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<b>let </b><font color="Maroon">e</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funcop_1.html#D6">FUNCOP_1:def 6</a><br/>



<b>assume </b><a NAME="E1:39_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">e</font>
 ;<br/>

<a NAME="E2:39_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E3:39_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:39_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">e</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font>, <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">r</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T121">FUNCT_2:121</a></i>;<br/>
<a NAME="E5:39_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:39_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">r</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/>
<a NAME="E7:39_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">q</font></span>)</span>,<span class="p1">(<span class="default"><a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">r</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:39_1_1"/>
<font color="Maroon">e</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is   <a href="funct_1.html#NM1">Function</a>
 <b>by </b><i><a class="ref" href="funct_2.html#T121">FUNCT_2:121</a></i>;<br/>


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