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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:33_1"/>
(  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 or  not  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> )
 </span><b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1"><b>suppose </b></a><a NAME="E1:33_1_1"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">l</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <b> such that </b><br/><a NAME="E3:33_1_1"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <font color="Maroon" title="c4">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T59" title="SCMFSA_2:th.59">SCMFSA_2:59</a></i>;<br/><a NAME="E4:33_1_1"/>
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E3:33_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="scmfsa_4.html#T14" target="_self" title="SCMFSA_4:th.14">Th14</a></i>;<br/><b>hence </b> <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font> = 
 <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T14" target="_self" title="SCMFSA_4:th.14">Th14</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T3" target="_self" title="SCMFSA_4:th.3">Th3</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E3:33_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="scmfsa_4.html#T14" target="_self" title="SCMFSA_4:th.14">Th14</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_2"><b>suppose </b></a><a NAME="E1:33_1_2"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">l</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c5">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:33_1_2"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <font color="Maroon" title="c4">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T60" title="SCMFSA_2:th.60">SCMFSA_2:60</a></i>;<br/><a NAME="E4:33_1_2"/>
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E3:33_1_2"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="scmfsa_4.html#T15" target="_self" title="SCMFSA_4:th.15">Th15</a></i>;<br/><b>hence </b> <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font> = 
<font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T15" target="_self" title="SCMFSA_4:th.15">Th15</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">=0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T3" target="_self" title="SCMFSA_4:th.3">Th3</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E3:33_1_2"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="scmfsa_4.html#T15" target="_self" title="SCMFSA_4:th.15">Th15</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_3"><b>suppose </b></a><a NAME="E1:33_1_3"/>
 <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">l</font> being   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> , <font color="Maroon" title="c5">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <b> such that </b><br/><a NAME="E3:33_1_3"/><i><font color="Green" title="E25">A3</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <font color="Maroon" title="c4">l</font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T61" title="SCMFSA_2:th.61">SCMFSA_2:61</a></i>;<br/><a NAME="E4:33_1_3"/>
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E3:33_1_3"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="scmfsa_4.html#T16" target="_self" title="SCMFSA_4:th.16">Th16</a></i>;<br/><b>hence </b> <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font> = 
<font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T16" target="_self" title="SCMFSA_4:th.16">Th16</a></i>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">&gt;0_goto</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">l</font> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#T3" target="_self" title="SCMFSA_4:th.3">Th3</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E3:33_1_3"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="scmfsa_4.html#T16" target="_self" title="SCMFSA_4:th.16">Th16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_4"><b>suppose </b></a><a NAME="E1:33_1_4"/><i><font color="Green" title="E25">A4</font></i>: 
not  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:33_1_4"/><b>then </b>
not  <a href="ami_5.html#K1" title="AMI_5:func.1">InsCode</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">6,7,8</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa_4.html#T22" target="_self" title="SCMFSA_4:th.22">Th22</a></i>;<br/><b>then </b> <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font> = 
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D3" target="_self" title="SCMFSA_4:def.3">Def3</a></i>
<br/>.= 
<font color="Maroon" title="c3">i</font>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:33_1_4"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="scmfsa_4.html#D3" target="_self" title="SCMFSA_4:def.3">Def3</a></i>
<br/>.= 
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_4.html#E1:33_1_4"><i><font color="Green" title="E25">A4</font></i></a>, <a class="ref" href="scmfsa_4.html#D3" target="_self" title="SCMFSA_4:def.3">Def3</a></i>
;<br/><b>hence </b><a NAME="E4:33_1_4"/>
 <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <span class="p1">(<span class="default"><a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c1">m</font></span>)</span>,<font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_4.html#K4" title="SCMFSA_4:func.4">IncAddr</a> <font color="Maroon" title="c3">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c2">n</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
