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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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b2">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b2">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">P</font> holds <br/>(  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> holds <br/>(  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> holds <br/>(  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> implies (  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:28"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<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="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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="c6">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> or  not <font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> or (  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> ) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E3:28"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c6">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</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#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> )</span><br/>

<a NAME="E4:28"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
 <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c7">J</font>,<font color="Maroon" title="c6">I</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</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="#E1:28"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th24</a></span>;<br/>
<a NAME="E5:28"/>
 <a href="scmfsa8b.html#K2" title="SCMFSA8B:func.2">if&gt;0</a> (<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c7">J</font>,<font color="Maroon" title="c6">I</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</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="#E1:28"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="scmfsa8b.html#T21" target="_self" title="SCMFSA8B:th.21">Th24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:28"/>
(  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <font color="Maroon" title="c5">s</font>,<font color="Maroon" title="c4">P</font> &amp;  <a href="scmfsa8b.html#K3" title="SCMFSA8B:func.3">if&lt;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> <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="#E1:28"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="scmfsa8b.html#T15" target="_self" title="SCMFSA8B:th.15">Th18</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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