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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th25</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: FUNCT_5:32</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b4">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <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#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b4">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="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Y</font> holds <br/> ex <font color="Olive" title="b5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> st <br/>( <span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry'</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">X</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b5">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">f</font> &amp; (  for <font color="Olive" title="b6">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b6">x</font>,<font color="Olive" title="b3">y</font>) ) )</div></div>
