<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="ami_3.html#K16">il.</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="ami_3.html#K16">il.</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="ami_3.html#K16">il.</a> 2;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="ami_3.html#K16">il.</a> 3;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="ami_3.html#K16">il.</a> 4;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="ami_3.html#K16">il.</a> 5;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="ami_3.html#K16">il.</a> 6;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="ami_3.html#K16">il.</a> 7;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="ami_3.html#K16">il.</a> 8;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> =  <a href="ami_3.html#K15">dl.</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="ami_3.html#K15">dl.</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="ami_3.html#K15">dl.</a> 2;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> =  <a href="ami_3.html#K15">dl.</a> 3;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> =  <a href="ami_3.html#K15">dl.</a> 4;<br/>
<b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:11"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>let </b><font color="Maroon">c<sub>16</sub></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">c<sub>15</sub></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/>

<b>consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:11"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>
<a NAME="E4:11"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K9">=0_goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 8</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E5:11"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="ami_3.html#K3">:=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7">Divide</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E7:11"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="ami_3.html#K9">=0_goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 6</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E8:11"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 4</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E9:11"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 5</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E10:11"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 6</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4">AddTo</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E11:11"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 7</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8">goto</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E12:11"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 8</span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E13:11"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>17</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>17</sub></font> <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> 0 )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>
<a NAME="E14:11"/><i><font color="Green">E22</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 implies for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> holds <br/>(  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is   <a href="nat_1.html#NM1">Nat</a> &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> ) );<br/>
<a NAME="E15:11"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:11_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<b>let </b><font color="Maroon">c<sub>18</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E2:11_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> 0</span>)</span>
 ;<br/>

<a NAME="E3:11_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/>
<b>hence </b><a NAME="E4:11_1"/>
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>

<b>thus </b><font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> = 
<font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> 1
<b>by </b><i><a class="txt" href="fib_fusc.html#E13:11"><i><font color="Green">E21</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="pre_ff.html#T2">PRE_FF:2</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9">NEWTON:9</a></i>
;<br/>

<b>thus </b><a NAME="E6:11_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is   <a href="nat_1.html#NM1">Nat</a>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a></i>;<br/>

<b>thus </b><a NAME="E7:11_1"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E13:11"><i><font color="Green">E21</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E16:11"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>18</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:11_2"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 implies for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> holds <br/>(  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is   <a href="nat_1.html#NM1">Nat</a> &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> ) )
 ;<br/>

<b>assume </b><a NAME="E2:11_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/>

<b>let </b><font color="Maroon">c<sub>19</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E3:11_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>20</sub></font> = 6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>;<br/>
<a NAME="E4:11_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E5:11_2"/><b>then </b><i><font color="Green">E29</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is   <a href="nat_1.html#NM1">Nat</a> )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E1:11_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E6:11_2"/>
<font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E2:11_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E7:11_2"/><b>then </b>
2 <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_ff.html#T10">PRE_FF:10</a></i>;<br/>
<a NAME="E8:11_2"/><b>then </b>
2 <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E1:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="power.html#D3">POWER:def 3</a></i>;<br/>
<a NAME="E9:11_2"/><b>then </b><i><font color="Green">E30</font></i>: 
( 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> &amp; 2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="newton.html#T102">NEWTON:102</a>, <a class="ref" href="power.html#T48">POWER:48</a></i>;<br/>
<a NAME="E10:11_2"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="pre_ff.html#T3">PRE_FF:3</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E11:11_2"/><i><font color="Green">E32</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="fib_fusc.html#E10:11_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<a NAME="E12:11_2"/><i><font color="Green">E33</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/>
<a NAME="E13:11_2"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E14:11_2"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E5:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="fib_fusc.html#E11:11_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scm_1.html#T18">SCM_1:18</a></i>;<br/>
<a NAME="E15:11_2"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E5:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="fib_fusc.html#E11:11_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="fib_fusc.html#E12:11_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="fib_fusc.html#E13:11_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scm_1.html#T18">SCM_1:18</a></i>;<br/>
<a NAME="E16:11_2"/><i><font color="Green">E37</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E5:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="fib_fusc.html#E11:11_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="fib_fusc.html#E12:11_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="fib_fusc.html#E13:11_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma8</font></i></a>, <a class="ref" href="scm_1.html#T18">SCM_1:18</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>24</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>;<br/>
<a NAME="E17:11_2"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3
 
