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

<b>set </b><font color="Maroon">c<sub>1</sub></font> = the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = <a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>3</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>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><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>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:69"/>
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/>

<a NAME="E2:69"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>;<br/>
<i><font color="Green">E63</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T28" target="_self">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>
;<br/>
<b>assume </b><a NAME="E4:69"/><i><font color="Green">E64</font></i>: 
 <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa8a.html#R1">is_pseudo-closed_on</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E5:69"/><i><font color="Green">E65</font></i>: 
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K5">';'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> 
 
<b>by </b><i><a class="ref" href="scmfsa8b.html#D2">SCMFSA8B:def 2</a></i>;<br/>
<a NAME="E6:69"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E7:69"/>
<font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T11">SCMFSA8A:11</a></i>;<br/>
<a NAME="E8:69"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa8a.html#R1">is_pseudo-closed_on</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmfsa8c.html#T52" target="_self">Th52</a></i>;<br/>
<a NAME="E9:69"/><i><font color="Green">E68</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</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="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E10:69"/>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E11:69"/><b>then </b><i><font color="Green">E69</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E12:69"/><i><font color="Green">E70</font></i>: 
 <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"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="sf_mastr.html#T65">SF_MASTR:65</a></i>;<br/>
<i><font color="Green">E71</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></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>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</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>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E12:69"><i><font color="Green">E70</font></i></a>, <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="sf_mastr.html#T66">SF_MASTR:66</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E9:69"><i><font color="Green">E68</font></i></a>, <a class="txt" href="scmfsa8c.html#E11:69"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E9:69"><i><font color="Green">E68</font></i></a>, <a class="ref" href="scmfsa6b.html#T7">SCMFSA6B:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T55" target="_self">Th55</a></i>
;<br/>
<a NAME="E15:69"/><b>then </b><i><font color="Green">E72</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E13:69"><i><font color="Green">E71</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>;<br/>
<div><i><font color="Green">E73</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_4"><b>now </b></a><div class="add"><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E15:69"><i><font color="Green">E72</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/></div><b>end;</b></div>
<div><i><font color="Green">E74</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_5"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</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="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K7">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E2:69"><i><font color="Green">E62</font></i></a>, <a class="txt" href="scmfsa8c.html#E3:69"><i><font color="Green">E63</font></i></a>, <a class="txt" href="scmfsa8c.html#E16:69"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E13:69"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmfsa_2.html#T32">SCMFSA_2:32</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E18:69"/><i><font color="Green">E75</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> 1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E19:69"/>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E20:69"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_6"><b>now </b></a><div class="add"><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E18:69"><i><font color="Green">E75</font></i></a>, <a class="txt" href="scmfsa8c.html#E20:69"><i><font color="Green">E76</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E18:69"><i><font color="Green">E75</font></i></a>, <a class="ref" href="scmfsa6b.html#T7">SCMFSA6B:7</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T55" target="_self">Th55</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E22:69"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E17:69"><i><font color="Green">E74</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>;<br/>
<i><font color="Green">E78</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
 <a href="ami_1.html#K9">Following</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E22:69"><i><font color="Green">E77</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
;<br/>
<a NAME="E24:69"/><i><font color="Green">E79</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="scmfsa7b.html#T6">SCMFSA7B:6</a></i>;<br/>
<a NAME="E25:69"/><i><font color="Green">E80</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E26:69"/>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8a.html#T9">SCMFSA8A:9</a></i>;<br/>
<a NAME="E27:69"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E25:69"><i><font color="Green">E80</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E28:69"/>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> 
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E5:69"><i><font color="Green">E65</font></i></a>, <a class="ref" href="scmfsa6a.html#D5">SCMFSA6A:def 5</a></i>;<br/>
<a NAME="E29:69"/><b>then </b>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62">SCMFSA6A:62</a></i>;<br/>
<a NAME="E30:69"/><b>then </b>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62">SCMFSA6A:62</a></i>;<br/>
<a NAME="E31:69"/><b>then </b>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K2">Macro</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T62">SCMFSA6A:62</a></i>;<br/>
<a NAME="E32:69"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>,2</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E24:69"><i><font color="Green">E79</font></i></a>, <a class="txt" href="scmfsa8c.html#E58"><i><font color="Green">Lemma45</font></i></a></i>;<br/>
<a NAME="E33:69"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>,2</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E27:69"><i><font color="Green">E81</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E34:69"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p2">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>,2</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2
 
