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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: SETLIM_1:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Y</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">f</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Olive" title="b1">Y</font> holds   <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">k</font></span>)</span> where <font color="Olive" title="b3">k</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> :  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">k</font> </span> } </span> </div></div>
