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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: SETLIM_2:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">A1</font>, <font color="Olive" title="b4">A2</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Olive" title="b2">X</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">A1</font> <a href="setlim_2.html#K4" title="SETLIM_2:func.4">(\+\)</a> <font color="Olive" title="b4">A2</font></span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">A1</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="setlim_2.html#K4" title="SETLIM_2:func.4">(\+\)</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">A2</font> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <font color="Olive" title="b1">k</font></span>)</span></div></div>
