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<span class="kw">let </span><font color="Maroon" title="c3">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  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b2">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b3">J</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">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="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">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="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Maroon" title="c3">P</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">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  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b1">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Olive" title="b2">J</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">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="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">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="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font>, <font color="Maroon" title="c6">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  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c5">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">J</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">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="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">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="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">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"> (  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c5">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">J</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> implies (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:44"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
 <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c5">I</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">J</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> or (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E2:44"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 <a href="scmfsa6a.html#K2" title="SCMFSA6A:func.2">Directed</a> <font color="Maroon" title="c6">J</font> <a href="scmfsa8a.html#R1" title="SCMFSA8A:pred.1">is_pseudo-closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">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="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:44_1_1"/>
( <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c7">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>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_1"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"> (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:44_1_1_1"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="ref" href="scmfsa8c.html#T37" target="_self" title="SCMFSA8C:th.37">Th66</a></span>; <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="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font></span><br/><span class="kw">thus </span><a NAME="E3:44_1_1_1"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:44"><span class="lab"><font color="Green" title="E37">A1</font></span></a>, <a class="txt" href="#E1:44_1_1_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="scmfsa8c.html#T37" target="_self" title="SCMFSA8C:th.37">Th66</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:44_1_1_2"/><span class="lab"><font color="Green" title="E39">A4</font></span>: 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Maroon" title="c7">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"> (  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> &amp;  <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:44_1_1_2"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="ref" href="scmfsa8c.html#T41" target="_self" title="SCMFSA8C:th.41">Th70</a></span>; <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="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font></span><br/><span class="kw">thus </span><a NAME="E3:44_1_1_2"/>
 <a href="scmfsa8b.html#K1" title="SCMFSA8B:func.1">if=0</a> (<font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">I</font>,<font color="Maroon" title="c6">J</font>) <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c3">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:44"><span class="lab"><font color="Green" title="E38">A2</font></span></a>, <a class="txt" href="#E1:44_1_1_2"><span class="lab"><font color="Green" title="E39">A4</font></span></a>, <a class="ref" href="scmfsa8c.html#T41" target="_self" title="SCMFSA8C:th.41">Th70</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div>


</div>
