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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: FUNCOP_1:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b2">Y</font>,<font color="Olive" title="b3">Z</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span><br/>  for <font color="Olive" title="b5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funcop_1.html#K1" title="FUNCOP_1:func.1">~</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">x</font></span>)</span> <a href="xtuple_0.html#K2" title="XTUPLE_0:func.2">`2</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">x</font></span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></div></div>
