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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:54_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="scm_halt.html#V2" target="_self">InitHalting</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/><a NAME="E2:54_1"/><i><font color="Green">E40</font></i>: 
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</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"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/><a NAME="E3:54_1"/>
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font> is <a href="ami_1.html#V12">halting</a>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:54_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="scm_halt.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E4:54_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:54_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/><b>hence </b><a NAME="E5:54_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2" target="_self">is_halting_onInit</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="scm_halt.html#D5" target="_self">Def5</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:54"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds <font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2" target="_self">is_halting_onInit</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><b>now </b></a><div class="add"><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>assume </b><a NAME="E1:54_2"/>
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:54_2"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="scm_halt.html#R2" target="_self">is_halting_onInit</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</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"><a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:54"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/><b>hence </b><a NAME="E3:54_2"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="ami_1.html#V9">halting</a>
 <b>by </b><i><a class="ref" href="scm_halt.html#D5" target="_self">Def5</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:54"/><b>then </b>
 <a href="scmfsa6a.html#K3">Initialized</a> <font color="Maroon">c<sub>2</sub></font> is <a href="ami_1.html#V12">halting</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D26">AMI_1:def 26</a></i>;<br/>
<b>hence </b><a NAME="E5:54"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="scm_halt.html#V2" target="_self">InitHalting</a>
 <b>by </b><i><a class="ref" href="scm_halt.html#D2" target="_self">Def2</a></i>;<br/>


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