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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">C</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">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K1">REAL</a> ;<br/>





<b>thus </b><a NAME="E1:70"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="rfunct_1.html#K5" target="_self">chi</a> <font color="Maroon">X</font>,<font color="Maroon">C</font> implies (  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp; ( for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds <br/> ( ( <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> 1 ) &amp; ( not <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> 0 ) ) ) ) )
 <b>by </b><i><a class="ref" href="funct_3.html#D3">FUNCT_3:def 3</a></i>;<br/>

<b>assume </b><a NAME="E2:70"/><i><font color="Green">E29</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp; ( for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds <br/> ( ( <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> 1 ) &amp; ( not <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">f</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> 0 ) ) ) )
 ;<br/>

<a NAME="E3:70"/><b>then </b>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> holds <br/>( ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> 1 ) &amp; ( not <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> implies <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> 0 ) )
 
;<br/>
<b>hence </b><a NAME="E4:70"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="rfunct_1.html#K5" target="_self">chi</a> <font color="Maroon">X</font>,<font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="rfunct_1.html#T16" target="_self">Th16</a>, <a class="ref" href="funct_3.html#D3">FUNCT_3:def 3</a></i>;<br/>


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