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<div>:: <span class="kw">deftheorem </span>   defines <a href="mesfun10.html#V1" title="MESFUN10:attr.1">uniformly_bounded</a> <a onclick="hs(this)" href="javascript:()">MESFUN10:def 1 : <br/></a><span> for <font color="Olive" title="b1">X</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="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> ( <font color="Olive" title="b2">F</font> is  <a href="mesfun10.html#V1" title="MESFUN10:attr.1">uniformly_bounded</a>  iff  ex <font color="Olive" title="b3">K</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/> for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b5">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> holds <br/><span class="p1"><a href="extreal1.html#K3" title="EXTREAL1:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">F</font> <a href="mesfunc5.html#K4" title="MESFUNC5:func.4">.</a> <font color="Olive" title="b4">n</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b5">x</font></span>)</span></span><a href="extreal1.html#K3" title="EXTREAL1:func.3">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">K</font> );<br/></span></div>
