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

<b>set </b><font color="Maroon">c<sub>16</sub></font> =  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> ;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  st  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>2</sub></font> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> holds <br/>ex <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>(  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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="Olive">b<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp;  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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="Olive">b<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>4</sub></font></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="Olive">b<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>4</sub></font></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="Olive">b<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>4</sub></font></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>5</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  st <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>5</sub></font> holds <br/>(  <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="Olive">b<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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="Olive">b<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>4</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="Olive">b<sub>1</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>5</sub></font> <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="Olive">b<sub>2</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>5</sub></font> ) ) );<br/>
<a NAME="E1:26"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font>;<br/>
<b>assume </b><a NAME="E1:26_1"/><i><font color="Green">E26</font></i>: 
(  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>18</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:26_1"/><i><font color="Green">E27</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5
 ;<br/>

<b>assume </b><a NAME="E3:26_1"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E4:26_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/>

<b>assume </b><a NAME="E5:26_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/>

<b>assume </b><a NAME="E6:26_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>
 ;<br/>

<b>assume </b><a NAME="E7:26_1"/><i><font color="Green">E29</font></i>: 
(  <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_1.html#K6">IC</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E8:26_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> )
 ;<br/>

<i><font color="Green">E31</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>17</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:26_1"><i><font color="Green">E27</font></i></a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E32</font></i>: <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">1 <a href="nat_1.html#K1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9">Following</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> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</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/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:26_1"><i><font color="Green">E31</font></i></a></i>
;<br/>
<i><font color="Green">E33</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>18</sub></font> = 
<font color="Maroon">c<sub>18</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:26_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_1"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9">Following</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_1"><i><font color="Green">E33</font></i></a></i>
;<br/>
<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> 1</span>)</span> = 
<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> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>17</sub></font>,9
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:26_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:26_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:26_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="scmpds_6.html#T23">SCMPDS_6:23</a></i>
;<br/>
<i><font color="Green">E36</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</a> <font color="Maroon">c<sub>18</sub></font>,9
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:26_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:26_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:26_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_6.html#T23">SCMPDS_6:23</a></i>
;<br/>
<b>take </b><font color="Maroon">c<sub>24</sub></font> = 1;<br/>

<b>thus </b> <a href="ami_1.html#K8">CurInstr</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> <font color="Maroon">c<sub>24</sub></font></span>)</span> = 
<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> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:26_1"><i><font color="Green">E35</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>

<b>thus </b><a NAME="E16:26_1"/>
<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> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E10:26_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>

<b>thus </b> <a href="ami_1.html#K8">CurInstr</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:26_1"><i><font color="Green">E36</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>18</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>

<b>thus </b><a NAME="E18:26_1"/>
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E12:26_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>

<b>thus </b><a NAME="E19:26_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 holds <br/>( <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></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> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E10:26_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:26_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>25</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>26</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:26_1_9"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>25</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>24</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font> )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_9_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1_9_1"/>
( <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1_9"><i><font color="Green">E37</font></i></a>, <a class="ref" href="cqc_the1.html#T2">CQC_THE1:2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_9_1_1"><b>suppose </b></a><a NAME="E1:26_1_9_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b> <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> <font color="Maroon">c<sub>25</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:26_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1_9_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/><br/><b>thus </b><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> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1_9_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_1_9"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_1_9_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_9_1_2"><b>suppose </b></a><a NAME="E1:26_1_9_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_1_9_1_2"/>
 <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> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E13:26_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:26_1"><i><font color="Green">E36</font></i></a></i>;<br/><b>thus </b><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> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:26_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_1_9_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>25</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E12:26_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_1_9"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_1_9_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