;<br/>
<a NAME="E18:11_2"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E6:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="fib_fusc.html#E14:11_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma8</font></i></a>, <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<a NAME="E19:11_2"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5">div</a> 2
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E6:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="fib_fusc.html#E14:11_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="fib_fusc.html#E15:11_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="fib_fusc.html#E16:11_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="fib_fusc.html#E17:11_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma8</font></i></a>, <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<b>then </b><i><font color="Green">E41</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> = 
<font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="card_4.html#K1">|^</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="fib_fusc.html#E9:11_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="pre_ff.html#T5">PRE_FF:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
;<br/>
<a NAME="E21:11_2"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> 2
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E6:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="fib_fusc.html#E14:11_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="fib_fusc.html#E15:11_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="fib_fusc.html#E16:11_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="fib_fusc.html#E17:11_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma8</font></i></a>, <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<a NAME="E22:11_2"/><i><font color="Green">E43</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E6:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="fib_fusc.html#E14:11_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="fib_fusc.html#E16:11_2"><i><font color="Green">E37</font></i></a>, <a class="txt" href="fib_fusc.html#E17:11_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fib_fusc.html#E7"><i><font color="Green">Lemma7</font></i></a>, <a class="txt" href="fib_fusc.html#E8"><i><font color="Green">Lemma8</font></i></a>, <a class="ref" href="scm_1.html#T22">SCM_1:22</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>25</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span>;<br/>
<a NAME="E23:11_2"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4
 
;<br/>
<b>set </b><font color="Maroon">c<sub>26</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span>;<br/>
<a NAME="E24:11_2"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5
 
;<br/>
<b>set </b><font color="Maroon">c<sub>27</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span>;<br/>
<a NAME="E25:11_2"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6
 
;<br/>
<a NAME="E26:11_2"/><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> 2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="int_1.html#D8">INT_1:def 8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_2_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_2_1"><b>suppose </b></a><a NAME="E1:11_2_2_1"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:11_2_2_1"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E15</font></i></a>, <a class="txt" href="fib_fusc.html#E18:11_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fib_fusc.html#E23:11_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E3:11_2_2_1"/><i><font color="Green">E50</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E15</font></i></a>, <a class="txt" href="fib_fusc.html#E18:11_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fib_fusc.html#E22:11_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="fib_fusc.html#E23:11_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E4:11_2_2_1"/><i><font color="Green">E51</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fib_fusc.html#E24:11_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2_2_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E5:11_2_2_1"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fib_fusc.html#E24:11_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2_2_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2_2_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E6:11_2_2_1"/><i><font color="Green">E53</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E8:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="fib_fusc.html#E24:11_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2_2_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2_2_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="fib_fusc.html#E7"><i><font color="Green">Lemma7</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E7:11_2_2_1"/><b>then </b><i><font color="Green">E54</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E17</font></i></a>, <a class="txt" href="fib_fusc.html#E25:11_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2_2_1"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><a NAME="E8:11_2_2_1"/><i><font color="Green">E55</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E17</font></i></a>, <a class="txt" href="fib_fusc.html#E25:11_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2_2_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2_2_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="fib_fusc.html#E6:11_2_2_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>thus </b><a NAME="E9:11_2_2_1"/>
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E9:11"><i><font color="Green">E17</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E20:11_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="fib_fusc.html#E25:11_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2_2_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E6:11_2_2_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>thus </b><a NAME="E10:11_2_2_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is   <a href="nat_1.html#NM1">Nat</a>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="fib_fusc.html#E19:11_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fib_fusc.html#E7:11_2_2_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">c<sub>29</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="fib_fusc.html#E19:11_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fib_fusc.html#E7:11_2_2_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a></i>;<br/><i><font color="Green">E56</font></i>: <font color="Maroon">c<sub>29</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E26:11_2"><i><font color="Green">E47</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>28</sub></font> <a href="nat_1.html#K2">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E19:11_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fib_fusc.html#E7:11_2_2_1"><i><font color="Green">E54</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="fib_fusc.html#E21:11_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="fib_fusc.html#E1:11_2_2_1"><i><font color="Green">E48</font></i></a>, <a class="ref" href="pre_ff.html#T6">PRE_FF:6</a></i>
;<br/><b>then </b><i><font color="Green">E57</font></i>: <font color="Maroon">c<sub>29</sub></font> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>28</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/><i><font color="Green">E58</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>29</sub></font>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>28</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E12:11_2_2_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>28</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
;<br/><i><font color="Green">E59</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="pre_ff.html#K5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>28</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E13:11_2_2_1"><i><font color="Green">E57</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
 <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
;<br/><b>reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">c<sub>31</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>32</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>, <font color="Maroon">c<sub>33</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> as   <a href="int_1.html#NM1">Integer</a> ;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>33</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>33</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E14:11_2_2_1"><i><font color="Green">E58</font></i></a>, <a class="txt" href="fib_fusc.html#E15:11_2_2_1"><i><font color="Green">E59</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E8:11_2_2_1"><i><font color="Green">E55</font></i></a></i>
;<br/><b>hence </b><a NAME="E19:11_2_2_1"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E1:11_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_2_2"><b>suppose </b></a><a NAME="E1:11_2_2_2"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:11_2_2_2"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 6
 <b>by </b><i><a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E15</font></i></a>, <a class="txt" href="fib_fusc.html#E18:11_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fib_fusc.html#E23:11_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E3:11_2_2_2"/><i><font color="Green">E50</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E7:11"><i><font color="Green">E15</font></i></a>, <a class="txt" href="fib_fusc.html#E18:11_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fib_fusc.html#E22:11_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="fib_fusc.html#E23:11_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/><a NAME="E4:11_2_2_2"/><i><font color="Green">E51</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E10:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="fib_fusc.html#E24:11_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2_2_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E5:11_2_2_2"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E10:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="fib_fusc.html#E24:11_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2_2_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2_2_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E6:11_2_2_2"/><i><font color="Green">E53</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 5</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E10:11"><i><font color="Green">E18</font></i></a>, <a class="txt" href="fib_fusc.html#E24:11_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2_2_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2_2_2"><i><font color="Green">E50</font></i></a>, <a class="txt" href="fib_fusc.html#E7"><i><font color="Green">Lemma7</font></i></a>, <a class="ref" href="scm_1.html#T19">SCM_1:19</a></i>;<br/><a NAME="E7:11_2_2_2"/><b>then </b><i><font color="Green">E54</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E11:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fib_fusc.html#E25:11_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2_2_2"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><a NAME="E8:11_2_2_2"/><i><font color="Green">E55</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 6</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E11:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fib_fusc.html#E25:11_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2_2_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2_2_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="fib_fusc.html#E6:11_2_2_2"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>thus </b><a NAME="E9:11_2_2_2"/>
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> is   <a href="nat_1.html#NM1">Nat</a> )
 <b>by </b><i><a class="txt" href="fib_fusc.html#E11:11"><i><font color="Green">E19</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="fib_fusc.html#E19:11_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fib_fusc.html#E20:11_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="fib_fusc.html#E25:11_2"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2_2_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="fib_fusc.html#E7:11_2_2_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a>, <a class="ref" href="scm_1.html#T23">SCM_1:23</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>28</sub></font> = <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">c<sub>29</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E5:11_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="fib_fusc.html#E19:11_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fib_fusc.html#E7:11_2_2_2"><i><font color="Green">E54</font></i></a>, <a class="ref" href="pre_ff.html#T7">PRE_FF:7</a></i>;<br/><i><font color="Green">E56</font></i>: <font color="Maroon">c<sub>29</sub></font> = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 0
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E19:11_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fib_fusc.html#E21:11_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="fib_fusc.html#E26:11_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="fib_fusc.html#E1:11_2_2_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="fib_fusc.html#E7:11_2_2_2"><i><font color="Green">E54</font></i></a></i>
<br/>.= 
2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>28</sub></font>

