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

<b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>17</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>18</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>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>;<br/>
<b>set </b><font color="Maroon">c<sub>20</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font>;<br/>
<b>assume </b><a NAME="E1:19"/><i><font color="Green">E19</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>
 ;<br/>

<b>assume </b><a NAME="E2:19"/><i><font color="Green">E20</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="E3:19"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <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> 
 ;<br/>

<b>assume </b><a NAME="E4:19"/><i><font color="Green">E22</font></i>: 
<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="E5:19"/><i><font color="Green">E23</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#NR4" target="_self">&gt;</a> 0
 ;<br/>

<i><font color="Green">E24</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#E2:19"><i><font color="Green">E20</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#E1:19"><i><font color="Green">E19</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">E25</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#E6:19"><i><font color="Green">E24</font></i></a></i>
;<br/>
<i><font color="Green">E26</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#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:19"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:19"><i><font color="Green">E25</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> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:19"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E27</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>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="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 6</span>)</span>

<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> 6</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> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:19"><i><font color="Green">E19</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">E28</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> 1</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> 1</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> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3</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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:19"><i><font color="Green">E27</font></i></a></i>
;<br/>
<a NAME="E11:19"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</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>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:19"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:19"><i><font color="Green">E25</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<a NAME="E12:19"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</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#E4:19"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:19"><i><font color="Green">E25</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<i><font color="Green">E31</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</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>16</sub></font> <a href="nat_1.html#K1">+</a> 3</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>16</sub></font>,3</span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:19"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:19"><i><font color="Green">E25</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/>
<i><font color="Green">E32</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</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>16</sub></font> <a href="nat_1.html#K1">+</a> 2</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>16</sub></font>,2</span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:19"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:19"><i><font color="Green">E25</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/>
<i><font color="Green">E33</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> 2</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> 2</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:19"><i><font color="Green">E28</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">6 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:19"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E34</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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> 2</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 7</span>)</span>

<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> 7</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#K16">Divide</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2,<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:19"><i><font color="Green">E19</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">E35</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">2 <a href="nat_1.html#K1">+</a> 1</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> 2</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#K16">Divide</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,2,<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3</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> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E16:19"><i><font color="Green">E34</font></i></a></i>
;<br/>
<a NAME="E18:19"/><i><font color="Green">E36</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6 <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>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:19"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E19:19"/><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/>
<a NAME="E20:19"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:19"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:19"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E21:19"/>
 <a href="scmp_gcd.html#K2" target="_self">GBP</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:19"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E22:19"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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#E10:19"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:19"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E39</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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>16</sub></font> <a href="nat_1.html#K1">+</a> 6</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>16</sub></font>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:19"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:19"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E18:19"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:19"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/>
<a NAME="E24:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6
 
;<br/>
<a NAME="E25:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:19"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E26:19"/><b>then </b><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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>16</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></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>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:19"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:19"><i><font color="Green">E31</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E27:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6
 
;<br/>
<a NAME="E28:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,6
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:19"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E29:19"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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>16</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></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>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:19"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:19"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E42</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> 3</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> 3</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E17:19"><i><font color="Green">E35</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E15:19"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E43</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</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> 3</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 8</span>)</span>

<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> 8</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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:19"><i><font color="Green">E19</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">E44</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">3 <a href="nat_1.html#K1">+</a> 1</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> 3</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> ,7 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3</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> 3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E31:19"><i><font color="Green">E43</font></i></a></i>
;<br/>
<a NAME="E33:19"/><i><font color="Green">E45</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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>16</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:19"><i><font color="Green">E37</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E34:19"/><b>then </b><i><font color="Green">E46</font></i>: 
 <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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/>
<a NAME="E35:19"/><i><font color="Green">E47</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3 <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>16</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:19"><i><font color="Green">E37</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E36:19"/><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/>
<a NAME="E37:19"/><b>then </b><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</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>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E17:19"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:19"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E34:19"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E38:19"/><i><font color="Green">E49</font></i>: 
 <a href="scmp_gcd.html#K2" target="_self">GBP</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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#E33:19"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E39:19"/>
 <a href="scmp_gcd.html#K2" target="_self">GBP</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E35:19"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E40:19"/><b>then </b><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</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#E17:19"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E22:19"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E38:19"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E41:19"/><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</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>16</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E17:19"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E26:19"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E29:19"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E33:19"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E35:19"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E42:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 2
 
;<br/>
<a NAME="E43:19"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</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#E33:19"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E44:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 3
 
;<br/>
<a NAME="E45:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E35:19"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E46:19"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</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>16</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>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>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E17:19"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E23:19"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E43:19"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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> 4</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E32:19"><i><font color="Green">E44</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">8 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:19"><i><font color="Green">E42</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E55</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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> 4</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 9</span>)</span>

<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> 9</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> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> ,1
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:19"><i><font color="Green">E19</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">E56</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">4 <a href="nat_1.html#K1">+</a> 1</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> 4</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> ,<span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2" target="_self">GBP</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> 4</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E48:19"><i><font color="Green">E55</font></i></a></i>
;<br/>
<a NAME="E50:19"/><i><font color="Green">E57</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,7 <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>16</sub></font> <a href="nat_1.html#K1">+</a> 7</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E37:19"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E51:19"/><b>then </b><i><font color="Green">E58</font></i>: 
 <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/>
<a NAME="E52:19"/><b>then </b><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E32:19"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E37:19"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E53:19"/>
 <a href="scmp_gcd.html#K2" target="_self">GBP</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E50:19"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E54:19"/><b>then </b><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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#E32:19"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E40:19"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E61</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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>16</sub></font> <a href="nat_1.html#K1">+</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>16</sub></font>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E32:19"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E37:19"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmp_gcd.html#E50:19"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E41:19"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/>
<a NAME="E56:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7
 
