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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: SUPINF_2:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">Y</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b3">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font> holds <br/> ( <font color="Olive" title="b3">F</font> is  <a href="supinf_2.html#V3" title="SUPINF_2:attr.3">bounded</a>  iff (  <a href="supinf_2.html#K10" title="SUPINF_2:func.10">sup</a> <font color="Olive" title="b3">F</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp;  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_2.html#K11" title="SUPINF_2:func.11">inf</a> <font color="Olive" title="b3">F</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="supinf_2.html#D5" target="_self" onmouseover="rs('supinf_2/D5')" onmouseout="rh()">Def5</a>, <a class="ref" href="supinf_2.html#D6" target="_self" onmouseover="rs('supinf_2/D6')" onmouseout="rh()">Def6</a></span>;<br/></div></div>
