<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: BINARI_3:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</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><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="binari_3.html#K1" title="BINARI_3:func.1">-BinarySequence</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <span class="p3">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K9" title="BINARITH:func.9">^</a> <span class="p1"><a href="binarith.html#K10" title="BINARITH:func.10">&lt;*</a><span class="default"><a href="margrel1.html#K7" title="MARGREL1:func.7">TRUE</a></span><a href="binarith.html#K10" title="BINARITH:func.10">*&gt;</a></span> <span class="kw">by</span> <span class="lab"><a class="txt" href="binari_3.html#E31"><span class="lab"><font color="Green" title="E24">Lm3</font></span></a></span>;<br/></div></div>
