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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: FUNCT_1:51</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">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Y</font> holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">X</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b2">Y</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">X</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T73" onmouseover="rs('relat_1/T73')" onmouseout="rh()">RELAT_1:73</a>, <a class="ref" href="relat_1.html#T74" onmouseover="rs('relat_1/T74')" onmouseout="rh()">RELAT_1:74</a></span>;<br/></div></div>
