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<div><span class="kw">theorem </span><a NAME="T36"><span class="comment"><font color="firebrick">:: PARTFUN1:36</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    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <span class="p1">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b5">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Y</font> holds <br/><span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Olive" title="b5">g</font>,<font color="Olive" title="b2">Y</font>,<font color="Olive" title="b3">Z</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><font color="Olive" title="b4">f</font>,<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="partfun1.html#K3" title="PARTFUN1:func.3">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b5">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font></span>)</span>,<font color="Olive" title="b1">X</font>,<font color="Olive" title="b3">Z</font></span><a href="partfun1.html#K3" title="PARTFUN1:func.3">:&gt;</a></span></div></div>
