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

<b>let </b><font color="Maroon">c<sub>31</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>32</sub></font>, <font color="Maroon">c<sub>33</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">c<sub>34</sub></font>, <font color="Maroon">c<sub>35</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:38"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>34</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 6 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>32</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>35</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>33</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>35</sub></font> &amp; <font color="Maroon">c<sub>32</sub></font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a> <font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>34</sub></font> &amp; <font color="Maroon">c<sub>33</sub></font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scpisort.html#K1" target="_self">insert-sort</a> <font color="Maroon">c<sub>35</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>34</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>36</sub></font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>37</sub></font> = <a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>38</sub></font> = <a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0;<br/>
<b>set </b><font color="Maroon">c<sub>39</sub></font> = <a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>40</sub></font> = <a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>41</sub></font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>42</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>43</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>44</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>45</sub></font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>46</sub></font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span>;<br/>
<a NAME="E2:38"/><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>;<br/>
<div><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>47</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:38_1"/>
<font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3
 ;<br/><a NAME="E2:38_1"/><b>then </b>
<font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E3:38_1"/><b>then </b>
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<font color="Maroon">c<sub>31</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E4:38"/><i><font color="Green">E28</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="scpisort.html#E2:38"><i><font color="Green">E26</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E5:38"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E30</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpisort.html#E2:38"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scpisort.html#E5:38"><i><font color="Green">E29</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<i><font color="Green">E31</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<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">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpisort.html#E4:38"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>47</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:38_4"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3
 ;<br/><a NAME="E2:38_4"/><b>then </b>
<font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:38_4"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,1
 <b>by </b><i><a class="txt" href="scpisort.html#E4:38"><i><font color="Green">E28</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">c<sub>31</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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E3:38_4"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>31</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E3:38"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scpisort.html#E1:38_4"><i><font color="Green">E33</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E9:38"/><i><font color="Green">E33</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scpisort.html#E6:38"><i><font color="Green">E30</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E10:38"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E35</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpisort.html#E6:38"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scpisort.html#E10:38"><i><font color="Green">E34</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E12:38"/><i><font color="Green">E36</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 
<b>by </b><i><a class="txt" href="scpisort.html#E9:38"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E37</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpisort.html#E7:38"><i><font color="Green">E31</font></i></a>, <a class="txt" href="scpisort.html#E12:38"><i><font color="Green">E36</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<i><font color="Green">E38</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="txt" href="scpisort.html#E9:38"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_8"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>47</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:38_8"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3
 ;<br/><a NAME="E2:38_8"/><b>then </b>
<font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:38_8"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scpisort.html#E9:38"><i><font color="Green">E33</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span>,<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">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E3:38_8"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>31</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>47</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E8:38"><i><font color="Green">E32</font></i></a>, <a class="txt" href="scpisort.html#E1:38_8"><i><font color="Green">E40</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E16:38"/><i><font color="Green">E40</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 3</span>)</span>
 
<b>by </b><i><a class="txt" href="scpisort.html#E11:38"><i><font color="Green">E35</font></i></a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<a NAME="E17:38"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E42</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpisort.html#E11:38"><i><font color="Green">E35</font></i></a>, <a class="txt" href="scpisort.html#E17:38"><i><font color="Green">E41</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E19:38"/><i><font color="Green">E43</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scpisort.html#E16:38"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E44</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="scpisort.html#E13:38"><i><font color="Green">E37</font></i></a>, <a class="txt" href="scpisort.html#E19:38"><i><font color="Green">E43</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E21:38"/><i><font color="Green">E45</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3
 
