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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: LPSPACE2:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">k</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/>( <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">b</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b1">a</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b2">b</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">k</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b1">a</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b2">b</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b1">a</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>,<span class="p3"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b2">b</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>)</span>)</span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">k</font> &amp; <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">b</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> (<span class="p3"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b1">a</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>,<span class="p3"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Olive" title="b2">b</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>)</span>)</span></span>)</span> <a href="power.html#K2" title="POWER:func.2">to_power</a> <font color="Olive" title="b3">k</font> )</div></div>