<b>by </b><i><a class="ref" href="ami_5.html#T64">AMI_5:64</a></i>;<br/>
<a NAME="E35:69"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>,2</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2
 
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>;<br/>
<a NAME="E36:69"/>
 <a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T55">SCMFSA6A:55</a></i>;<br/>
<a NAME="E37:69"/><b>then </b>
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,2</span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K2">Goto</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="scmfsa6a.html#K4">';'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span></span>)</span></span>)</span>,2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E38:69"/><b>then </b><i><font color="Green">E83</font></i>: 
 <a href="ami_5.html#K6">ProgramPart</a> <span class="p1">(<span class="default"><a href="scmfsa_5.html#K1">Relocated</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,2</span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E35:69"><i><font color="Green">E82</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<i><font color="Green">E84</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</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="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> 2
<b>by </b><i><a class="txt" href="scmfsa8c.html#E23:69"><i><font color="Green">E78</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/>
<a NAME="E40:69"/>
<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> <a href="funct_7.html#R1">equal_outside</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="scmfsa8a.html#T14">SCMFSA8A:14</a></i>;<br/>
<a NAME="E41:69"/><b>then </b><i><font color="Green">E85</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T39">SCMFSA6A:39</a></i>;<br/>
<div><i><font color="Green">E86</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E41:69"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E16:69"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E23:69"><i><font color="Green">E78</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="scmfsa_2.html#M2">FinSeq-Location</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E41:69"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 1</span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E16:69"><i><font color="Green">E73</font></i></a>, <a class="ref" href="scmfsa_2.html#T97">SCMFSA_2:97</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="scmfsa_2.html#K21">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E23:69"><i><font color="Green">E78</font></i></a>, <a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E44:69"/><b>then </b><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K2">Int-Locations</a>  <a href="xboole_0.html#K2">\/</a> <a href="scmfsa_2.html#K3">FinSeq-Locations</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E42:69"><i><font color="Green">E86</font></i></a>, <a class="ref" href="scmfsa6a.html#T38">SCMFSA6A:38</a></i>;<br/>
<a NAME="E45:69"/>
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E46:69"/><b>then </b><i><font color="Green">E88</font></i>: 
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T5">SCMFSA6B:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_11"><b>now </b></a><div class="add"><b>thus </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T15">SCMFSA8B:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>

;<br/></div><b>end;</b></div>
<a NAME="E48:69"/><b>then </b><i><font color="Green">E89</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E49:69"/><b>then </b><i><font color="Green">E90</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/>
<div><i><font color="Green">E91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_12"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> 2
<b>by </b><i><a class="txt" href="scmfsa8c.html#E6:69"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmfsa8c.html#E8:69"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmfsa8c.html#E38:69"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scmfsa8c.html#E39:69"><i><font color="Green">E84</font></i></a>, <a class="txt" href="scmfsa8c.html#E44:69"><i><font color="Green">E87</font></i></a>, <a class="ref" href="scmfsa8c.html#T51" target="_self">Th51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> 2
<b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmfsa8c.html#T50" target="_self">Th50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> 2
<b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmfsa8a.html#D5">SCMFSA8A:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> 2
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>
;<br/></div><b>end;</b></div>
<b>then </b><i><font color="Green">E92</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E46:69"><i><font color="Green">E88</font></i></a>, <a class="txt" href="scmfsa8c.html#E49:69"><i><font color="Green">E90</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K13">goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8c.html#T64" target="_self">Th64</a></i>
;<br/>
<a NAME="E52:69"/>
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/>
<a NAME="E53:69"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6b.html#T5">SCMFSA6B:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_14"><b>now </b></a><div class="add"><b>thus </b> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T15">SCMFSA8B:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1