</div><b>end;</b></div>
<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>17</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:26_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>17</sub></font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>set </b><font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font>;<br/><b>assume </b><a NAME="E1:26_2_1"/><i><font color="Green">E28</font></i>: 
(  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>19</sub></font> )
 ;<br/><b>assume </b><a NAME="E2:26_2_1"/><i><font color="Green">E29</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5
 ;<br/><b>assume </b><a NAME="E3:26_2_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><b>assume </b><a NAME="E4:26_2_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><b>assume </b><a NAME="E5:26_2_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><b>assume </b><a NAME="E6:26_2_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>
 ;<br/><b>assume </b><a NAME="E7:26_2_1"/><i><font color="Green">E34</font></i>: 
(  <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_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><b>assume </b><a NAME="E8:26_2_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>24</sub></font> = <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="scmp_gcd.html#E5:26_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_2_1_1"/>
( <font color="Maroon">c<sub>24</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font> or <font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E4:26_2_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_1"><b>suppose </b></a><a NAME="E1:26_2_1_1_1"/>
<font color="Maroon">c<sub>24</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>(  <a href="ami_1.html#K8">CurInstr</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp;  <a href="ami_1.html#K8">CurInstr</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 holds <br/>( <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> holds <br/>(  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:26_2_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1"><i><font color="Green">E35</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2"><b>suppose </b></a><a NAME="E1:26_2_1_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><a NAME="E2:26_2_1_1_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T21">NAT_1:21</a></i>;<br/><a NAME="E3:26_2_1_1_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>24</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>25</sub></font> = <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E5:26_2_1_1_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 ;<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8;<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8;<br/><a NAME="E6:26_2_1_1_2"/><i><font color="Green">E40</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 7</span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8 <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 7</span>)</span></span>)</span>,<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4 &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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 7</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp;  <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 7</span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8 <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 7</span>)</span></span>)</span>,<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4 &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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 7</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> &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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 11 &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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> &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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 11 )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E28"><i><font color="Green">Lemma22</font></i></a></i>;<br/><i><font color="Green">E41</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span>,2 = 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>

;<br/><i><font color="Green">E42</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span>,3 = 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>

;<br/><a NAME="E9:26_2_1_1_2"/><i><font color="Green">E43</font></i>: 
(  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8 &amp;  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8 )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/><i><font color="Green">E44</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 7</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> 5
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmp_gcd.html#T6" target="_self">Th6</a></i>
;<br/><a NAME="E11:26_2_1_1_2"/><i><font color="Green">E45</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>;<br/><a NAME="E12:26_2_1_1_2"/><i><font color="Green">E46</font></i>: 
4 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E13:26_2_1_1_2"/><b>then </b><i><font color="Green">E47</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E14:26_2_1_1_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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>;<br/><b>set </b><font color="Maroon">c<sub>28</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span>;<br/><b>set </b><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>;<br/><i><font color="Green">E49</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> = 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<font color="Maroon">c<sub>24</sub></font>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <font color="Maroon">c<sub>24</sub></font>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><a NAME="E17:26_2_1_1_2"/><b>then </b><i><font color="Green">E51</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>24</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="ref" href="newton.html#T79">NEWTON:79</a></i>;<br/><a NAME="E18:26_2_1_1_2"/><b>then </b><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E19:26_2_1_1_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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E16:26_2_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="newton.html#T78">NEWTON:78</a></i>;<br/><i><font color="Green">E54</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K19">ICplusConst</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 7</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
