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<b>let </b><font color="Maroon" title="c1">N</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c1">N</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/>

<b>let </b><font color="Maroon" title="c2">S</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of 0,0,0, <a href="fib_fusc.html#K3" title="FIB_FUSC:func.3">Fusc_Program</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">2</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default"><font color="Maroon" title="c1">N</font></span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">1</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="scm_1.html#K1" title="SCM_1:func.1">&lt;*</a><span class="default">0</span><a href="scm_1.html#K1" title="SCM_1:func.1">*&gt;</a></span>;<br/>

<a NAME="E2:14"/>
 <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c1">N</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">N</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E3:14"/>
( <font color="Maroon" title="c2">S</font> is <a href="ami_1.html#V9" title="AMI_1:attr.9">halting</a> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K12" title="AMI_1:func.12">Result</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_ff.html#K5" title="PRE_FF:func.5">Fusc</a> <font color="Maroon" title="c1">N</font> &amp; ( <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies  <a href="scm_1.html#K2" title="SCM_1:func.2">Complexity</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c1">N</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 implies  <a href="scm_1.html#K2" title="SCM_1:func.2">Complexity</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">6 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="int_1.html#K1" title="INT_1:func.1">[\</a><span class="default"><span class="p4">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> 2,<font color="Maroon" title="c1">N</font></span>)</span></span><a href="int_1.html#K1" title="INT_1:func.1">/]</a></span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 ) )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E1:14"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="fib_fusc.html#T5" target="_self" title="FIB_FUSC:th.5">Th5</a></i>;<br/>


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