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

<b>let </b><font color="Maroon">c<sub>16</sub></font> be    <a href="ami_1.html#M1">FinPartState</a> of  <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font> be   <a href="int_1.html#NM1">Integer</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="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> =  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 9;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 10;<br/>
<b>assume </b><a NAME="E1:28"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="funct_4.html#K4">--&gt;</a> <font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>18</sub></font> )
 ;<br/>

<a NAME="E2:28"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K7">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T65">FUNCT_4:65</a></i>;<br/>
<a NAME="E3:28"/><i><font color="Green">E28</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T27">SCMPDS_4:27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="xboole_0.html#NR5" target="_self">meets</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>23</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:28_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> &amp; <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>16</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><a NAME="E4:28_1"/>
( <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 9 or <font color="Maroon">c<sub>23</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 10 )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:28"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:28_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E5:28_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_4.html#T31">SCMPDS_4:31</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:28"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33">FUNCT_4:33</a></i>;<br/>
<a NAME="E6:28"/><i><font color="Green">E30</font></i>: 
(  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 9 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 10 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>16</sub></font> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:28"><i><font color="Green">E27</font></i></a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E7:28"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a>  st <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>23</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:28_2"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>23</sub></font>
 ;<br/>

<a NAME="E2:28_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E3:28_2"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:28_2"/><i><font color="Green">E34</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> 9 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> 10
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>23</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> 9</span>)</span> = 
<font color="Maroon">c<sub>16</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:28"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:28_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>17</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:28_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>23</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> 10</span>)</span> = 
<font color="Maroon">c<sub>16</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:28"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:28_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:28_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funct_4.html#T66">FUNCT_4:66</a></i>
;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E8:28"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font> is <a href="ami_1.html#V11">autonomic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>23</sub></font>, <font color="Maroon">c<sub>24</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D25">AMI_1:def 25</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:28_3"/><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>23</sub></font>
 <b>and </b><br/><a NAME="E2:28_3"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>24</sub></font>
 ;<br/>

<a NAME="E3:28_3"/><i><font color="Green">E34</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>23</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:28"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:28_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:28_3"/><b>then </b><i><font color="Green">E35</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>23</sub></font>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E5:28_3"/><i><font color="Green">E36</font></i>: 
 <a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>24</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:28"><i><font color="Green">E29</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E6:28_3"/><b>then </b><i><font color="Green">E37</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>24</sub></font>
 
<b>by </b><i><a class="ref" href="scmpds_4.html#T57">SCMPDS_4:57</a></i>;<br/>
<a NAME="E7:28_3"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>23</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> 9</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>23</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> 10</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:28"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:28_3"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E8:28_3"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>24</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> 9</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>24</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> 10</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:28"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3"><i><font color="Green">E33</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>25</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>26</sub></font> =  <a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>27</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4;<br/>
<b>set </b><font color="Maroon">c<sub>28</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4;<br/>
<a NAME="E9:28_3"/><i><font color="Green">E40</font></i>: 
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>
<a NAME="E10:28_3"/><i><font color="Green">E41</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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</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 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</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> 7 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">7 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</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> 10</span>)</span> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmp_gcd.html#T15" target="_self">Th15</a></i>;<br/>
<b>then </b><i><font color="Green">E42</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>23</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>23</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>,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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">7 <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<font color="Maroon">c<sub>18</sub></font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:28"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:28_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a></i>
;<br/>
<a NAME="E12:28_3"/><i><font color="Green">E43</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>23</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>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E13:28_3"/><b>then </b><i><font color="Green">E44</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>23</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>23</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>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:28"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:28_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a></i>;<br/>
<a NAME="E14:28_3"/><i><font color="Green">E45</font></i>: 
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:28_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ami_3.html#T38">AMI_3:38</a></i>;<br/>
<a NAME="E15:28_3"/><i><font color="Green">E46</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 5 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</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 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</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> 7 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">7 <a href="nat_1.html#K1">+</a> <a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_3.html#K2">inspos</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>24</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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>24</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> 10</span>)</span> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E5:28_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmp_gcd.html#T15" target="_self">Th15</a></i>;<br/>
<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>24</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>24</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>,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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">7 <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</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>23</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>,3</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:28"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:28_3"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:28_3"><i><font color="Green">E46</font></i></a></i>
;<br/>
<a NAME="E17:28_3"/>
 <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>24</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>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p1">(<span class="default">7 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E15:28_3"><i><font color="Green">E46</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E18:28_3"/><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>24</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>24</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>,2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</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>23</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>,2</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E7:28"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:28_3"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:28_3"><i><font color="Green">E46</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>29</sub></font> =  <a href="ami_1.html#K10">Computation</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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>30</sub></font> =  <a href="ami_1.html#K10">Computation</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>31</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E20:28_3"/><i><font color="Green">E49</font></i>: 
(  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp;  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</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> <a href="xcmplx_0.html#K2">+</a> 1 holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="scmpds_2.html#M1">Int_position</a>  st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> holds <br/>(  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:28_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E9:28_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:28_3"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:28_3"><i><font color="Green">E43</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:28_3"><i><font color="Green">E45</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:28_3"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmp_gcd.html#E16:28_3"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scmp_gcd.html#E18:28_3"><i><font color="Green">E48</font></i></a>, <a class="txt" href="scmp_gcd.html#E30"><i><font color="Green">Lemma24</font></i></a></i>;<br/>
<i><font color="Green">E50</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="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> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<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> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">7 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> 2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
;<br/>
<i><font color="Green">E51</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="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> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<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> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> <span class="p2">(<span class="default">7 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E15:28_3"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self">Th5</a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> 2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E10:28_3"><i><font color="Green">E41</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:28_3"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scmpds_1.html#D23">SCMPDS_1:def 23</a></i>
;<br/>
<i><font color="Green">E52</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 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> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a></i>
;<br/>
<i><font color="Green">E53</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E23:28_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E21:28_3"><i><font color="Green">E50</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self">Th3</a></i>
;<br/>
<b>then </b><i><font color="Green">E54</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 4</span>)</span>