 <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:26_2_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="scmp_gcd.html#T6" target="_self">Th6</a></i>
;<br/><a NAME="E21:26_2_1_1_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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>;<br/><a NAME="E22:26_2_1_1_2"/><i><font color="Green">E56</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>;<br/><b>set </b><font color="Maroon">c<sub>30</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span>;<br/><i><font color="Green">E57</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> = 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E15:26_2_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E16:26_2_1_1_2"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><b>then consider </b><font color="Maroon">c<sub>31</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E26:26_2_1_1_2"/><i><font color="Green">E58</font></i>: 
(  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp;  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 holds <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></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> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></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> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> &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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> holds <br/>(  <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> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</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> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <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> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:26_2_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:26_2_1_1_2"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:26_2_1_1_2"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:26_2_1_1_2"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:26_2_1_1_2"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmp_gcd.html#E17:26_2_1_1_2"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmp_gcd.html#E18:26_2_1_1_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmp_gcd.html#E19:26_2_1_1_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:26_2_1_1_2"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:26_2_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E22:26_2_1_1_2"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E23:26_2_1_1_2"><i><font color="Green">E57</font></i></a></i>;<br/><b>set </b><font color="Maroon">c<sub>32</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span>;<br/><b>set </b><font color="Maroon">c<sub>33</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span>;<br/><a NAME="E27:26_2_1_1_2"/><i><font color="Green">E59</font></i>: 
 <a href="ami_1.html#K8">CurInstr</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><a NAME="E28:26_2_1_1_2"/><i><font color="Green">E60</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><i><font color="Green">E61</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">8 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9">Following</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E27:26_2_1_1_2"><i><font color="Green">E59</font></i></a></i>
;<br/><a NAME="E30:26_2_1_1_2"/><i><font color="Green">E62</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E12:26_2_1_1_2"><i><font color="Green">E46</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E31:26_2_1_1_2"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4 <a href="xxreal_0.html#NR3" target="_self">&lt;</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><b>then </b><i><font color="Green">E64</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:26_2_1_1_2"><i><font color="Green">E62</font></i></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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><a NAME="E33:26_2_1_1_2"/>
5 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E34:26_2_1_1_2"/><b>then </b><i><font color="Green">E65</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><i><font color="Green">E66</font></i>:  <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span>,1
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><i><font color="Green">E67</font></i>:  <a href="scmpds_3.html#K2">inspos</a> 11 = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E34:26_2_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E28:26_2_1_1_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scmp_gcd.html#E35:26_2_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
;<br/><a NAME="E37:26_2_1_1_2"/><i><font color="Green">E68</font></i>: 
 <a href="ami_1.html#K8">CurInstr</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><a NAME="E38:26_2_1_1_2"/><i><font color="Green">E69</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:26_2_1_1_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>;<br/><i><font color="Green">E70</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">8 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9">Following</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E37:26_2_1_1_2"><i><font color="Green">E68</font></i></a></i>
;<br/><i><font color="Green">E71</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:26_2_1_1_2"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmp_gcd.html#E31:26_2_1_1_2"><i><font color="Green">E63</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><i><font color="Green">E72</font></i>:  <a href="scmpds_3.html#K2">inspos</a> 11 = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E34:26_2_1_1_2"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E35:26_2_1_1_2"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmp_gcd.html#E38:26_2_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
;<br/><i><font color="Green">E73</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:26_2_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">11 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E36:26_2_1_1_2"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self">Th3</a></i>
;<br/><b>then </b><i><font color="Green">E74</font></i>:  <a href="ami_1.html#K8">CurInstr</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 13</span>)</span>