;<br/></div><b>end;</b></div>
<a NAME="E55:69"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E56:69"/><b>then </b><i><font color="Green">E94</font></i>: 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/>
<div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_15"><b>now </b></a><div class="add"><b>thus </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>
<br/>.= 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E51:69"><i><font color="Green">E92</font></i></a>, <a class="ref" href="ami_1.html#D18">AMI_1:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K13">goto</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p0">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</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>
<b>by </b><i><a class="ref" href="ami_1.html#D15">AMI_1:def 15</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa_2.html#T95">SCMFSA_2:95</a></i>
;<br/></div><b>end;</b></div>
<b>then </b><i><font color="Green">E96</font></i>:  <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E53:69"><i><font color="Green">E93</font></i></a>, <a class="txt" href="scmfsa8c.html#E56:69"><i><font color="Green">E94</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
<b>by </b><i><a class="ref" href="scmfsa8c.html#T62" target="_self">Th62</a></i>
;<br/>
<a NAME="E59:69"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> is <a href="ami_1.html#V9">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D20">AMI_1:def 20</a></i>;<br/>
<b>hence </b><a NAME="E60:69"/>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D8">SCMFSA7B:def 8</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_17"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_17_1"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> 0 or ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> 1 ) or ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>16</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 ) or ( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_1"><b>suppose </b></a><a NAME="E1:69_17_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:69_17_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/><a NAME="E3:69_17_1_1"/><b>then </b>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></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="scmfsa8c.html#T31" target="_self">Th31</a></i>;<br/><b>hence </b><a NAME="E4:69_17_1_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T54" target="_self">Th54</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_2"><b>suppose </b></a><a NAME="E1:69_17_1_2"/>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> 1 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_17_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E17:69"><i><font color="Green">E74</font></i></a>, <a class="ref" href="scmfsa8c.html#T54" target="_self">Th54</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_3"><b>suppose </b></a><a NAME="E1:69_17_1_3"/><i><font color="Green">E98</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <font color="Maroon">c<sub>16</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 )
 ;<br/><div class="add"><a NAME="E2:69_17_1_3"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E3:69_17_1_3"/><b>then </b>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E1:69_17_1_3"><i><font color="Green">E98</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E4:69_17_1_3"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:69_17_1_3"/><i><font color="Green">E99</font></i>: 
2 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E7:69_17_1_3"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E1:69_17_1_3"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa8c.html#E6:69_17_1_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E8:69_17_1_3"/><b>then </b><i><font color="Green">E101</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmfsa8c.html#T50" target="_self">Th50</a></i>;<br/><i><font color="Green">E102</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E6:69_17_1_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> 2
<b>by </b><i><a class="txt" href="scmfsa8c.html#E6:69"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmfsa8c.html#E8:69"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmfsa8c.html#E38:69"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scmfsa8c.html#E39:69"><i><font color="Green">E84</font></i></a>, <a class="txt" href="scmfsa8c.html#E44:69"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scmfsa8c.html#E7:69_17_1_3"><i><font color="Green">E100</font></i></a>, <a class="ref" href="scmfsa8c.html#T51" target="_self">Th51</a></i>
;<br/><b>consider </b><font color="Maroon">c<sub>18</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E11:69_17_1_3"/><i><font color="Green">E103</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T21">SCMFSA_2:21</a></i>;<br/><a NAME="E12:69_17_1_3"/>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>18</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#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmfsa8c.html#E8:69_17_1_3"><i><font color="Green">E101</font></i></a>, <a class="txt" href="scmfsa8c.html#E11:69_17_1_3"><i><font color="Green">E103</font></i></a>, <a class="ref" href="scmfsa8a.html#T31">SCMFSA8A:31</a></i>;<br/><a NAME="E13:69_17_1_3"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><a NAME="E14:69_17_1_3"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E15:69_17_1_3"/><b>then </b><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>;<br/> <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmfsa8b.html#T15">SCMFSA8B:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span>

