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<span class="kw">set </span><font color="Maroon" title="c2">SAt</font> =  <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>);<br/>
<span class="kw">let </span><font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c3">I</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  iff  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">P</font> being   <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> holds  <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">P</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:34"/>
( <font color="Maroon" title="c3">I</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  implies  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">P</font> being   <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> holds  <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">P</font> )
  <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">P</font> being   <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> holds  <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">P</font> ) implies <font color="Maroon" title="c3">I</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:34_1"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c3">I</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</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">P</font> being   <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> holds  <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">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">P</font> being   <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> holds  <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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"> <font color="Maroon" title="c3">I</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="c5">P</font></span><br/>



<a NAME="E2:34_1"/>
<font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">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/>
<span class="kw">hence </span><a NAME="E3:34_1"/>
<font color="Maroon" title="c5">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">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="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="scmfsa7b.html#D7" target="_self" title="SCMFSA7B:def.7">SCMFSA7B:def 7</a> <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="E2:34"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
 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">P</font> being   <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> holds  <font color="Maroon" title="c3">I</font> <a href="scmfsa7b.html#R6" title="SCMFSA7B:pred.6">is_halting_on</a> <font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">P</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="c3">I</font> is  <a href="amistd_1.html#V7" title="AMISTD_1:attr.7">parahalting</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_1.html#D11" title="AMISTD_1:def.11">AMISTD_1:def 11</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font> )</span><br/>

<a NAME="E3:34"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 <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>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T29" title="MEMSTR_0:th.29">MEMSTR_0:29</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">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"> (  not <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</font> or <font color="Maroon" title="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:34"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</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="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E5:34"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<font color="Maroon" title="c5">P</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c5">P</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c3">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>;<br/>
<a NAME="E6:34"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c4">s</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>;<br/>
<a NAME="E7:34"/>
<font color="Maroon" title="c3">I</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="c5">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34"><span class="lab"><font color="Green" title="E16">A4</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:34"/>
<font color="Maroon" title="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:34"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E6:34"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="scmfsa7b.html#D7" target="_self" title="SCMFSA7B:def.7">Def8</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>