<br/>.= 
<font color="Maroon">c<sub>18</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 13</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,6
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/><i><font color="Green">E75</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">9 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9">Following</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,6</span>)</span>,<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E43:26_2_1_1_2"><i><font color="Green">E74</font></i></a></i>
;<br/><i><font color="Green">E76</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span>,<a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E28:26_2_1_1_2"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scmp_gcd.html#E29:26_2_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_1.html#D22">SCMPDS_1:def 22</a></i>
<br/>.= 
<font color="Maroon">c<sub>25</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E32:26_2_1_1_2"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/><i><font color="Green">E77</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E39:26_2_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">11 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E41:26_2_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self">Th3</a></i>
;<br/><b>then </b><i><font color="Green">E78</font></i>:  <a href="ami_1.html#K8">CurInstr</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 13</span>)</span>

<br/>.= 
<font color="Maroon">c<sub>19</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 13</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,6
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/><i><font color="Green">E79</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">9 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9">Following</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,6</span>)</span>,<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:26_2_1_1_2"><i><font color="Green">E78</font></i></a></i>
;<br/><i><font color="Green">E80</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span>,<a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E38:26_2_1_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scmp_gcd.html#E39:26_2_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_1.html#D22">SCMPDS_1:def 22</a></i>
<br/>.= 
<font color="Maroon">c<sub>25</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E40:26_2_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/><i><font color="Green">E81</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10</span>)</span></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:26_2_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">13 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E42:26_2_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/><i><font color="Green">E82</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10</span>)</span></span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E48:26_2_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">13 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E46:26_2_1_1_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/><div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon">c<sub>34</sub></font> = <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10;<br/><b>thus </b> <a href="ami_1.html#K8">CurInstr</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E50:26_2_1_1_2"><i><font color="Green">E81</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>18</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/><a NAME="E2:26_2_1_1_2_26"/><i><font color="Green">E83</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E3:26_2_1_1_2_26"/><b>then </b>
 <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/><b>hence </b><a NAME="E4:26_2_1_1_2_26"/>
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E44:26_2_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/><b>thus </b> <a href="ami_1.html#K8">CurInstr</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 10</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E51:26_2_1_1_2"><i><font color="Green">E82</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>19</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/><a NAME="E6:26_2_1_1_2_26"/><i><font color="Green">E84</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E49:26_2_1_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E7:26_2_1_1_2_26"/><b>then </b>
 <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/><b>hence </b><a NAME="E8:26_2_1_1_2_26"/>
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E48:26_2_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmp_gcd.html#E49:26_2_1_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>35</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:26_2_1_1_2_26_3"/><i><font color="Green">E85</font></i>: 
( 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>35</sub></font> &amp; <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 )
 ;<br/><a NAME="E2:26_2_1_1_2_26_3"/>
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="xxreal_0.html#R1">&lt;=</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E3:26_2_1_1_2_26_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </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="E4:26_2_1_1_2_26_3"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E5:26_2_1_1_2_26_3"/><i><font color="Green">E87</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/><b>then </b><i><font color="Green">E88</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:26_2_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:26_2_1_1_2_26_3"><i><font color="Green">E86</font></i></a></i>
;<br/><a NAME="E7:26_2_1_1_2_26_3"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E8:26_2_1_1_2_26_3"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:26_2_1_1_2_26"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E9:26_2_1_1_2_26_3"/>
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E24"><i><font color="Green">Lemma19</font></i></a></i>;<br/><b>hence </b><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:26_2_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2_26_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1_1_2_26_3"><i><font color="Green">E90</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/><br/><i><font color="Green">E91</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E39:26_2_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1_1_2_26_3"><i><font color="Green">E87</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:26_2_1_1_2_26_3"><i><font color="Green">E86</font></i></a></i>
;<br/><a NAME="E12:26_2_1_1_2_26_3"/><i><font color="Green">E92</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2_26"><i><font color="Green">E84</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2_26_3"><i><font color="Green">E89</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E13:26_2_1_1_2_26_3"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/><a NAME="E14:26_2_1_1_2_26_3"/>
<font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>25</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a></i>;<br/><a NAME="E15:26_2_1_1_2_26_3"/><b>then </b>
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_3"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:26_2_1_1_2_26_3"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E24"><i><font color="Green">Lemma19</font></i></a></i>;<br/><b>hence </b><font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> = 
<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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E48:26_2_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2_26_3"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:26_2_1_1_2_26_3"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/><br/></div>
<b>end;</b></div><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>35</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>36</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:26_2_1_1_2_26_4"/><i><font color="Green">E85</font></i>: 
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>34</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> )
 ;<br/><a NAME="E2:26_2_1_1_2_26_4"/>
<font color="Maroon">c<sub>34</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E3:26_2_1_1_2_26_4"/><b>then </b><i><font color="Green">E86</font></i>: 
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9 or <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>34</sub></font> )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4"><i><font color="Green">E85</font></i></a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E4:26_2_1_1_2_26_4"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">8 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div><i><font color="Green">E88</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_1_1_2_26_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_2_1_1_2_26_4_1"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_2_1_1_2_26_4_1_1"/>
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 7 <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_1_1_1"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_1_1_1"/>
<font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 7 <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_2_26_4_1_1_1"/>
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 7 or ( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8 ) )
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_1_1_2"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_1_1_2"/>
<font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_2_26_4_1_1_2"/>
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 7 or ( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8 ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_1"><i><font color="Green">E89</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><i><font color="Green">E89</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E29"><i><font color="Green">Lemma23</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T66">SCMPDS_2:66</a></i>
;<br/><div><i><font color="Green">E90</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_1_1_2_26_4_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>37</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:26_2_1_1_2_26_4_3"/><i><font color="Green">E91</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_2_1_1_2_26_4_3_1"/>
