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<b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="scmfsa7b.html#V1">good</a> <a href="scm_halt.html#V2" target="_self">InitHalting</a> <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  <a href="sf_mastr.html#V1">read-write</a>  <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/>



<b>assume </b><a NAME="E1:97"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R4">does_not_destroy</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:97"/><i><font color="Green">E70</font></i>: 
 <a href="scmfsa8c.html#K2">Times</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa8b.html#K2">if&gt;0</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">c<sub>5</sub></font>,<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> 2</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<a href="scmfsa_4.html#K5">SCM+FSA-Stop</a> 
 
<b>by </b><i><a class="ref" href="scmfsa8c.html#D5">SCMFSA8C:def 5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:97_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1"><b>suppose </b></a><a NAME="E1:97_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:97_1_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
( <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="scmfsa6c.html#T3">SCMFSA6C:3</a></i>;<br/><a NAME="E3:97_1_1_1"/>
 <a href="scmfsa6a.html#K1">Directed</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">c<sub>5</sub></font>,<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> 2</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="scmfsa8c.html#K1">loop</a> <span class="p1">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">c<sub>5</sub></font>,<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> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa8a.html#T40">SCMFSA8A:40</a></i>;<br/><a NAME="E4:97_1_1_1"/><b>then </b>
 <a href="scmfsa6a.html#K1">Directed</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K1">loop</a> <span class="p2">(<span class="default"><a href="scmfsa8b.html#K1">if=0</a> <font color="Maroon">c<sub>5</sub></font>,<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> 2</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="scmfsa6a.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>5</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="scmfsa8a.html#R1">is_pseudo-closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:97"><i><font color="Green">E69</font></i></a>, <a class="txt" href="scm_halt.html#E2:97_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scm_halt.html#T73" target="_self">Th73</a></i>;<br/><a NAME="E5:97_1_1_1"/><b>then </b>
 <a href="scmfsa8c.html#K2">Times</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:97"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scm_halt.html#E2:97_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmfsa8c.html#T68">SCMFSA8C:68</a></i>;<br/><b>hence </b><a NAME="E6:97_1_1_1"/>
 <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K2">Times</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa7b.html#R6">is_halting_on</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T22">SCMFSA8C:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_2"><b>suppose </b></a><a NAME="E1:97_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:97_1_1_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="scmfsa_2.html#K20">.</a> <font color="Maroon">c<sub>5</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/><a NAME="E3:97_1_1_2"/>
(  <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a>  <a href="scmfsa7b.html#R5">is_closed_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="scmfsa_4.html#K5">SCM+FSA-Stop</a>  <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T24">SCMFSA7B:24</a>, <a class="ref" href="scmfsa7b.html#T25">SCMFSA7B:25</a></i>;<br/><a NAME="E4:97_1_1_2"/><b>then </b>
 <a href="scmfsa8c.html#K2">Times</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmfsa7b.html#R6">is_halting_on</a>  <a href="scmfsa6c.html#K1">Initialize</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:97"><i><font color="Green">E70</font></i></a>, <a class="txt" href="scm_halt.html#E2:97_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmfsa8b.html#T24">SCMFSA8B:24</a></i>;<br/><b>hence </b><a NAME="E5:97_1_1_2"/>
 <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K2">Times</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="scmfsa7b.html#R6">is_halting_on</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T22">SCMFSA8C:22</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:97"/>
 <a href="scmfsa6a.html#K3">Initialized</a> <span class="p1">(<span class="default"><a href="scmfsa8c.html#K2">Times</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="ami_1.html#V12">halting</a>
 <b>by </b><i><a class="ref" href="scmfsa8c.html#T24">SCMFSA8C:24</a></i>;<br/>


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