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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>then </b><span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K6">log</a> 2,<span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span> = 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K6">log</a> 2,<span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="power.html#K6">log</a> 2,2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">n</font></span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span>
<b>by </b><i>, <a class="ref" href="power.html#T61">POWER:61</a></i>
<br/>.= 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="int_1.html#K1">/]</a></span>
<b>by </b><i><a class="ref" href="power.html#T60">POWER:60</a></i>
<br/>.= 
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">n</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="int_1.html#T51">INT_1:51</a></i>
;<br/>
<b>hence </b><a NAME="E3:16"/>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">n</font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default"><a href="power.html#K6">log</a> 2,<span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span>
 ;<br/>


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