<?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>, <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="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> ;<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>set </b><font color="Maroon">c<sub>21</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font>;<br/>
<b>assume </b><a NAME="E1:25"/><i><font color="Green">E24</font></i>: 
(  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>17</sub></font> &amp;  <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>18</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:25"/><i><font color="Green">E25</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="E3:25"/><i><font color="Green">E26</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="E4:25"/><i><font color="Green">E27</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="E5:25"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E6:25"/><i><font color="Green">E29</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E7:25"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,2</span>)</span> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span> )
 ;<br/>

<i><font color="Green">E31</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>17</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green">E25</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#E1:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E32</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E8:25"><i><font color="Green">E31</font></i></a></i>
;<br/>
<i><font color="Green">E33</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <font color="Maroon">c<sub>18</sub></font> = 
<font color="Maroon">c<sub>18</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 5</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" target="_self">SBP</a> ,3 <a href="scmpds_2.html#K9">&lt;=0_goto</a> 9</span>)</span>,<font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:25"><i><font color="Green">E33</font></i></a></i>
;<br/>
<i><font color="Green">E35</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
 <a href="scmpds_2.html#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#E5:25"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:25"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green">E25</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>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#E1:25"><i><font color="Green">E24</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>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#E13:25"><i><font color="Green">E36</font></i></a></i>
;<br/>
<a NAME="E15:25"/><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> 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#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:25"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<a NAME="E16:25"/><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> 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#E4:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:25"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>;<br/>
<i><font color="Green">E40</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 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#E5:25"><i><font color="Green">E28</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:25"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:25"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><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">E41</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#E1:25"><i><font color="Green">E24</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">E42</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#E18:25"><i><font color="Green">E41</font></i></a></i>
;<br/>
<i><font color="Green">E43</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#E14:25"><i><font color="Green">E37</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#E12:25"><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">E44</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#E1:25"><i><font color="Green">E24</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">E45</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#E21:25"><i><font color="Green">E44</font></i></a></i>
;<br/>
<a NAME="E23:25"/><i><font color="Green">E46</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#E15:25"><i><font color="Green">E38</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E24:25"/><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="E25:25"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E14:25"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:25"><i><font color="Green">E38</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E26:25"/>
 <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#E23:25"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E27:25"/><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> 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#E14:25"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E16:25"><i><font color="Green">E39</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E49</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E19:25"><i><font color="Green">E42</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#E17:25"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E50</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#E1:25"><i><font color="Green">E24</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">E51</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#E29:25"><i><font color="Green">E50</font></i></a></i>
;<br/>
<i><font color="Green">E52</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#E22:25"><i><font color="Green">E45</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#E20:25"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E53</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#E1:25"><i><font color="Green">E24</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">E54</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#E32:25"><i><font color="Green">E53</font></i></a></i>
;<br/>
<a NAME="E34:25"/><i><font color="Green">E55</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#E25:25"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E35:25"/><b>then </b><i><font color="Green">E56</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="E36:25"/><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> 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#E25:25"><i><font color="Green">E47</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E37:25"/><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="E38:25"/><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>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#E22:25"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E35:25"><i><font color="Green">E56</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<a NAME="E39:25"/><i><font color="Green">E59</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#E34:25"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E40:25"/>
 <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#E36:25"><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="E41:25"/><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> 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#E22:25"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E27:25"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmp_gcd.html#E39:25"><i><font color="Green">E59</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/>
<i><font color="Green">E61</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#E30:25"><i><font color="Green">E51</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#E28:25"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E62</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#E1:25"><i><font color="Green">E24</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">E63</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#E43:25"><i><font color="Green">E62</font></i></a></i>
;<br/>
<i><font color="Green">E64</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#E33:25"><i><font color="Green">E54</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#E31:25"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E65</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#E1:25"><i><font color="Green">E24</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">E66</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#E46:25"><i><font color="Green">E65</font></i></a></i>
;<br/>
<a NAME="E48:25"/><i><font color="Green">E67</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#E38:25"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E49:25"/><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> 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="E50:25"/><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> 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#E33:25"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E38:25"><i><font color="Green">E58</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<a NAME="E51:25"/>