<b>by </b><i><a class="txt" href="scpisort.html#E16:38"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E46</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="txt" href="scpisort.html#E14:38"><i><font color="Green">E38</font></i></a>, <a class="txt" href="scpisort.html#E21:38"><i><font color="Green">E45</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<i><font color="Green">E47</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> 3</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="scpisort.html#E16:38"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E24:38"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 6 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="scpisort.html#E1:38"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_13"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>47</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:38_13"/><i><font color="Green">E49</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>47</sub></font> &amp; <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>32</sub></font> )
 ;<br/><b>set </b><font color="Maroon">c<sub>48</sub></font> = <font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font>;<br/><a NAME="E2:38_13"/>
<font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scpisort.html#E1:38_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:38_13"/><b>then </b>
<font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 7
 <b>by </b><i><a class="txt" href="scpisort.html#E24:38"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:38_13"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:38_13"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3
 <b>by </b><i><a class="txt" href="scpisort.html#E16:38"><i><font color="Green">E40</font></i></a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E5:38_13"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>31</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E15:38"><i><font color="Green">E39</font></i></a>, <a class="txt" href="scpisort.html#E4:38_13"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>32</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>47</sub></font>
<b>by </b><i><a class="txt" href="scpisort.html#E1:38"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpisort.html#E1:38_13"><i><font color="Green">E49</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self">Def1</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E26:38"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>32</sub></font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font>,<font color="Maroon">c<sub>34</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E27:38"/><i><font color="Green">E50</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>31</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>31</sub></font> )
 
<b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/>
<a NAME="E28:38"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<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">intpos</a> 3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 7
 
<b>by </b><i><a class="txt" href="scpisort.html#E20:38"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E23:38"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scpisort.html#E24:38"><i><font color="Green">E48</font></i></a></i>;<br/>
<a NAME="E29:38"/><b>then </b><i><font color="Green">E51</font></i>: 
(  <a href="scmpds_7.html#K2">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,3</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font> &amp;  <a href="scmpds_7.html#K2">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,3</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font> )
 
<b>by </b><i><a class="txt" href="scpisort.html#E18:38"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scpisort.html#E28"><i><font color="Green">Lemma20</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_14"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>47</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:38_14"/>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>47</sub></font> &amp; <font color="Maroon">c<sub>47</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>33</sub></font> )
 ;<br/><b>hence </b><font color="Maroon">c<sub>33</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>47</sub></font> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scpisort.html#K1" target="_self">insert-sort</a> <font color="Maroon">c<sub>35</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<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">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E1:38"><i><font color="Green">E25</font></i></a>, <a class="ref" href="scpisort.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_7.html#K2">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,3</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p1">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<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">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K2">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,3</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p0">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</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">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>47</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scpisort.html#E27:38"><i><font color="Green">E50</font></i></a>, <a class="txt" href="scpisort.html#E29:38"><i><font color="Green">E51</font></i></a>, <a class="ref" href="scmpds_7.html#T49">SCMPDS_7:49</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E31:38"/><b>then </b>
<font color="Maroon">c<sub>33</sub></font> <a href="scpisort.html#R1" target="_self">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_7.html#K2">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,4 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,3</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,1</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K3">while&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><a href="scmpds_2.html#K14">SubFrom</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K3">';'</a> <span class="p5">(<span class="default"><a href="scmpds_6.html#K3">if&gt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,5,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,5 <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="scmpds_2.html#K17">:=</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 4</span>)</span>,0 <a href="scmpds_2.html#K17">:=</a> <a href="scmp_gcd.html#K2">GBP</a> ,5</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,4,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,6,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p0">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,6 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,1 <a href="scmpds_2.html#K11">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,2 <a href="scmpds_2.html#K11">:=</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>35</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a> ,3 <a href="scmpds_2.html#K11">:=</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>34</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>31</sub></font></span>)</span>,<font color="Maroon">c<sub>34</sub></font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E32:38"/>
( <font color="Maroon">c<sub>32</sub></font>,<font color="Maroon">c<sub>33</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  &amp; <font color="Maroon">c<sub>33</sub></font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> 1,<font color="Maroon">c<sub>35</sub></font> )
 <b>by </b><i><a class="txt" href="scpisort.html#E1:38"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpisort.html#E18:38"><i><font color="Green">E42</font></i></a>, <a class="txt" href="scpisort.html#E20:38"><i><font color="Green">E44</font></i></a>, <a class="txt" href="scpisort.html#E22:38"><i><font color="Green">E46</font></i></a>, <a class="txt" href="scpisort.html#E23:38"><i><font color="Green">E47</font></i></a>, <a class="txt" href="scpisort.html#E26:38"><i><font color="Green">E49</font></i></a>, <a class="txt" href="scpisort.html#E34"><i><font color="Green">Lemma24</font></i></a></i>;<br/>


</div>
