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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th82</font></span>: <a NAME="T82"><span class="comment"><font color="firebrick">:: RFUNCT_1:82</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">f</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b2">f</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">Y</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  holds <br/>( <span class="p1">(<span class="default"><a href="valued_1.html#NK57" title="VALUED_1:NK.57">abs</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">Y</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  &amp; <span class="p1">(<span class="default"><a href="valued_1.html#K30" title="VALUED_1:func.30">-</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b1">Y</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  )</div></div>
