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:9"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="ens_1.html#K1" target="_self">Funcs</a> <font color="Maroon">V</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:9"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">f</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><span class="p3"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">A'</font>,<font color="Olive">B'</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Olive">f'</font></span><a href="domain_1.html#K1">]</a></span> where <font color="Olive">A'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font>, <font color="Olive">B'</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font>, <font color="Olive">f'</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="ens_1.html#K1" target="_self">Funcs</a> <font color="Maroon">V</font> : ( ( <font color="Olive">B'</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Olive">A'</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; <font color="Olive">f'</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Olive">A'</font>,<font color="Olive">B'</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:9"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="domain_1.html#K1">]</a></span>,<font color="Maroon">f</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="ens_1.html#K2" target="_self">Maps</a> <font color="Maroon">V</font>
 ;<br/>


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