 <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#E48:25"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmp_gcd.html#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E52:25"/><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> 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#E33:25"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E41:25"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E70</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#E44:25"><i><font color="Green">E63</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#E42:25"><i><font color="Green">E61</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E71</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#E1:25"><i><font color="Green">E24</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">E72</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#E54:25"><i><font color="Green">E71</font></i></a></i>
;<br/>
<i><font color="Green">E73</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E47:25"><i><font color="Green">E66</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#E45:25"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E74</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E1:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E75</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E57:25"><i><font color="Green">E74</font></i></a></i>
;<br/>
<a NAME="E59:25"/>
 <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#E50:25"><i><font color="Green">E68</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="E60:25"/><b>then </b>
 <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#E21"><i><font color="Green">Lemma16</font></i></a></i>;<br/>
<a NAME="E61:25"/><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> 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#E47:25"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmp_gcd.html#E52:25"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/>
<i><font color="Green">E77</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E55:25"><i><font color="Green">E72</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#E53:25"><i><font color="Green">E70</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E78</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E1:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E79</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E63:25"><i><font color="Green">E78</font></i></a></i>
;<br/>
<i><font color="Green">E80</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#E58:25"><i><font color="Green">E75</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#E56:25"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<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> 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#E1:25"><i><font color="Green">E24</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">E82</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#E66:25"><i><font color="Green">E81</font></i></a></i>
;<br/>
<i><font color="Green">E83</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> 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#E64:25"><i><font color="Green">E79</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#E62:25"><i><font color="Green">E77</font></i></a>, <a class="ref" href="scmpds_4.html#T70">SCMPDS_4:70</a></i>
;<br/>
<b>then </b><i><font color="Green">E84</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#E1:25"><i><font color="Green">E24</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">E85</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#E69:25"><i><font color="Green">E84</font></i></a></i>
;<br/>
<div><i><font color="Green">E86</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_41"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_41"/>
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:25"><i><font color="Green">E32</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E11:25"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T68">SCMPDS_2:68</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E72:25"/><i><font color="Green">E87</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  st <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_42"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/>

<b>assume </b><a NAME="E1:25_42"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_42_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_42_1"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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 or <font color="Maroon">c<sub>22</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>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 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_42_1_1"><b>suppose </b></a><a NAME="E1:25_42_1_1"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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
 ;<br/><div class="add"><a NAME="E2:25_42_1_1"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:25"><i><font color="Green">E86</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>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#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:25"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:25"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_42_1_1"><i><font color="Green">E89</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>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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:25"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:25"><i><font color="Green">E86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:25"><i><font color="Green">E86</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:25"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_42_1_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_42_1_2"><b>suppose </b></a><a NAME="E1:25_42_1_2"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>22</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>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
 ;<br/><div class="add"><a NAME="E2:25_42_1_2"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>22</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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E71:25"><i><font color="Green">E86</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E14:25"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_42_1_2"><i><font color="Green">E89</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E71:25"><i><font color="Green">E86</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_42"><i><font color="Green">E88</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E19:25"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_42_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<div><i><font color="Green">E88</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_43"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_43"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/><b>set </b><font color="Maroon">c<sub>23</sub></font> =  <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;<br/><b>set </b><font color="Maroon">c<sub>24</sub></font> =  <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;<br/><b>set </b><font color="Maroon">c<sub>25</sub></font> =  <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;<br/><b>set </b><font color="Maroon">c<sub>26</sub></font> =  <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;<br/><a NAME="E2:25_43"/><i><font color="Green">E90</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="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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a></i>;<br/><a NAME="E3:25_43"/><i><font color="Green">E91</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="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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_43_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_43_1"/>
( ( <font color="Maroon">c<sub>22</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>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 &amp; <font color="Maroon">c<sub>22</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>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 ) or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_43_1_1"><b>suppose </b></a><a NAME="E1:25_43_1_1"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">c<sub>22</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>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 &amp; <font color="Maroon">c<sub>22</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>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 )
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:25"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_43"><i><font color="Green">E89</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:25"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_43"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:25_43"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_43_1_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_43_1_2"><b>suppose </b></a><a NAME="E1:25_43_1_2"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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
 ;<br/><div class="add"><a NAME="E2:25_43_1_2"/><i><font color="Green">E93</font></i>: 
<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> 3
