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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: RINFSUP1:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">seq</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a> holds <br/> ( (  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b2">seq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> ) iff ( <font color="Olive" title="b2">seq</font> is <a href="seq_2.html#V1" title="SEQ_2:attr.1">V95</a>() &amp;  <a href="rinfsup1.html#K1" title="RINFSUP1:func.1">upper_bound</a> <font color="Olive" title="b2">seq</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> ) )</div></div>
