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

<b>let </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>18</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>19</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font>;<br/>
<b>assume </b><a NAME="E1:20"/><i><font color="Green">E20</font></i>: 
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>18</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:20"/><i><font color="Green">E21</font></i>: 
 <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5
 ;<br/>

<b>assume </b><a NAME="E3:20"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 ;<br/>

<b>assume </b><a NAME="E4:20"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>assume </b><a NAME="E5:20"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E6:20"/><i><font color="Green">E25</font></i>: 
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/>

<b>assume </b><a NAME="E7:20"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<i><font color="Green">E27</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>18</sub></font> = 
<font color="Maroon">c<sub>18</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:20"><i><font color="Green">E21</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#E1:20"><i><font color="Green">E20</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:20"><i><font color="Green">E27</font></i></a></i>
;<br/>
<i><font color="Green">E29</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:20"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:20"><i><font color="Green">E28</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#E2:20"><i><font color="Green">E21</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E30</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="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>18</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#E1:20"><i><font color="Green">E20</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">E31</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 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>18</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>18</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#E11:20"><i><font color="Green">E30</font></i></a></i>
;<br/>
<a NAME="E13:20"/><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>18</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#E3:20"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:20"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<a NAME="E14:20"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</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#E4:20"><i><font color="Green">E23</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:20"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<a NAME="E15:20"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<i><font color="Green">E35</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</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>18</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>18</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#E12:20"><i><font color="Green">E31</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#E10:20"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E36</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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>18</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#E1:20"><i><font color="Green">E20</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">E37</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">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>18</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>18</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#E17:20"><i><font color="Green">E36</font></i></a></i>
;<br/>
<a NAME="E19:20"/><i><font color="Green">E38</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E13:20"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E20:20"/><b>then </b>
 <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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="E21:20"/><b>then </b><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>18</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#E12:20"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:20"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E22:20"/>
 <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>18</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#E19:20"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E23:20"/><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>18</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#E12:20"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:20"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E24:20"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 6
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E25:20"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E19:20"><i><font color="Green">E38</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E26:20"/><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>18</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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E12:20"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:20"><i><font color="Green">E34</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>18</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>18</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>18</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#E18:20"><i><font color="Green">E37</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#E16:20"><i><font color="Green">E35</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>18</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>18</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>18</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#E1:20"><i><font color="Green">E20</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>18</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>18</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>18</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#E28:20"><i><font color="Green">E43</font></i></a></i>
;<br/>
<a NAME="E30:20"/><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>18</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#E21:20"><i><font color="Green">E39</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E31:20"/><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>18</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="E32:20"/><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>18</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#E21:20"><i><font color="Green">E39</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E33:20"/><b>then </b>
 <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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="E34:20"/><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>18</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#E18:20"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:20"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E31:20"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E35:20"/><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>18</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#E30:20"><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="E36:20"/>
 <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>18</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#E32:20"><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="E37:20"/><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>18</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#E18:20"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E23:20"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E35:20"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E38:20"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E39:20"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:20"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E40:20"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 3
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E41:20"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E32:20"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E42:20"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:20"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E26:20"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E39:20"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<i><font color="Green">E53</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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>18</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#E29:20"><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#E27:20"><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">E54</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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>18</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#E1:20"><i><font color="Green">E20</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">E55</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">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>18</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>18</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#E44:20"><i><font color="Green">E54</font></i></a></i>
;<br/>
<a NAME="E46:20"/><i><font color="Green">E56</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E34:20"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E47:20"/><b>then </b>
 <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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="E48:20"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</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#E29:20"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E34:20"><i><font color="Green">E48</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E49:20"/>
 <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>18</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#E46:20"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E50:20"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E29:20"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E37:20"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E51:20"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 7
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E52:20"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E46:20"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E53:20"/><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>18</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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:20"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E42:20"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E60</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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>18</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#E45:20"><i><font color="Green">E55</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#E43:20"><i><font color="Green">E53</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E61</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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>18</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#E1:20"><i><font color="Green">E20</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">E62</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">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>18</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>18</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#E55:20"><i><font color="Green">E61</font></i></a></i>
;<br/>
<a NAME="E57:20"/><i><font color="Green">E63</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E48:20"><i><font color="Green">E57</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="E58:20"/><b>then </b>
 <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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="E59:20"/><b>then </b><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E45:20"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E48:20"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E60:20"/>
 <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>18</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#E57:20"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E61:20"/><b>then </b><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E45:20"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E50:20"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E62:20"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 4
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E63:20"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E57:20"><i><font color="Green">E63</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E64:20"/><b>then </b><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E45:20"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E53:20"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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#E56:20"><i><font color="Green">E62</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#E54:20"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E67</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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>18</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#E1:20"><i><font color="Green">E20</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">E68</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">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>18</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>18</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#E66:20"><i><font color="Green">E67</font></i></a></i>
;<br/>
<a NAME="E68:20"/><i><font color="Green">E69</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E61:20"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E69:20"/><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>18</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#E56:20"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmp_gcd.html#E59:20"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/>
<a NAME="E70:20"/>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E6:20"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:20"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E71:20"/><b>then </b><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>18</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> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E56:20"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmp_gcd.html#E64:20"><i><font color="Green">E66</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/>
<i><font color="Green">E72</font></i>:  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E69:20"><i><font color="Green">E70</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="E73:20"/>
<font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 5
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E74:20"/><b>then </b>
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E7:20"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:20"><i><font color="Green">E72</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><a NAME="E75:20"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E67:20"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:20"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/>


</div>
