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<div><span class="kw">theorem </span><a NAME="T140"><span class="comment"><font color="firebrick">:: SEQ_4:140</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">v</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   ex <font color="Olive" title="b2">v1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <br/>(  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b1">v</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b1">v</font></span>)</span> &amp; <font color="Olive" title="b2">v1</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  ) <span class="kw">by</span> <span class="lab"><a class="txt" href="seq_4.html#E177"><span class="lab"><font color="Green" title="E91">Lm12</font></span></a></span>;<br/></div></div>
