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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: NEWTON04:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b2">g</font> being   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>   <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative-yielding</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st (  for <font color="Olive" title="b3">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b2">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> ) holds <br/><font color="Olive" title="b1">f</font> is  <a href="partfun3.html#V4" title="PARTFUN3:attr.4">nonnegative-yielding</a> </div></div>
