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<b>let </b><font color="Maroon">N</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:14"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">N</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>let </b><font color="Maroon">S</font> be    <a href="scm_1.html#M1">State-consisting</a> of 0,0,0, <a href="fib_fusc.html#K3" target="_self">Fusc_Program</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1">&lt;*</a><span class="default">2</span><a href="scm_1.html#K1">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1">&lt;*</a><span class="default"><font color="Maroon">N</font></span><a href="scm_1.html#K1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1">&lt;*</a><span class="default">1</span><a href="scm_1.html#K1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="scm_1.html#K1">&lt;*</a><span class="default">0</span><a href="scm_1.html#K1">*&gt;</a></span>;<br/>

<a NAME="E2:14"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon">N</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E3:14"/>
( <font color="Maroon">S</font> is <a href="ami_1.html#V9">halting</a> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">S</font></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">N</font> &amp; ( <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> 0 implies  <a href="scm_1.html#K2">Complexity</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> 1 ) &amp; ( <font color="Maroon">N</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 implies  <a href="scm_1.html#K2">Complexity</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5">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</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 ) )
 <b>by </b><i>, </i>;<br/>


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