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<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:34_1"/>
(  <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6 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  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#K1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1">}</a></span> )
 </span><b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_1"><b>suppose </b></a><a NAME="E1:34_1_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:34_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59">SCMFSA_2:59</a></i>;<br/><a NAME="E4:34_1_1"/>
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>;<br/><b>hence </b> <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">n</font> = 
 <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">m</font></span>)</span> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_2"><b>suppose </b></a><a NAME="E1:34_1_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:34_1_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:34_1_2"/>
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>;<br/><b>hence </b> <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">n</font> = 
<font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">m</font></span>)</span> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">a</font> <a href="scmfsa_2.html#K14">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_3"><b>suppose </b></a><a NAME="E1:34_1_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">l</font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> , <font color="Maroon">a</font> being    <a href="scmfsa_2.html#M1">Int-Location</a> <b> such that </b><br/><a NAME="E3:34_1_3"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <font color="Maroon">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:34_1_3"/>
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>;<br/><b>hence </b> <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">n</font> = 
<font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">m</font></span>)</span> <a href="scmfsa_4.html#K2" target="_self">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">a</font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="scmfsa_4.html#K2" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="34_1_4"><b>suppose </b></a><a NAME="E1:34_1_4"/><i><font color="Green">E32</font></i>: 
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#K1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:34_1_4"/><b>then </b>
not  <a href="ami_5.html#K1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i/>;<br/><b>then </b> <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">n</font> = 
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>
<br/>.= 
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T1" target="_self">Th1</a>, </i>
;<br/><b>hence </b><a NAME="E4:34_1_4"/>
 <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<font color="Maroon">m</font></span>)</span>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_4.html#K4" target="_self">IncAddr</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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