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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>assume </b><a NAME="E1:55_1_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/><a NAME="E2:55_1_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_2.html#K8">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T30" target="_self">Th30</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:55_1_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_2.html#K8">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> )
 </span><b>by </b><i><a class="txt" href="scmfsa7b.html#E1:55_1_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="scmfsa7b.html#E2:55_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:55_1_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R3" target="_self">does_not_destroy</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T11" target="_self">Th11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:55_1_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_2.html#K8">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_1_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R3" target="_self">does_not_destroy</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T12" target="_self">Th12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:55_1_1_1_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_1_1_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R3" target="_self">does_not_destroy</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_1_1_4"><b>suppose </b></a><a NAME="E1:55_1_1_1_1_4"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:55_1_1_1_1_4"/>
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R3" target="_self">does_not_destroy</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T14" target="_self">Th14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E2:55_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>3</sub></font> <a href="scmfsa7b.html#R4" target="_self">does_not_destroy</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:55_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>3</sub></font> is <a href="scmfsa7b.html#V1" target="_self">good</a>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D5" target="_self">Def5</a></i>;<br/>


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