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<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><br/>  for <font color="Olive" title="b2">I</font> being   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <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">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>   st  not <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Olive" title="b2">I</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b2">I</font>,<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b3">f</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">  for <font color="Olive" title="b1">I</font> being   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <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="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>   st  not <font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Olive" title="b1">I</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Olive" title="b1">I</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b2">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">I</font> be   <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a>  <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">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>   st  not <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c6">I</font> holds <br/><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">s</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> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c6">I</font> implies <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font> )</span><br/>







<a NAME="E1:11"/>
( <font color="Maroon" title="c7">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> &amp; <font color="Maroon" title="c7">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T57" title="SCMFSA_2:th.57">SCMFSA_2:57</a>, <a class="ref" href="scmfsa_2.html#T58" title="SCMFSA_2:th.58">SCMFSA_2:58</a></span>;<br/>
<a NAME="E2:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">B1</font></span>: 
 not <font color="Maroon" title="c7">f</font> <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#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6a.html#T42" title="SCMFSA6A:th.42">SCMFSA6A:42</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E3:11"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa6b.html#D1" title="SCMFSA6B:def.1">SCMFSA6B:def 1</a></span>;<br/>
<a NAME="E4:11"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="scmfsa_3.html#K1" title="SCMFSA_3:func.1">.--&gt;</a> 1</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</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="E5:11"/>
<font color="Maroon" title="c6">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="c6">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="E6:11"/><span class="kw">then </span>
<font color="Maroon" title="c5">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#D2" target="_self" title="SCM_HALT:def.2">Def2</a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E11">A3</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">n</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="E8:11"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></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">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Maroon" title="c8">n</font>)
 <span class="kw">and </span><br/><a NAME="E9:11"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c5">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>)</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#D9" title="EXTPRO_1:def.9">EXTPRO_1:def 9</a></span>;<br/>
<a NAME="E10:11"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
<font color="Maroon" title="c6">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="c6">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="E11:11"/><span class="lab"><font color="Green" title="E14">A7</font></span>: 
 for <font color="Olive" title="b1">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>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">n</font> holds <br/> <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">p</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c6">I</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span>,<font color="Olive" title="b1">m</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="c6">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_halt.html#D1" target="_self" title="SCM_HALT:def.1">Def1</a>, <a class="txt" href="#E10:11"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E11">A3</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E12:11"/>
 not <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K4" title="SF_MASTR:func.4">UsedInt*Loc</a> <font color="Maroon" title="c6">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font></span><br/>

<span class="kw">hence </span><span class="p1">(<span class="default"><a href="scmfsa6b.html#K2" title="SCMFSA6B:func.2">IExec</a> (<font color="Maroon" title="c6">I</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c4">s</font>)</span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font> = 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c4">s</font></span>)</span> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E8:11"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E11:11"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a>, <a class="ref" href="sf_mastr.html#T63" title="SF_MASTR:th.63">SF_MASTR:63</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font> <a href="scmfsa_2.html#K19" title="SCMFSA_2:func.19">.</a> <font color="Maroon" title="c7">f</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E9">B1</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
;<br/> <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>
