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

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>





<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/>
<a NAME="E1:13"/>
 <a href="ami_1.html#K2">IC</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T24">SCMFSA6A:24</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></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="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></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="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 0
<b>by </b><i><a class="ref" href="scmfsa6a.html#T46">SCMFSA6A:46</a></i>
;<br/>
<a NAME="E3:13"/><b>then </b><i><font color="Green">E7</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> 0
 
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>;<br/>
<a NAME="E4:13"/>
 <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T45">SCMFSA6A:45</a></i>;<br/>
<b>then </b><i><font color="Green">E8</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="scmfsa6a.html#T46">SCMFSA6A:46</a></i>
;<br/>
<a NAME="E6:13"/><i><font color="Green">E9</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:13"/>
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T26">SCMFSA6A:26</a></i>;<br/>
<a NAME="E8:13"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa7b.html#E6:13"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:13"/><i><font color="Green">E11</font></i>: 
 <a href="scmfsa6b.html#K3">IExec</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#D1">SCMFSA6B:def 1</a></i>;<br/>
<a NAME="E10:13"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T84">SCMFSA_2:84</a></i>;<br/>
<a NAME="E11:13"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E12:13"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E9:13"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E3:13"><i><font color="Green">E7</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:13"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scmfsa7b.html#E8:13"><i><font color="Green">E10</font></i></a>, <a class="ref" href="scmfsa_7.html#T38">SCMFSA_7:38</a></i>
;<br/><br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>assume </b><a NAME="E1:13_4"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:13_4"/><i><font color="Green">E13</font></i>: 
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T48">SCMFSA6A:48</a></i>;<br/><a NAME="E3:13_4"/>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T84">SCMFSA_2:84</a></i>;<br/><a NAME="E4:13_4"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:13_4"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E9:13"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E3:13"><i><font color="Green">E7</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:13"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scmfsa7b.html#E8:13"><i><font color="Green">E10</font></i></a>, <a class="txt" href="scmfsa7b.html#E1:13_4"><i><font color="Green">E12</font></i></a>, <a class="ref" href="scmfsa_7.html#T38">SCMFSA_7:38</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E2:13_4"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/>

<a NAME="E15:13"/><i><font color="Green">E12</font></i>: 
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T49">SCMFSA6A:49</a></i>;<br/>
<a NAME="E16:13"/>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_2.html#T85">SCMFSA_2:85</a></i>;<br/>
<a NAME="E17:13"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E18:13"/><b>then </b>
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="scmfsa6b.html#K3">IExec</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K12">Result</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E9:13"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E3:13"><i><font color="Green">E7</font></i></a>, <a class="txt" href="scmfsa7b.html#E5:13"><i><font color="Green">E8</font></i></a>, <a class="txt" href="scmfsa7b.html#E8:13"><i><font color="Green">E10</font></i></a>, <a class="ref" href="scmfsa_7.html#T38">SCMFSA_7:38</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="scmfsa7b.html#E15:13"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
;<br/><br/>


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