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<span class="kw">let </span><font color="Maroon" title="c4">P1</font>, <font color="Maroon" title="c5">P2</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">s1</font>, <font color="Olive" title="b2">s2</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="b3">I</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>  st  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Olive" title="b2">s2</font> &amp; <font color="Olive" title="b3">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Olive" title="b1">s1</font>,<font color="Maroon" title="c4">P1</font> &amp; <font color="Olive" title="b3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s1</font>,<font color="Maroon" title="c4">P1</font> holds <br/>( <font color="Olive" title="b3">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Olive" title="b2">s2</font>,<font color="Maroon" title="c5">P2</font> &amp; <font color="Olive" title="b3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b2">s2</font>,<font color="Maroon" title="c5">P2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</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> 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>  st  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c7">s2</font> &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="c6">s1</font>,<font color="Maroon" title="c4">P1</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="c6">s1</font>,<font color="Maroon" title="c4">P1</font> holds <br/>( <font color="Olive" title="b1">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</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="c7">s2</font>,<font color="Maroon" title="c5">P2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c8">I</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"> (  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c7">s2</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</font> implies ( <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c9">S1</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">S2</font> =  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,$1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,$1)</span>)</span> &amp;  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,$1)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,$1)</span>)</span>) &amp;  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,$1)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,$1)</span>)</span> );<br/>
<a NAME="E1:4"/><span class="lab"><font color="Green" title="E6">A4</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>;<br/>
<a NAME="E2:4"/><span class="lab"><font color="Green" title="E7">C5</font></span>: 
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T15" title="MEMSTR_0:th.15">MEMSTR_0:15</a></span>;<br/>
<span class="lab"><font color="Green" title="E8">A6</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E7">C5</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
;<br/>
<a NAME="E4:4"/><span class="lab"><font color="Green" title="E9">A7</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E10">A8</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E7">C5</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E6:4"/>
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c7">s2</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="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</font> or  not <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</font> or ( <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> ) )</span><br/>

<a NAME="E7:4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A9</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E9">A7</font></span></a>, <a class="ref" href="scmfsa8b.html#T4" target="_self" title="SCMFSA8B:th.4">Th7</a></span>;<br/>
<span class="kw">assume </span><a NAME="E8:4"/><span class="lab"><font color="Green" title="E12">A10</font></span>: 
<font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</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="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</font> or ( <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> ) )</span><br/>

<div><span class="lab"><font color="Green" title="E13">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="4_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/><span class="lab"><font color="Green" title="E14">A12</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span>)

;<br/><span class="kw">assume </span><a NAME="E2:4_3"/><span class="lab"><font color="Green" title="E15">A13</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><a NAME="E3:4_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A14</font></span>: 
 for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T7" title="SCMFSA6A:th.7">SCMFSA6A:7</a></span>;<br/><a NAME="E4:4_3"/>
 for <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span> <a href="scmfsa_2.html#K18" title="SCMFSA_2:func.18">.</a> <font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4_3"><span class="lab"><font color="Green" title="E15">A13</font></span></a>, <a class="ref" href="scmfsa6a.html#T7" title="SCMFSA6A:th.7">SCMFSA6A:7</a></span>;<br/><a NAME="E5:4_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A15</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">k</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4_3"><span class="lab"><font color="Green" title="E15">A13</font></span></a>, <a class="txt" href="#E3:4_3"><span class="lab"><font color="Green" title="E16">A14</font></span></a>, <a class="ref" href="scmfsa_2.html#T61" title="SCMFSA_2:th.61">SCMFSA_2:61</a></span>;<br/><a NAME="E6:4_3"/><span class="lab"><font color="Green" title="E18">A16</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:4"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="ref" href="scmfsa7b.html#D6" title="SCMFSA7B:def.6">SCMFSA7B:def 6</a></span>;<br/> <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">k</font>)</span>)</span>)

