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<span class="kw">let </span><font color="Maroon" title="c4">p</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">I</font>, <font color="Olive" title="b3">J</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b4">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Olive" title="b1">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b3">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Olive" title="b3">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">p</font> holds <br/>(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b4">a</font>,<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">p</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">s</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font> being   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b3">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Olive" title="b2">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> holds <br/>(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">I</font>, <font color="Maroon" title="c7">J</font> be   <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>   st <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> holds <br/>(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Olive" title="b1">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">a</font> be   <a href="sf_mastr.html#NV2" title="SF_MASTR:NV.2">read-write</a>   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> implies (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c9">Is</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font>;<br/>
<span class="kw">assume </span><a NAME="E1:58"/>
<font color="Maroon" title="c5">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> or  not <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> or (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> ) )</span><br/>

<a NAME="E2:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font></span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6c.html#T3" title="SCMFSA6C:th.3">SCMFSA6C:3</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:58"/>
<font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> or (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> ) )</span><br/>

<a NAME="E4:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<font color="Maroon" title="c7">J</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T30" target="_self" title="SCM_HALT:th.30">Th40</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:58"/>
<font color="Maroon" title="c7">J</font> <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> )</span><br/>

<a NAME="E6:58"/><span class="kw">then </span>
<font color="Maroon" title="c7">J</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T31" target="_self" title="SCM_HALT:th.31">Th41</a></span>;<br/>
<a NAME="E7:58"/><span class="kw">then </span>
(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:58"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="scmfsa8b.html#T15" title="SCMFSA8B:th.15">SCMFSA8B:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:58"/>
(  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c7">J</font>) <a href="scm_halt.html#R2" title="SCM_HALT:pred.2">is_halting_onInit</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">p</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#T30" target="_self" title="SCM_HALT:th.30">Th40</a>, <a class="ref" href="scm_halt.html#T31" target="_self" title="SCM_HALT:th.31">Th41</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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