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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">Th32</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: LIOUVIL1:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">b</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="liouvil1.html#K7" title="LIOUVIL1:func.7">ALiouville_seq</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="liouvil1.html#K6" title="LIOUVIL1:func.6">BLiouville_seq</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><a href="liouvil1.html#K2" title="LIOUVIL1:func.2">FinSeq</a> (<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="b3">b</font>)</span>)</span>,<font color="Olive" title="b2">n</font>)</span>)</span></div></div>