 ;<br/><a NAME="E3:25_43_1_2"/><b>then </b><i><font color="Green">E94</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#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#E34:25"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E36:25"><i><font color="Green">E57</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/><a NAME="E4:25_43_1_2"/><i><font color="Green">E95</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#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#E34:25"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E36:25"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_43"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:25_43"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_43_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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#K5">div</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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:25"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_43_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:25_43_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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#K5">div</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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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#K5">div</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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:25"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_43"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:25_43"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_43_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:25_43_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_43_1_3"><b>suppose </b></a><a NAME="E1:25_43_1_3"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:25"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <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"><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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:25"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E30:25"><i><font color="Green">E51</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_43"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:25_43"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_43_1_3"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E89</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_44"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_44"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_44_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_44_1"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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 or <font color="Maroon">c<sub>22</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>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 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_44_1_1"><b>suppose </b></a><a NAME="E1:25_44_1_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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
 ;<br/><div class="add"><a NAME="E2:25_44_1_1"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:25"><i><font color="Green">E88</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:25"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_44_1_1"><i><font color="Green">E91</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>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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:25"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:25"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E38:25"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:25"><i><font color="Green">E88</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:25"><i><font color="Green">E88</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:25"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_44_1_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_44_1_2"><b>suppose </b></a><a NAME="E1:25_44_1_2"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>22</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>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
 ;<br/><div class="add"><a NAME="E2:25_44_1_2"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>22</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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E73:25"><i><font color="Green">E88</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E33:25"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_44_1_2"><i><font color="Green">E91</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 3</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E73:25"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_44"><i><font color="Green">E90</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E44:25"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_44_1_2"><i><font color="Green">E92</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E90</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_45"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_45"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/><i><font color="Green">E92</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span> = 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E52:25"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E52:25"><i><font color="Green">E69</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_45_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_45_2"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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> or <font color="Maroon">c<sub>22</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>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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_45_2_1"><b>suppose </b></a><a NAME="E1:25_45_2_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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>
 ;<br/><div class="add"><a NAME="E2:25_45_2_1"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E74:25"><i><font color="Green">E89</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:25"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_45_2_1"><i><font color="Green">E93</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>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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E74:25"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_45"><i><font color="Green">E92</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E74:25"><i><font color="Green">E89</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E55:25"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_45_2_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_45_2_2"><b>suppose </b></a><a NAME="E1:25_45_2_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>22</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>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>
 ;<br/><div class="add"><a NAME="E2:25_45_2_2"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E74:25"><i><font color="Green">E89</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E47:25"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_45_2_2"><i><font color="Green">E93</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>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E74:25"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_45"><i><font color="Green">E91</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E55:25"><i><font color="Green">E72</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_45_2_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_46"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_46"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/><i><font color="Green">E93</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span> = 
<font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E61:25"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E61:25"><i><font color="Green">E76</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_46_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_46_2"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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 or <font color="Maroon">c<sub>22</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>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 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_46_2_1"><b>suppose </b></a><a NAME="E1:25_46_2_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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
 ;<br/><div class="add"><a NAME="E2:25_46_2_1"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E4:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E75:25"><i><font color="Green">E90</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<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> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E58:25"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_46_2_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2" target="_self">GBP</a> </span>)</span>,1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E75:25"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_46"><i><font color="Green">E93</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E75:25"><i><font color="Green">E90</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E64:25"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_46_2_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_46_2_2"><b>suppose </b></a><a NAME="E1:25_46_2_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</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>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