;<br/><a NAME="E17:69_17_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E18:69_17_1_3"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E15:69_17_1_3"><i><font color="Green">E104</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E19:69_17_1_3"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><b>hence </b><a NAME="E20:69_17_1_3"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E9:69_17_1_3"><i><font color="Green">E102</font></i></a>, <a class="txt" href="scmfsa8c.html#E11:69_17_1_3"><i><font color="Green">E103</font></i></a>, <a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_4"><b>suppose </b></a><a NAME="E1:69_17_1_4"/><i><font color="Green">E98</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> )
 ;<br/><div class="add"><div><b>hereby </b>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_17_1_4_1_1"/>
( <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font> or <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font> )
 </span><b>by </b><i><a class="txt" href="scmfsa8c.html#E1:69_17_1_4"><i><font color="Green">E98</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_4_1_1_1"><b>suppose </b></a><a NAME="E1:69_17_1_4_1_1_1"/>
<span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_17_1_4_1_1_1"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E48:69"><i><font color="Green">E89</font></i></a>, <a class="txt" href="scmfsa8c.html#E50:69"><i><font color="Green">E91</font></i></a>, <a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_17_1_4_1_1_2"><b>suppose </b></a><a NAME="E1:69_17_1_4_1_1_2"/>
<span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><div class="add"><a NAME="E2:69_17_1_4_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><b>hence </b><a NAME="E3:69_17_1_4_1_1_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E56:69"><i><font color="Green">E94</font></i></a>, <a class="txt" href="scmfsa8c.html#E57:69"><i><font color="Green">E95</font></i></a>, <a class="txt" href="scmfsa8c.html#E58:69"><i><font color="Green">E96</font></i></a>, <a class="ref" href="ami_1.html#T52">AMI_1:52</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E62:69"/>
 <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="scmfsa7b.html#R5">is_closed_on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#D7">SCMFSA7B:def 7</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_18"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>16</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:69_18"/><i><font color="Green">E98</font></i>: 
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> 
 ;<br/><b>assume </b><a NAME="E2:69_18"/><i><font color="Green">E99</font></i>: 
not <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/><a NAME="E3:69_18"/>
 <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K15">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E15:69"><i><font color="Green">E72</font></i></a>, <a class="ref" href="ami_1.html#D19">AMI_1:def 19</a></i>;<br/><a NAME="E4:69_18"/><b>then </b><i><font color="Green">E100</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E22:69"><i><font color="Green">E77</font></i></a>, <a class="txt" href="scmfsa8c.html#E1:69_18"><i><font color="Green">E98</font></i></a>, <a class="ref" href="scmfsa_2.html#T47">SCMFSA_2:47</a>, <a class="ref" href="scmfsa_2.html#T49">SCMFSA_2:49</a>, <a class="ref" href="scmfsa_2.html#T124">SCMFSA_2:124</a></i>;<br/><a NAME="E5:69_18"/>
0 <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><a NAME="E6:69_18"/><b>then </b><i><font color="Green">E101</font></i>: 
(  <a href="scmfsa_2.html#K5">insloc</a> 2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T57" target="_self">Th57</a></i>;<br/> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E39:69"><i><font color="Green">E84</font></i></a>, <a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E6:69_18"><i><font color="Green">E101</font></i></a>, <a class="ref" href="scmfsa8c.html#T26" target="_self">Th26</a></i>
;<br/><a NAME="E8:69_18"/><b>then </b>
2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E1:69_18"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa8c.html#E4:69_18"><i><font color="Green">E100</font></i></a>, <a class="txt" href="scmfsa8c.html#E6:69_18"><i><font color="Green">E101</font></i></a>, <a class="ref" href="cqc_the1.html#T3">CQC_THE1:3</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>17</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:69_18"/><i><font color="Green">E102</font></i>: 
2 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/><a NAME="E11:69_18"/>
<font color="Maroon">c<sub>16</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E2:69_18"><i><font color="Green">E99</font></i></a></i>;<br/><a NAME="E12:69_18"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E10:69_18"><i><font color="Green">E102</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E13:69_18"/><b>then </b><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>18</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E15:69_18"/><i><font color="Green">E104</font></i>: 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa_2.html#T21">SCMFSA_2:21</a></i>;<br/><i><font color="Green">E105</font></i>:  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> = 
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> 2</span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E10:69_18"><i><font color="Green">E102</font></i></a>, <a class="ref" href="ami_1.html#T51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span></span>)</span> <a href="scmfsa_4.html#K2">+</a> 2