;<br/><i><font color="Green">E57</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>29</sub></font>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>28</sub></font>
<b>by </b><i><a class="txt" href="fib_fusc.html#E11:11_2_2_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
 <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
;<br/><i><font color="Green">E58</font></i>:  <a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> = 
 <a href="pre_ff.html#K5">Fusc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>29</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>28</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E11:11_2_2_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>28</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
;<br/><b>reconsider </b><font color="Maroon">c<sub>30</sub></font> = <font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">c<sub>31</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span>, <font color="Maroon">c<sub>32</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span>, <font color="Maroon">c<sub>33</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></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> as   <a href="int_1.html#NM1">Integer</a> ;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>33</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>33</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>33</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E12:11_2_2_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="fib_fusc.html#E13:11_2_2_2"><i><font color="Green">E58</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>32</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <font color="Maroon">c<sub>30</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>33</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>30</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>

;<br/><b>hence </b><a NAME="E16:11_2_2_2"/>
 <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E1:11_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="fib_fusc.html#E2:11_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="fib_fusc.html#E3:11_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="fib_fusc.html#E8:11_2_2_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E17:11"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="fib_fusc.html#E15:11"><i><font color="Green">E23</font></i></a>, <a class="txt" href="fib_fusc.html#E16:11"><i><font color="Green">E24</font></i></a>);<br/></i>
<b>set </b><font color="Maroon">c<sub>18</sub></font> = <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">c<sub>15</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span>;<br/>
<a NAME="E18:11"/><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</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,<font color="Maroon">c<sub>15</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span>
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E19:11"/>
<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E1:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E20:11"/><b>then </b>
 <a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="power.html#K6">log</a> 2,1
 
