<?xml version="1.0"?>
<div class="add">

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





<b>assume </b><a NAME="E1:50"/><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:50_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/><b>hence </b><a NAME="E3:50_1"/>
(  <a href="funct_5.html#K4" target="_self">uncurry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="funct_5.html#K6" target="_self">uncurry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:50_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:50_2"/><b>then </b>
( <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">Y</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/><a NAME="E3:50_2"/><b>then </b>
(  <a href="funct_5.html#K3" target="_self">curry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4" target="_self">uncurry</a> <span class="p2">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font> &amp;  <a href="funct_5.html#K5" target="_self">curry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K6" target="_self">uncurry'</a> <span class="p2">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4" target="_self">uncurry</a> <span class="p2">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K6" target="_self">uncurry'</a> <span class="p2">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:50_2"/>
(  <a href="funct_5.html#K4" target="_self">uncurry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="funct_5.html#K6" target="_self">uncurry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="txt" href="funct_5.html#E2:50"><i><font color="Green">E32</font></i></a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:50"/>
(  <a href="funct_5.html#K4" target="_self">uncurry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" target="_self">curry</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp;  <a href="funct_5.html#K6" target="_self">uncurry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" target="_self">curry'</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 <b>by </b><i/>;<br/>


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