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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>





<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E36">A1</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ;<br/>

<div><i><font color="Green" title="E37">A2</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" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E2:50_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T64" title="RELAT_1:th.64">RELAT_1:64</a></i>;<br/><b>hence </b><a NAME="E3:50_1"/>
(  <a href="funct_5.html#K4" title="FUNCT_5:func.4">uncurry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="funct_5.html#K6" title="FUNCT_5:func.6">uncurry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> )
 <b>by </b><i><a class="ref" href="funct_5.html#T49" target="_self" title="FUNCT_5:th.49">Th49</a>, <a class="ref" href="funct_5.html#T50" target="_self" title="FUNCT_5:th.50">Th50</a></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" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E2:50_2"/><b>then </b>
( <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c2">Y</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">X</font>,<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> )
 <b>by </b><i><a class="txt" href="funct_5.html#E1:50"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="funct_5.html#T31" target="_self" title="FUNCT_5:th.31">Th31</a>, <a class="ref" href="funct_5.html#T42" target="_self" title="FUNCT_5:th.42">Th42</a>, <a class="ref" href="zfmisc_1.html#T113" title="ZFMISC_1:th.113">ZFMISC_1:113</a></i>;<br/><a NAME="E3:50_2"/><b>then </b>
(  <a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4" title="FUNCT_5:func.4">uncurry</a> <span class="p2">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K6" title="FUNCT_5:func.6">uncurry'</a> <span class="p2">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4" title="FUNCT_5:func.4">uncurry</a> <span class="p2">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="funct_5.html#K6" title="FUNCT_5:func.6">uncurry'</a> <span class="p2">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <b>by </b><i><a class="ref" href="funct_5.html#T33" target="_self" title="FUNCT_5:th.33">Th33</a>, <a class="ref" href="funct_5.html#T55" target="_self" title="FUNCT_5:th.55">Th55</a></i>;<br/><b>hence </b><a NAME="E4:50_2"/>
(  <a href="funct_5.html#K4" title="FUNCT_5:func.4">uncurry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="funct_5.html#K6" title="FUNCT_5:func.6">uncurry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> )
 <b>by </b><i><a class="txt" href="funct_5.html#E1:50"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="funct_5.html#T51" target="_self" title="FUNCT_5:th.51">Th51</a>, <a class="ref" href="funct_5.html#T52" target="_self" title="FUNCT_5:th.52">Th52</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:50"/>
(  <a href="funct_5.html#K4" title="FUNCT_5:func.4">uncurry</a> <span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="funct_5.html#K6" title="FUNCT_5:func.6">uncurry'</a> <span class="p1">(<span class="default"><a href="funct_5.html#K5" title="FUNCT_5:func.5">curry'</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> )
 <b>by </b><i><a class="txt" href="funct_5.html#E2:50"><i><font color="Green" title="E37">A2</font></i></a></i>;<br/>


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