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<b>let </b><font color="Maroon">J</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">K</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">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">j</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">J</font>;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">J</font>,<font color="Maroon">K</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">D</font>;<br/>











<b>thus </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="waybel_5.html#K6" target="_self">curry</a> <font color="Maroon">F</font></span>)</span> = 
 <a href="funct_5.html#K1">proj1</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#D3">FUNCT_5:def 3</a></i>
<br/>.= 
 <a href="funct_5.html#K1">proj1</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">J</font>,<font color="Maroon">K</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
<font color="Maroon">J</font>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
;<br/>

<a NAME="E2:39"/>
( <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">J</font>,<font color="Maroon">K</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>  &amp;  <a href="relset_1.html#K4">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">J</font>,<font color="Maroon">K</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</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/>
<a NAME="E3:39"/><b>then </b>
 ex <font color="Olive">g</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <span class="p1">(<span class="default"><a href="waybel_5.html#K6" target="_self">curry</a> <font color="Maroon">F</font></span>)</span> <a href="waybel_5.html#K1" target="_self">.</a> <font color="Maroon">j</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> <font color="Maroon">K</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">g</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> &amp; ( for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">K</font> holds <br/><font color="Olive">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">j</font>,<font color="Olive">i</font> ) )
 
<b>by </b><i><a class="ref" href="funct_5.html#T36">FUNCT_5:36</a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_5.html#K6" target="_self">curry</a> <font color="Maroon">F</font></span>)</span> <a href="waybel_5.html#K1" target="_self">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">K</font>
 ;<br/>

<a NAME="E5:39"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">j</font>,<font color="Maroon">k</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">J</font>,<font color="Maroon">K</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<a NAME="E6:39"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">j</font>,<font color="Maroon">k</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:39"/>
<font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">j</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_5.html#K6" target="_self">curry</a> <font color="Maroon">F</font></span>)</span> <a href="waybel_5.html#K1" target="_self">.</a> <font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="funct_5.html#T27">FUNCT_5:27</a></i>;<br/>


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