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<div class="add">

<b>let </b><font color="Maroon" title="c13">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c14">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c14">s</font> <a href="ami_3.html#R1" title="AMI_3:pred.1">starts_at</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 0
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green" title="E13">A2</font></i>: 
 <a href="ami_4.html#K1" title="AMI_4:func.1">Euclide-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">s</font>
 <b>and </b><br/><a NAME="E3:13"/><i><font color="Green" title="E14">A3</font></i>: 
( <font color="Maroon" title="c14">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Maroon" title="c14">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 <b>and </b><br/><a NAME="E4:13"/><i><font color="Green" title="E15">A4</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/>

<b>set </b><font color="Maroon" title="c15">c4</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c16">c5</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c17">c6</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c18">c7</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span>;<br/>
<a NAME="E5:13"/><i><font color="Green" title="E16">A5</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E6:13"/><i><font color="Green" title="E17">A6</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E7:13"/><i><font color="Green" title="E18">A7</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E8:13"/>
( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 0 ) or ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp;  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 4 ) )
 
<b>by </b><i><a class="txt" href="ami_4.html#E1:13"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="ami_4.html#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_4.html#E3:13"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="ami_4.html#E12"><i><font color="Green" title="E10">Lm2</font></i></a></i>;<br/>
<a NAME="E9:13"/><b>then </b><i><font color="Green" title="E19">A8</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 1 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_4.html#E4:13"><i><font color="Green" title="E15">A4</font></i></a>, <a class="ref" href="ami_4.html#T5" target="_self" title="AMI_4:th.5">Th5</a></i>;<br/>
<a NAME="E10:13"/><b>then </b><i><font color="Green" title="E20">A9</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</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" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 2</span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_4.html#E5:13"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="ami_4.html#T6" target="_self" title="AMI_4:th.6">Th6</a></i>;<br/>
<a NAME="E11:13"/><b>then </b><i><font color="Green" title="E21">A10</font></i>: 
(  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_3.html#K16" title="AMI_3:func.16">il.</a> 3 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 2</span>)</span> )
 
<b>by </b><i><a class="txt" href="ami_4.html#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_4.html#E6:13"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="ami_4.html#T7" target="_self" title="AMI_4:th.7">Th7</a></i>;<br/>
<b>hence </b><a NAME="E12:13"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_4.html#E7:13"><i><font color="Green" title="E18">A7</font></i></a>, <a class="txt" href="ami_4.html#E9:13"><i><font color="Green" title="E19">A8</font></i></a>, <a class="txt" href="ami_4.html#E10:13"><i><font color="Green" title="E20">A9</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>;<br/>

<b>thus </b><a NAME="E13:13"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 0</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</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" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c14">s</font></span>)</span> <a href="ami_1.html#K11" title="AMI_1:func.11">.</a> <span class="p3">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Maroon" title="c13">k</font></span>)</span></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p2">(<span class="default"><a href="ami_3.html#K15" title="AMI_3:func.15">dl.</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="ami_4.html#E7:13"><i><font color="Green" title="E18">A7</font></i></a>, <a class="txt" href="ami_4.html#E9:13"><i><font color="Green" title="E19">A8</font></i></a>, <a class="txt" href="ami_4.html#E10:13"><i><font color="Green" title="E20">A9</font></i></a>, <a class="txt" href="ami_4.html#E11:13"><i><font color="Green" title="E21">A10</font></i></a>, <a class="ref" href="ami_4.html#T8" target="_self" title="AMI_4:th.8">Th8</a></i>;<br/>


</div>
