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<b>let </b><font color="Maroon">J</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">K</font> be    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">J</font>;<br/><b>let </b><font color="Maroon">D</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="waybel_5.html#NM1">DoubleIndexedSet</a> of <font color="Maroon">K</font>,<font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>









<b>assume </b><a NAME="E1:19"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K3">Frege</a> <font color="Maroon">F</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">j</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E2:19"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font>
 ;<br/>

<a NAME="E3:19"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:19"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:19"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">K</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>,<font color="Maroon">D</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:19"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>


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