 ;<br/><div class="add"><a NAME="E2:25_46_2_2"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>22</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#E4:25"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E75:25"><i><font color="Green">E90</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E58:25"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_46_2_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 5</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E75:25"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_46"><i><font color="Green">E92</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E64:25"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_46_2_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><i><font color="Green">E92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_47"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_47"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_47_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_47_1"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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>  or <font color="Maroon">c<sub>22</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>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>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_47_1_1"><b>suppose </b></a><a NAME="E1:25_47_1_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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> 
 ;<br/><div class="add"><a NAME="E2:25_47_1_1"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E76:25"><i><font color="Green">E91</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
 <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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E67:25"><i><font color="Green">E82</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_47_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E65:25"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:25"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scmp_gcd.html#E70:25"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_47_1_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_47_1_2"><b>suppose </b></a><a NAME="E1:25_47_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</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>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> 
 ;<br/><div class="add"><a NAME="E2:25_47_1_2"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>22</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#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E76:25"><i><font color="Green">E91</font></i></a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E67:25"><i><font color="Green">E82</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_47_1_2"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 6</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E76:25"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_47"><i><font color="Green">E93</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 7</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>22</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E70:25"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:25_47_1_2"><i><font color="Green">E95</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>22</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>23</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:25_48"/><i><font color="Green">E93</font></i>: 
( <font color="Maroon">c<sub>22</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 7 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_48_1"/>
( <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 7 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="ref" href="cqc_the1.html#T8">CQC_THE1:8</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_1"><b>suppose </b></a><a NAME="E1:25_48_1_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</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#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:25"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/><br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25_48_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_2"><b>suppose </b></a><a NAME="E1:25_48_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_48_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E12:25"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E17:25"><i><font color="Green">E40</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_48_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E71:25"><i><font color="Green">E86</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_2"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_3"><b>suppose </b></a><a NAME="E1:25_48_1_3"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_48_1_3"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E20:25"><i><font color="Green">E43</font></i></a>, <a class="txt" href="scmp_gcd.html#E28:25"><i><font color="Green">E49</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_48_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E72:25"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_3"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_4"><b>suppose </b></a><a NAME="E1:25_48_1_4"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_48_1_4"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E31:25"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmp_gcd.html#E42:25"><i><font color="Green">E61</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_48_1_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E73:25"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_4"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_5"><b>suppose </b></a><a NAME="E1:25_48_1_5"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_48_1_5"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E45:25"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmp_gcd.html#E53:25"><i><font color="Green">E70</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_48_1_5"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E74:25"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_5"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_6"><b>suppose </b></a><a NAME="E1:25_48_1_6"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_48_1_6"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E56:25"><i><font color="Green">E73</font></i></a>, <a class="txt" href="scmp_gcd.html#E62:25"><i><font color="Green">E77</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_48_1_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E75:25"><i><font color="Green">E90</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_6"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_7"><b>suppose </b></a><a NAME="E1:25_48_1_7"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>hence </b><a NAME="E2:25_48_1_7"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E65:25"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:25"><i><font color="Green">E83</font></i></a></i>;<br/><b>thus </b><a NAME="E3:25_48_1_7"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E76:25"><i><font color="Green">E91</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_7"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_48_1_8"><b>suppose </b></a><a NAME="E1:25_48_1_8"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>22</sub></font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><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> <font color="Maroon">c<sub>22</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></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> 6</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E65:25"><i><font color="Green">E80</font></i></a>, <a class="txt" href="scmp_gcd.html#E67:25"><i><font color="Green">E82</font></i></a>, <a class="txt" href="scmp_gcd.html#E68:25"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_8"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></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>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E70:25"><i><font color="Green">E85</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_8"><i><font color="Green">E94</font></i></a>, <a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>

;<br/><b>thus </b><a NAME="E3:25_48_1_8"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>22</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>23</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E77:25"><i><font color="Green">E92</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:25_48_1_8"><i><font color="Green">E94</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>


</div>
