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<b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>



<b>assume </b><a NAME="E1:11"/>
not  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,4,5,6</span><a href="enumset1.html#K3">}</a></span>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E30</font></i>: 
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 4 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 5 &amp;  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 6 )
 
<b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<a NAME="E3:11"/><i><font color="Green">E31</font></i>: 
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> 13
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T15">SCMPDS_2:15</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12 or  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 13 )
 </span><b>by </b><i>, , <a class="ref" href="scmpds_3.html#T1">SCMPDS_3:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1"><b>suppose </b></a><a NAME="E1:11_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><a NAME="E2:11_1_1"/><b>then </b>
 ex <font color="Olive">a</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmpds_2.html#K6">:=</a> <font color="Olive">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T37">SCMPDS_2:37</a></i>;<br/><b>hence </b><a NAME="E3:11_1_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2"><b>suppose </b></a><a NAME="E1:11_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><a NAME="E2:11_1_2"/><b>then </b>
 ex <font color="Olive">a</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K7">saveIC</a> <font color="Olive">a</font>,<font color="Olive">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T38">SCMPDS_2:38</a></i>;<br/><b>hence </b><a NAME="E3:11_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T71">SCMPDS_2:71</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_3"><b>suppose </b></a><a NAME="E1:11_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><a NAME="E2:11_1_3"/><b>then </b>
 ex <font color="Olive">a</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font>,<font color="Olive">k1</font> <a href="scmpds_2.html#K11">:=</a> <font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T42">SCMPDS_2:42</a></i>;<br/><b>hence </b><a NAME="E3:11_1_3"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_4"><b>suppose </b></a><a NAME="E1:11_1_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><a NAME="E2:11_1_4"/><b>then </b>
 ex <font color="Olive">a</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K12">AddTo</a> <font color="Olive">a</font>,<font color="Olive">k1</font>,<font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T43">SCMPDS_2:43</a></i>;<br/><b>hence </b><a NAME="E3:11_1_4"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_5"><b>suppose </b></a><a NAME="E1:11_1_5"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 9
 ;<br/><div class="add"><a NAME="E2:11_1_5"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K13">AddTo</a> <font color="Olive">a</font>,<font color="Olive">k1</font>,<font color="Olive">b</font>,<font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T44">SCMPDS_2:44</a></i>;<br/><b>hence </b><a NAME="E3:11_1_5"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_6"><b>suppose </b></a><a NAME="E1:11_1_6"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 10
 ;<br/><div class="add"><a NAME="E2:11_1_6"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K14">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">k1</font>,<font color="Olive">b</font>,<font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T45">SCMPDS_2:45</a></i>;<br/><b>hence </b><a NAME="E3:11_1_6"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T62">SCMPDS_2:62</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_7"><b>suppose </b></a><a NAME="E1:11_1_7"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 11
 ;<br/><div class="add"><a NAME="E2:11_1_7"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K15">MultBy</a> <font color="Olive">a</font>,<font color="Olive">k1</font>,<font color="Olive">b</font>,<font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T46">SCMPDS_2:46</a></i>;<br/><b>hence </b><a NAME="E3:11_1_7"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T63">SCMPDS_2:63</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_8"><b>suppose </b></a><a NAME="E1:11_1_8"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 12
 ;<br/><div class="add"><a NAME="E2:11_1_8"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K16">Divide</a> <font color="Olive">a</font>,<font color="Olive">k1</font>,<font color="Olive">b</font>,<font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T47">SCMPDS_2:47</a></i>;<br/><b>hence </b><a NAME="E3:11_1_8"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T64">SCMPDS_2:64</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_9"><b>suppose </b></a><a NAME="E1:11_1_9"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 13
 ;<br/><div class="add"><a NAME="E2:11_1_9"/><b>then </b>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmpds_2.html#M1">Int_position</a>  ex <font color="Olive">k1</font>, <font color="Olive">k2</font> being  <a href="int_1.html#NM1">Integer</a> st <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font>,<font color="Olive">k1</font> <a href="scmpds_2.html#K17">:=</a> <font color="Olive">b</font>,<font color="Olive">k2</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T48">SCMPDS_2:48</a></i>;<br/><b>hence </b><a NAME="E3:11_1_9"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <font color="Maroon">i</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="scmpds_2.html#K1">SCMPDS</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K18">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T59">SCMPDS_2:59</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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