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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">Th33</font></span>: <a NAME="T33"><span class="comment"><font color="firebrick">:: RINFSUP1:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>  st <font color="Olive" title="b1">seq</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  holds <br/> for <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">R</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b3">R</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="b1">seq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">k</font></span>)</span> where <font color="Olive" title="b4">k</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">k</font> </span> } </span>  holds <br/><font color="Olive" title="b3">R</font> is  <a href="xxreal_2.html#V5" title="XXREAL_2:attr.5">real-bounded</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="rinfsup1.html#T31" target="_self" onmouseover="rs('rinfsup1/T31')" onmouseout="rh()">Th31</a>, <a class="ref" href="rinfsup1.html#T32" target="_self" onmouseover="rs('rinfsup1/T32')" onmouseout="rh()">Th32</a></span>;<br/></div></div>
