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<div><span class="kw">theorem </span><a NAME="T55"><span class="comment"><font color="firebrick">:: FUNCOP_1:55</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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="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="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Olive" title="b1">X</font><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="b2">Y</font>,<font color="Olive" title="b1">X</font><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="b3">F</font> <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> (<font color="Olive" title="b5">x</font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Olive" title="b1">X</font></span>)</span>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">F</font> <a href="funcop_1.html#K10" title="FUNCOP_1:func.10">[;]</a> (<font color="Olive" title="b5">x</font>,<font color="Olive" title="b4">f</font>)</div></div>
