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<div><span class="kw">theorem </span><a NAME="T9"><span class="comment"><font color="firebrick">:: TOPMETR3:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">s</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b4">S</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K2" title="TOPMETR:func.2">Closed-Interval-MSpace</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span>)</span>  st <font color="Olive" title="b4">S</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">s</font> &amp; <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">s</font> is  <a href="valued_0.html#V7" title="VALUED_0:attr.7">non-decreasing</a>  holds <br/><font color="Olive" title="b4">S</font> is  <a href="tbsp_1.html#V2" title="TBSP_1:attr.2">convergent</a> </div></div>