<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>23</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> 4</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<font color="Maroon">c<sub>23</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 4</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<i><font color="Green">E55</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 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> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5">return</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a></i>
;<br/>
<i><font color="Green">E56</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> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K3" target="_self">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:28_3"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E22:28_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self">Th3</a></i>
;<br/>
<b>then </b><i><font color="Green">E57</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 4</span>)</span>

<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>24</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> 4</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<font color="Maroon">c<sub>24</sub></font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2">inspos</a> 4</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:28_3"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green">Lemma14</font></i></a></i>
;<br/>
<a NAME="E29:28_3"/><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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:28_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:28_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E31"><i><font color="Green">Lemma25</font></i></a></i>;<br/>
<a NAME="E30:28_3"/><i><font color="Green">E59</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:28_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:28_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E31"><i><font color="Green">Lemma25</font></i></a></i>;<br/>
<a NAME="E31:28_3"/><i><font color="Green">E60</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> 9 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>then </b><i><font color="Green">E61</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E23:28_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmp_gcd.html#E29:28_3"><i><font color="Green">E58</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> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:28_3"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E31:28_3"><i><font color="Green">E60</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
;<br/>
<a NAME="E33:28_3"/><i><font color="Green">E62</font></i>: 
 <a href="scmp_gcd.html#K1" target="_self">intpos</a> 10 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" target="_self">SBP</a> 
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4" target="_self">Th4</a></i>;<br/>
<b>then </b><i><font color="Green">E63</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E23:28_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:28_3"><i><font color="Green">E59</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> <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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:28_3"><i><font color="Green">E55</font></i></a>, <a class="txt" href="scmp_gcd.html#E33:28_3"><i><font color="Green">E62</font></i></a>, <a class="ref" href="scmpds_2.html#T70">SCMPDS_2:70</a></i>
;<br/>
<div><i><font color="Green">E64</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_3_13"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>32</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:28_3_13"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 5 )
 ;<br/><div><i><font color="Green">E66</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_3_13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_3_13_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 4
 ;<br/><a NAME="E2:28_3_13_1"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 3 <a href="nat_1.html#K1">+</a> 1 or <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_3_13_1_1"/>
( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 3 or <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E2:28_3_13_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_1_1_1"><b>case </b></a><a NAME="E1:28_3_13_1_1_1"/>
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 3
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_3_13_1_1_1"/>
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 3
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_1_1_2"><b>case </b></a><a NAME="E1:28_3_13_1_1_2"/>
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4
 ;<br/><div class="add"><b>hence </b><a NAME="E2:28_3_13_1_1_2"/>
( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4 &amp; <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 4 )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28_3_13_1"><i><font color="Green">E67</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_3_13_2"/>
( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 3 or ( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4 &amp; <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 4 ) or <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 5 )
 </span><b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28_3_13"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3_13"><i><font color="Green">E66</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_2_1"><b>suppose </b></a><a NAME="E1:28_3_13_2_1"/>
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 3
 ;<br/><div class="add"><a NAME="E2:28_3_13_2_1"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 4
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E3:28_3_13_2_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:28_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:28_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E31"><i><font color="Green">Lemma25</font></i></a></i>;<br/><b>thus </b><a NAME="E4:28_3_13_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:28_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:28_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3_13_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmp_gcd.html#E31"><i><font color="Green">Lemma25</font></i></a></i>;<br/><b>thus </b><a NAME="E5:28_3_13_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="scmp_gcd.html#E7:28_3"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:28_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:28_3_13_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmp_gcd.html#E31"><i><font color="Green">Lemma25</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_2_2"><b>suppose </b></a><a NAME="E1:28_3_13_2_2"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4 &amp; <font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 4 )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>33</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:28_3_13_2_2"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R1">=</a> 4 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E4:28_3_13_2_2"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>33</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>31</sub></font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:28_3_13_2_2"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmp_gcd.html#E29:28_3"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:28_3_13_2_2"><i><font color="Green">E69</font></i></a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmp_gcd.html#E29:28_3"><i><font color="Green">E58</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:28_3_13_2_2"><i><font color="Green">E69</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:28_3"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:28_3"><i><font color="Green">E59</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:28_3_13_2_2"><i><font color="Green">E69</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_2"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_3_13_2_3"><b>suppose </b></a><a NAME="E1:28_3_13_2_3"/>
<font color="Maroon">c<sub>32</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 5
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>33</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:28_3_13_2_3"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E4:28_3_13_2_3"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E3:28_3_13_2_3"><i><font color="Green">E67</font></i></a></i>;<br/><a NAME="E5:28_3_13_2_3"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3_13_2_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E24:28_3"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:28_3"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E27:28_3"><i><font color="Green">E56</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3_13_2_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E28:28_3"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3_13_2_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3_13_2_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3_13_2_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E25:28_3"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E32:28_3"><i><font color="Green">E61</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3_13_2_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E28:28_3"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3_13_2_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3_13_2_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3_13_2_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E25:28_3"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmp_gcd.html#E34:28_3"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3_13_2_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> 4</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>31</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>33</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E28:28_3"><i><font color="Green">E57</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:28_3_13_2_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>32</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3_13_2_3"><i><font color="Green">E68</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>32</sub></font> = <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8">}</a></span>;<br/>
<i><font color="Green">E65</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:28"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scmp_gcd.html#E3:28"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K7">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span>
<b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>
;<br/>
<b>let </b><font color="Maroon">c<sub>33</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E37:28_3"/><i><font color="Green">E66</font></i>: 
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:28_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ami_3.html#T43">AMI_3:43</a></i>;<br/>
<a NAME="E38:28_3"/>
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E4:28_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="ami_3.html#T43">AMI_3:43</a></i>;<br/>
<b>then </b><i><font color="Green">E67</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> = 
 <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> 
<b>by </b><i><a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E37:28_3"><i><font color="Green">E66</font></i></a>, <a class="ref" href="grfunc_1.html#T64">GRFUNC_1:64</a></i>
;<br/>
<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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</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> = 
 <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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span>

<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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E35:28_3"><i><font color="Green">E64</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</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 NAME="E41:28_3"/><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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span> )
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E35:28_3"><i><font color="Green">E64</font></i></a></i>;<br/>
 <a href="relat_1.html#K1">dom</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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <a href="scmpds_2.html#K1">SCMPDS</a> 
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</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>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T36">AMI_3:36</a></i>
;<br/>
<a NAME="E43:28_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" target="_self">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8">}</a></span>
 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E40:28_3"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmp_gcd.html#E41:28_3"><i><font color="Green">E69</font></i></a>, <a class="ref" href="ami_3.html#T26">AMI_3:26</a></i>;<br/>
<b>hence </b><a NAME="E44:28_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>23</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>24</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>33</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K2">Initialized</a> <a href="scmp_gcd.html#K4" target="_self">GCD-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E36:28_3"><i><font color="Green">E65</font></i></a>, <a class="txt" href="scmp_gcd.html#E39:28_3"><i><font color="Green">E67</font></i></a>, <a class="ref" href="relat_1.html#T185">RELAT_1:185</a></i>;<br/>


</div><b>end;</b></div>


</div>
