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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: LOPBAN_3:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">seq</font>, <font color="Olive" title="b3">seq1</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">seq</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a>  &amp;  ex <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b2">seq</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">seq1</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Olive" title="b4">k</font> holds <br/><font color="Olive" title="b3">seq1</font> is  <a href="normsp_1.html#V3" title="NORMSP_1:attr.3">convergent</a> </div></div>
