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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th36</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: LIOUVIL1:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b2">b</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">a</font> is  <a href="liouvil1.html#V1" title="LIOUVIL1:attr.1">eventually-non-zero</a>  &amp;  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">b</font> holds <br/> <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="liouvil1.html#K4" title="LIOUVIL1:func.4">Liouville_seq</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)</span>)</span> <a href="nat_1.html#K7" title="NAT_1:func.7">^\</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </div></div>