<b>by </b><i><a class="txt" href="scmfsa8c.html#E6:69"><i><font color="Green">E66</font></i></a>, <a class="txt" href="scmfsa8c.html#E8:69"><i><font color="Green">E67</font></i></a>, <a class="txt" href="scmfsa8c.html#E38:69"><i><font color="Green">E83</font></i></a>, <a class="txt" href="scmfsa8c.html#E39:69"><i><font color="Green">E84</font></i></a>, <a class="txt" href="scmfsa8c.html#E44:69"><i><font color="Green">E87</font></i></a>, <a class="txt" href="scmfsa8c.html#E13:69_18"><i><font color="Green">E103</font></i></a>, <a class="ref" href="scmfsa8c.html#T51" target="_self">Th51</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E15:69_18"><i><font color="Green">E104</font></i></a>, <a class="ref" href="scmfsa_4.html#D1">SCMFSA_4:def 1</a></i>
;<br/><a NAME="E17:69_18"/><i><font color="Green">E106</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmfsa8c.html#E13:69_18"><i><font color="Green">E103</font></i></a>, <a class="ref" href="scmfsa8c.html#T50" target="_self">Th50</a></i>;<br/><div><i><font color="Green">E107</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="69_18_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_18_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_18_3_1"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> or <font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 </span><b>by </b><i><a class="txt" href="scmfsa8c.html#E17:69_18"><i><font color="Green">E106</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_18_3_1_1"><b>suppose </b></a><a NAME="E1:69_18_3_1_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><div class="add"><b>then </b> <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> = 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="ami_5.html#K6">ProgramPart</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmfsa8a.html#D5">SCMFSA8A:def 5</a></i>
<br/>.= 
 <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_5.html#T72">AMI_5:72</a></i>
;<br/><b>then </b><i><font color="Green">E108</font></i>: <font color="Maroon">c<sub>18</sub></font> = 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E15:69_18"><i><font color="Green">E104</font></i></a>, <a class="ref" href="scmfsa_2.html#T18">SCMFSA_2:18</a></i>
<br/>.= 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>
;<br/><a NAME="E4:69_18_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><a NAME="E5:69_18_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>hence </b><a NAME="E6:69_18_3_1_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E3:69_18_3_1_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_18_3_1_2"><b>suppose </b></a><a NAME="E1:69_18_3_1_2"/>
<font color="Maroon">c<sub>17</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:69_18_3_1_2"/><b>then </b>
 <a href="scmfsa_2.html#K5">insloc</a> <font color="Maroon">c<sub>18</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#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmfsa8c.html#E15:69_18"><i><font color="Green">E104</font></i></a>, <a class="ref" href="scmfsa8a.html#T31">SCMFSA8A:31</a></i>;<br/><a NAME="E3:69_18_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa6a.html#T15">SCMFSA6A:15</a></i>;<br/><a NAME="E4:69_18_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E5:69_18_3_1_2"/><b>then </b><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2
 <b>by </b><i><a class="ref" href="scmfsa8a.html#T34">SCMFSA8A:34</a></i>;<br/><a NAME="E6:69_18_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E7:69_18_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><b>hence </b><a NAME="E8:69_18_3_1_2"/>
<font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E5:69_18_3_1_2"><i><font color="Green">E108</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E19:69_18"/><b>then </b><i><font color="Green">E108</font></i>: 
(  <a href="scmfsa_2.html#K5">insloc</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T57" target="_self">Th57</a></i>;<br/> <a href="ami_1.html#K8">CurInstr</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D17">AMI_1:def 17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54">AMI_1:54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6">IC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p0">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>16</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa8c.html#E16:69_18"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa8c.html#E19:69_18"><i><font color="Green">E108</font></i></a>, <a class="ref" href="scmfsa8c.html#T26" target="_self">Th26</a></i>
;<br/><b>hence </b><a NAME="E21:69_18"/>
contradiction
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E1:69_18"><i><font color="Green">E98</font></i></a>, <a class="txt" href="scmfsa8c.html#E16:69_18"><i><font color="Green">E105</font></i></a>, <a class="txt" href="scmfsa8c.html#E18:69_18"><i><font color="Green">E107</font></i></a>, <a class="ref" href="scmfsa8c.html#T57" target="_self">Th57</a></i>;<br/></div><b>end;</b></div>
<a NAME="E64:69"/><b>then </b><i><font color="Green">E98</font></i>: 
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E58:69"><i><font color="Green">E96</font></i></a>, <a class="txt" href="scmfsa8c.html#E59:69"><i><font color="Green">E97</font></i></a>, <a class="ref" href="scm_1.html#D2">SCM_1:def 2</a></i>;<br/>
<a NAME="E65:69"/>
 <a href="scmfsa8a.html#K3">pseudo-LifeSpan</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K1">Directed</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="scmfsa8c.html#T58" target="_self">Th58</a></i>;<br/>
<b>hence </b><a NAME="E66:69"/>
 <a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scm_1.html#NK3" target="_self">LifeSpan</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="scmfsa6a.html#K4">';'</a> <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 3
 <b>by </b><i><a class="txt" href="scmfsa8c.html#E4:69"><i><font color="Green">E64</font></i></a>, <a class="txt" href="scmfsa8c.html#E64:69"><i><font color="Green">E98</font></i></a>, <a class="ref" href="scmfsa8c.html#T50" target="_self">Th50</a></i>;<br/>


</div>