;<br/><a NAME="E8:4_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A17</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4_3"><span class="lab"><font color="Green" title="E15">A13</font></span></a>, <a class="txt" href="#E5:4_3"><span class="lab"><font color="Green" title="E17">A15</font></span></a>, <a class="txt" href="#E1:4_3"><span class="lab"><font color="Green" title="E14">A12</font></span></a></span>;<br/><a NAME="E9:4_3"/><span class="lab"><font color="Green" title="E20">A18</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:4_3"><span class="lab"><font color="Green" title="E19">A17</font></span></a></span>;<br/><a NAME="E10:4_3"/><span class="lab"><font color="Green" title="E21">A19</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/><a NAME="E11:4_3"/><span class="lab"><font color="Green" title="E22">A20</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/><a NAME="E12:4_3"/><span class="lab"><font color="Green" title="E23">A21</font></span>: 
<font color="Maroon" title="c8">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/><a NAME="E13:4_3"/><span class="lab"><font color="Green" title="E24">A22</font></span>: 
<font color="Maroon" title="c8">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/> <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
<font color="Maroon" title="c8">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:4_3"><span class="lab"><font color="Green" title="E18">A16</font></span></a>, <a class="txt" href="#E10:4_3"><span class="lab"><font color="Green" title="E21">A19</font></span></a>, <a class="txt" href="#E12:4_3"><span class="lab"><font color="Green" title="E23">A21</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:4_3"><span class="lab"><font color="Green" title="E20">A18</font></span></a>, <a class="txt" href="#E6:4_3"><span class="lab"><font color="Green" title="E18">A16</font></span></a>, <a class="txt" href="#E11:4_3"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E13:4_3"><span class="lab"><font color="Green" title="E24">A22</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
;<br/><span class="kw">hence </span><a NAME="E15:4_3"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c11">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:4_3"><span class="lab"><font color="Green" title="E19">A17</font></span></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>
<span class="kw">assume </span><a NAME="E10:4"/>
<font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c4">P1</font>
 ; <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="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> &amp; <font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font> )</span><br/>

<a NAME="E11:4"/><span class="kw">then </span>
<font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#D7" title="SCMFSA7B:def.7">SCMFSA7B:def 7</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E13:4"/><span class="lab"><font color="Green" title="E14">A23</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c11">m</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T29" title="EXTPRO_1:th.29">EXTPRO_1:29</a></span>;<br/>
<a NAME="E14:4"/><span class="lab"><font color="Green" title="E15">A24</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/>
<a NAME="E15:4"/><span class="lab"><font color="Green" title="E16">A25</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p3">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/>
<a NAME="E16:4"/><span class="lab"><font color="Green" title="E17">A26</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:4"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="ref" href="scmfsa8b.html#T1" target="_self" title="SCMFSA8B:th.1">Th3</a></span>;<br/>
<span class="kw">then </span> <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>) = 
<font color="Maroon" title="c8">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E8">A6</font></span></a>, <a class="txt" href="#E14:4"><span class="lab"><font color="Green" title="E15">A24</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
<br/>.= 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:4"><span class="lab"><font color="Green" title="E10">A8</font></span></a>, <a class="txt" href="#E16:4"><span class="lab"><font color="Green" title="E17">A26</font></span></a>, <a class="txt" href="#E15:4"><span class="lab"><font color="Green" title="E16">A25</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>
;<br/>
<a NAME="E18:4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A27</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:4"><span class="lab"><font color="Green" title="E11">A9</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">I</font></span><br/><a NAME="E1:4_5"/><span class="lab"><font color="Green" title="E19">A28</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c4">P1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c6">s1</font></span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:4"><span class="lab"><font color="Green" title="E12">A10</font></span></a>, <a class="ref" href="scmfsa7b.html#D6" title="SCMFSA7B:def.6">SCMFSA7B:def 6</a></span>;<br/><a NAME="E2:4_5"/>
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E18:4"><span class="lab"><font color="Green" title="E18">A27</font></span></a>, <a class="txt" href="#E9:4"><span class="lab"><font color="Green" title="E13">A11</font></span></a>);<br/></span><span class="kw">hence </span><a NAME="E3:4_5"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c12">k</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4_5"><span class="lab"><font color="Green" title="E19">A28</font></span></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>
<span class="kw">hence </span><a NAME="E20:4"/>
<font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R5" title="SCMFSA7B:pred.5">is_closed_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#D6" title="SCMFSA7B:def.6">SCMFSA7B:def 6</a></span>; <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="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font></span><br/>

<a NAME="E21:4"/>
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E18:4"><span class="lab"><font color="Green" title="E18">A27</font></span></a>, <a class="txt" href="#E9:4"><span class="lab"><font color="Green" title="E13">A11</font></span></a>);<br/></span>
<a NAME="E22:4"/><span class="kw">then </span>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font></span>)</span>,<font color="Maroon" title="c11">m</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:4"><span class="lab"><font color="Green" title="E14">A23</font></span></a></span>;<br/>
<a NAME="E23:4"/><span class="kw">then </span>
<font color="Maroon" title="c5">P2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c8">I</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c7">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T29" title="EXTPRO_1:th.29">EXTPRO_1:29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:4"/>
<font color="Maroon" title="c8">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c5">P2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa7b.html#D7" title="SCMFSA7B:def.7">SCMFSA7B:def 7</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>
