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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E58">Th55</font></span>: <a NAME="T55"><span class="comment"><font color="firebrick">:: EC_PF_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">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">S</font> being   <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b3">S</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/><font color="Olive" title="b3">S</font> is  <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> </div></div>
