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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">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Z</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="E1:19"/><i><font color="Green">E40</font></i>: 
<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> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:19"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</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>,<font color="Maroon">Z</font>
 ;<br/>

<a NAME="E3:19"/><b>then </b><i><font color="Green">E41</font></i>: 
 ex <font color="Olive">g</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">g</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> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<a NAME="E4:19"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3">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#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5">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="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> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">Y</font>,<font color="Maroon">Z</font> &amp;  <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> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">X</font>,<font color="Maroon">Z</font> )
 
<b>by </b><i><a class="ref" href="funct_5.html#T42">FUNCT_5:42</a>, <a class="ref" href="funct_5.html#T63">FUNCT_5:63</a></i>;<br/>
<a NAME="E5:19"/><b>then </b>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3">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>,<font color="Maroon">Z</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5">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>,<font color="Maroon">Z</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3">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#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5">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="funct_5.html#T31">FUNCT_5:31</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E6:19"/>
(  <a href="funct_5.html#K3">curry</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">Y</font>,<font color="Maroon">Z</font></span>)</span> &amp;  <a href="funct_5.html#K5">curry'</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">Y</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">X</font>,<font color="Maroon">Z</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>


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