<b>by </b><i><a class="ref" href="pre_ff.html#T12">PRE_FF:12</a></i>;<br/>
<a NAME="E21:11"/><b>then </b><i><font color="Green">E27</font></i>: 
(  <a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</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,<font color="Maroon">c<sub>15</sub></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="txt" href="fib_fusc.html#E18:11"><i><font color="Green">E26</font></i></a>, <a class="ref" href="power.html#T59">POWER:59</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<a NAME="E22:11"/><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,<font color="Maroon">c<sub>15</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E23:11"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;=</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,<font color="Maroon">c<sub>15</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span>
 
<b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>19</sub></font> = <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">c<sub>15</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<a NAME="E25:11"/>
<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">c<sub>15</sub></font></span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E26:11"/><b>then </b>
<font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E27:11"/><b>then </b><i><font color="Green">E28</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 0 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>15</sub></font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">2 <a href="card_4.html#K1">|^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp;  <a href="pre_ff.html#K5">Fusc</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E17:11"><i><font color="Green">E25</font></i></a></i>;<br/>
<a NAME="E28:11"/>
2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E21:11"><i><font color="Green">E27</font></i></a>, <a class="ref" href="power.html#T44">POWER:44</a></i>;<br/>
<a NAME="E29:11"/><b>then </b>
2 <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E1:11"><i><font color="Green">E10</font></i></a>, <a class="ref" href="power.html#D3">POWER:def 3</a></i>;<br/>
<a NAME="E30:11"/><b>then </b>
2 <a href="card_4.html#K1">|^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="power.html#T48">POWER:48</a></i>;<br/>
<a NAME="E31:11"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E14:11"><i><font color="Green">E22</font></i></a>, <a class="txt" href="fib_fusc.html#E27:11"><i><font color="Green">E28</font></i></a>, <a class="ref" href="pre_ff.html#T4">PRE_FF:4</a></i>;<br/>
<b>then </b><i><font color="Green">E30</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p5">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p4">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="fib_fusc.html#K2" target="_self">Fusc'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p5">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a>, <a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="pre_ff.html#K5">Fusc</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="fib_fusc.html#E31:11"><i><font color="Green">E29</font></i></a>, <a class="ref" href="fib_fusc.html#D2" target="_self">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></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>
<b>by </b><i><a class="ref" href="pre_ff.html#T17">PRE_FF:17</a></i>
;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<a NAME="E33:11"/><i><font color="Green">E31</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 8
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="fib_fusc.html#E27:11"><i><font color="Green">E28</font></i></a>, <a class="txt" href="fib_fusc.html#E31:11"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<a NAME="E34:11"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></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>
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="fib_fusc.html#E27:11"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scm_1.html#T24">SCM_1:24</a></i>;<br/>
<b>thus </b><a NAME="E35:11"/>
<font color="Maroon">c<sub>16</sub></font> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E20</font></i></a>, <a class="txt" href="fib_fusc.html#E33:11"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scm_1.html#T3">SCM_1:3</a></i>;<br/>

<b>thus </b><a NAME="E36:11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <font color="Maroon">c<sub>16</sub></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">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="txt" href="fib_fusc.html#E12:11"><i><font color="Green">E20</font></i></a>, <a class="txt" href="fib_fusc.html#E27:11"><i><font color="Green">E28</font></i></a>, <a class="txt" href="fib_fusc.html#E32:11"><i><font color="Green">E30</font></i></a>, <a class="txt" href="fib_fusc.html#E33:11"><i><font color="Green">E31</font></i></a>, <a class="txt" href="fib_fusc.html#E34:11"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scm_1.html#T4">SCM_1:4</a></i>;<br/>

<a NAME="E37:11"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a>  &amp; <font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default">6 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="ami_3.html#K1">SCM</a>  )
 
<b>by </b><i><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="txt" href="fib_fusc.html#E4:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="fib_fusc.html#E27:11"><i><font color="Green">E28</font></i></a>, <a class="txt" href="fib_fusc.html#E33:11"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scm_1.html#T14">SCM_1:14</a>, <a class="ref" href="scm_1.html#T26">SCM_1:26</a></i>;<br/>
<b>hence </b><a NAME="E38:11"/>
 <a href="scm_1.html#K2">Complexity</a> <font color="Maroon">c<sub>16</sub></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#K6">log</a> 2,<font color="Maroon">c<sub>15</sub></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><a class="txt" href="fib_fusc.html#E3:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="scm_1.html#T17">SCM_1:17</a></i>;<br/>


</div>