;<br/>
<a NAME="E57:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,7
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E50:19"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E58:19"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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>16</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>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>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E32:19"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E46:19"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E63</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> 5</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> 5</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E49:19"><i><font color="Green">E56</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">9 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:19"><i><font color="Green">E54</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E64</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</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> 5</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 10</span>)</span>

<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> 10</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#K12">AddTo</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> ,1,4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:19"><i><font color="Green">E19</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">E65</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">5 <a href="nat_1.html#K1">+</a> 1</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> 5</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#K12">AddTo</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> ,1,4</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> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E60:19"><i><font color="Green">E64</font></i></a></i>
;<br/>
<a NAME="E62:19"/><i><font color="Green">E66</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span> <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>16</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">4 <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E52:19"><i><font color="Green">E59</font></i></a>, <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/>
<a NAME="E63:19"/><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green">Lemma17</font></i></a></i>;<br/>
<a NAME="E64:19"/><b>then </b><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</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>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E49:19"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E52:19"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E65:19"/>
 <a href="scmp_gcd.html#K2" target="_self">GBP</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E62:19"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E66:19"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</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#E49:19"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E54:19"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E67:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4
 
;<br/>
<a NAME="E68:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E62:19"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E69:19"/><b>then </b><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</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>16</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>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E49:19"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E55:19"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E70:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4
 
;<br/>
<a NAME="E71:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default">4 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K22">RetSP</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E62:19"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E72:19"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</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>16</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>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>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E49:19"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E58:19"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</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>16</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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> 0,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E49:19"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E54:19"><i><font color="Green">E60</font></i></a>, <a class="txt" href="scmp_gcd.html#E62:19"><i><font color="Green">E66</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</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">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<font color="Maroon">c<sub>16</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E32:19"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E37:19"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmp_gcd.html#E51:19"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/>
<i><font color="Green">E72</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> 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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:19"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">10 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E59:19"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E73</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 11</span>)</span>

<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> 11</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#K7">saveIC</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,<a href="scmpds_1.html#K23">RetIC</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:19"><i><font color="Green">E19</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">E74</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">6 <a href="nat_1.html#K1">+</a> 1</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> 6</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#K7">saveIC</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> ,<a href="scmpds_1.html#K23">RetIC</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E75:19"><i><font color="Green">E73</font></i></a></i>
;<br/>
<a NAME="E77:19"/><i><font color="Green">E75</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E66:19"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E78:19"/><b>then </b><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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>16</sub></font> <a href="nat_1.html#K1">+</a> 4
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:19"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E64:19"><i><font color="Green">E67</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/>
<a NAME="E79:19"/><i><font color="Green">E77</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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#E61:19"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E66:19"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmp_gcd.html#E77:19"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmp_gcd.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/>
<a NAME="E80:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E81:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E77:19"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E82:19"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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>16</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>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:19"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E69:19"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/>
<a NAME="E83:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E84:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E77:19"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E85:19"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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>16</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>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>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:19"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:19"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/>
<a NAME="E86:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E87:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E77:19"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E88:19"/><b>then </b><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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>16</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>16</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:19"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:19"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</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> 7</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</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> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E74:19"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</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> 7</span>)</span>

;<br/>

<b>then </b><i><font color="Green">E81</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</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> 7</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 12</span>)</span>

<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> 12</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#K4">goto</a> <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#E1:19"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<b>thus </b><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> 8 = 
<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">7 <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</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#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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E90:19"><i><font color="Green">E81</font></i></a></i>
;<br/>

<i><font color="Green">E82</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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>  = 
 <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>16</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E78:19"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</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>

;<br/>
<a NAME="E93:19"/><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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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> 
 
<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="E94:19"/>
<span 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> 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>16</sub></font> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmp_gcd.html#E78:19"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>

<a NAME="E95:19"/>
 <a href="scmp_gcd.html#K2" target="_self">GBP</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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E92:19"><i><font color="Green">E82</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<b>hence </b><a NAME="E96:19"/>
<span 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> 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
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmp_gcd.html#E79:19"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>

<a NAME="E97:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 5
 
;<br/>
<a NAME="E98:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E92:19"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E99:19"/>
<span 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> 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>16</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>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<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></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmp_gcd.html#E82:19"><i><font color="Green">E78</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>

<a NAME="E100:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 5
 
;<br/>
<a NAME="E101:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E92:19"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E102:19"/>
<span 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> 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>16</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>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>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmp_gcd.html#E85:19"><i><font color="Green">E79</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>

<a NAME="E103:19"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 5
 
;<br/>
<a NAME="E104:19"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <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>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</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> 
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E92:19"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E105:19"/>
<span 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> 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>16</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>16</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmp_gcd.html#E88:19"><i><font color="Green">E80</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>

<b>thus </b><a NAME="E106:19"/>
<span 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> 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>16</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#E74:19"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmp_gcd.html#E76:19"><i><font color="Green">E74</font></i></a>, <a class="txt" href="scmp_gcd.html#E92:19"><i><font color="Green">E82</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>


</div>
