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<span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 implies <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:88"/>
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font></span><br/>

<a NAME="E2:88"/><span class="kw">then </span>
 <a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="power.html#K3" title="POWER:func.3">log</a> (2,<span class="p1">(<span class="default">2 <a href="square_1.html#K1" title="SQUARE_1:func.1">^2</a></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_ff.html#T10" onmouseover="rs('pre_ff/T10')" onmouseout="rh()">PRE_FF:10</a></span>;<br/>
<a NAME="E3:88"/><span class="kw">then </span>
 <a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="power.html#K3" title="POWER:func.3">log</a> (2,<span class="p1">(<span class="default">2 <a href="series_1.html#K5" title="SERIES_1:func.5">to_power</a> 2</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T46" onmouseover="rs('power/T46')" onmouseout="rh()">POWER:46</a></span>;<br/>
<a NAME="E4:88"/><span class="kw">then </span>
 <a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (2,2)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T55" onmouseover="rs('power/T55')" onmouseout="rh()">POWER:55</a></span>;<br/>
<a NAME="E5:88"/><span class="kw">then </span>
 <a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>) <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="power.html#T52" onmouseover="rs('power/T52')" onmouseout="rh()">POWER:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:88"/>
<font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="power.html#K3" title="POWER:func.3">log</a> (2,<font color="Maroon" title="c2">n</font>)</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T64" onmouseover="rs('xreal_1/T64')" onmouseout="rh()">XREAL_1:64</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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