( <font color="Maroon">c<sub>37</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a>  or <font color="Maroon">c<sub>37</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_3_1_1"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_3_1_1"/>
<font color="Maroon">c<sub>37</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_2_26_4_3_1_1"/>
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="txt" href="scmp_gcd.html#E49:26_2_1_1_2"><i><font color="Green">E80</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_3_1_2"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_3_1_2"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>37</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 ;<br/><div class="add"><b>hence </b><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:26_2_1_1_2"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_3"><i><font color="Green">E91</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>37</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E39:26_2_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_3_1_2"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><i><font color="Green">E91</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6</span>)</span> = 
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:26_2_1_1_2"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E23:26_2_1_1_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_1_1_2_26_4_5"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_2_1_1_2_26_4_5_1"/>
( <font color="Maroon">c<sub>36</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2 or <font color="Maroon">c<sub>36</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_5_1_1"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_5_1_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>36</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2
 ;<br/><div class="add"><b>hence </b><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:26_2_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="txt" href="scmp_gcd.html#E49:26_2_1_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2_26_4"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2_26_4"><i><font color="Green">E90</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E48:26_2_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_5_1_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_5_1_2"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_5_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>36</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2
 ;<br/><div class="add"><b>hence </b><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:26_2_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="txt" href="scmp_gcd.html#E49:26_2_1_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E45:26_2_1_1_2"><i><font color="Green">E76</font></i></a>, <a class="txt" href="scmp_gcd.html#E49:26_2_1_1_2"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2_26_4"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1_1_2_26_4"><i><font color="Green">E91</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>34</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E48:26_2_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_5_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_6"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_2_1_1_2_26_4_6"/>
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 7 or ( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8 ) or <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9 or <font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>34</sub></font> )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2_26_4"><i><font color="Green">E86</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:26_2_1_1_2_26_4"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1_1_2_26_4"><i><font color="Green">E88</font></i></a>, <a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_6_1"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_6_1"/>
<font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 7
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_2_26_4_6_1"/>
(  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:26_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:26_2_1_1_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E29"><i><font color="Green">Lemma23</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_6_2"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_6_2"/><i><font color="Green">E93</font></i>: 
( <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 8 &amp; <font color="Maroon">c<sub>35</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 8 )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>37</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:26_2_1_1_2_26_4_6_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> 8 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>37</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E4:26_2_1_1_2_26_4_6_2"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>37</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_6_2"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2_26_4_6_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> = 
 <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> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>37</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2_26_4_6_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
 <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> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>37</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2_26_4"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:26_2_1_1_2_26_4_6_2"><i><font color="Green">E95</font></i></a></i>
<br/>.= 
 <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2_26_4_6_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><b>thus </b><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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>37</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2_26_4_6_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 8</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>37</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:26_2_1_1_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2_26_4"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:26_2_1_1_2_26_4_6_2"><i><font color="Green">E95</font></i></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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26_2_1_1_2_26_4_6_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_6_3"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_6_3"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 9
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_2_26_4_6_3"/>
 <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E42:26_2_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scmp_gcd.html#E46:26_2_1_1_2"><i><font color="Green">E77</font></i></a></i>;<br/><b>thus </b><a NAME="E3:26_2_1_1_2_26_4_6_3"/>
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:26_2_1_1_2_26_4"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:26_2_1_1_2_26_4"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_6_3"><i><font color="Green">E93</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_2_1_1_2_26_4_6_4"><b>suppose </b></a><a NAME="E1:26_2_1_1_2_26_4_6_4"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>35</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>34</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_2_1_1_2_26_4_6_4"/>
 <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E50:26_2_1_1_2"><i><font color="Green">E81</font></i></a>, <a class="txt" href="scmp_gcd.html#E51:26_2_1_1_2"><i><font color="Green">E82</font></i></a></i>;<br/><b>thus </b><a NAME="E3:26_2_1_1_2_26_4_6_4"/>
<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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font> <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>19</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>35</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>36</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:26_2_1_1_2_26_4"><i><font color="Green">E92</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:26_2_1_1_2_26_4_6_4"><i><font color="Green">E93</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:26_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>17</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E3:26"/><i><font color="Green">E27</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="scmp_gcd.html#E1:26"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:26"><i><font color="Green">E26</font></i></a>);<br/></i>
<b>let </b><font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E4:26"/><i><font color="Green">E28</font></i>: 
(  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> &amp;  <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_1.html#K6">IC</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</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/>
<a NAME="E6:26"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>19</sub></font>]
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:26"><i><font color="Green">E27</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>(  <a href="ami_1.html#K8">CurInstr</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> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp;  <a href="ami_1.html#K8">CurInstr</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 holds <br/>( <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></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> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>2</sub></font></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> holds <br/>(  <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> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</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> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> <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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E4:26"><i><font color="Green">E28</font></i></a></i>;<br/>


</div>
