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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: EC_PF_1:57</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="finset_1.html#V1" title="FINSET_1:attr.1">finite</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><br/>  for <font color="Olive" title="b4">L</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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>  &amp; <font color="Olive" title="b3">S</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b4">L</font> &amp; (  for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">S</font> holds <br/><font color="Olive" title="b4">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span> ) holds <br/> <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Olive" title="b4">L</font></div></div>
