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<div><span class="kw">theorem </span><a NAME="T67"><span class="comment"><font color="firebrick">:: VALUED_1:67</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">f</font> being   <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <a href="relat_1.html#V4" title="RELAT_1:attr.4">-defined</a>   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="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="funct_4.html#K8" title="FUNCT_4:func.8">+~</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</span>)</span>,<font color="Olive" title="b1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="funct_4.html#K8" title="FUNCT_4:func.8">+~</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</div></div>
