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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="scmring1.html#V1" title="SCMRING1:attr.1">good</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</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#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>  st <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> holds <br/><font color="Olive" title="b1">I</font> is  <a href="extpro_1.html#V2" title="EXTPRO_1:attr.2">halting</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</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="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> implies <font color="Maroon" title="c2">I</font> is  <a href="extpro_1.html#V2" title="EXTPRO_1:attr.2">halting</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:26"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
<font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</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="c2">I</font> is  <a href="extpro_1.html#V2" title="EXTPRO_1:attr.2">halting</a> </span><br/>

<a NAME="E2:26"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c2">I</font> <a href="recdef_2.html#K3" title="RECDEF_2:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="recdef_2.html#D3" title="RECDEF_2:def.3">RECDEF_2:def 3</a></span>;<br/>
<a NAME="E3:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A3</font></span>: 
( (  for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>   holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">ml</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> ) &amp; (  for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>   holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">2,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">ml</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D3" title="RECDEF_2:def.3">RECDEF_2:def 3</a></span>;<br/>
<a NAME="E4:26"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
 for <font color="Olive" title="b1">mk</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> <br/>  for <font color="Olive" title="b2">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">5,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">r</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="recdef_2.html#D3" title="RECDEF_2:def.3">RECDEF_2:def 3</a></span>;<br/>
<a NAME="E5:26"/>
<font color="Maroon" title="c2">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/>
<a NAME="E6:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A5</font></span>: 
( (  for <font color="Olive" title="b1">mk</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">6,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> ) &amp; (  for <font color="Olive" title="b1">mk</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/>  for <font color="Olive" title="b2">ml</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>   holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">7,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">ml</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">L</font> = <font color="Maroon" title="c2">I</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="scmring1.html#T18" title="SCMRING1:th.18">SCMRING1:18</a></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 <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D3" title="EXTPRO_1:def.3">EXTPRO_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E8:26"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
 the <a href="memstr_0.html#U1" title="MEMSTR_0:sel.1">Object-Kind</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="scmring1.html#K2" title="SCMRING1:func.2">SCM-OK</a> <font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">t</font> = <font color="Maroon" title="c4">s</font> as   <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Maroon" title="c1">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:26"><span class="lab"><font color="Green" title="E24">A6</font></span></a>, <a class="ref" href="card_3.html#T107" title="CARD_3:th.107">CARD_3:107</a></span>;<br/>
<a NAME="E10:26"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
( (  for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>   holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">3,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">ml</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> ) &amp; (  for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>   holds  not <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">4,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">ml</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="recdef_2.html#D3" title="RECDEF_2:def.3">RECDEF_2:def 3</a></span>;<br/>
<span class="kw">thus </span> <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c4">s</font>) = 
 <a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> (<font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c5">t</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmring2.html#T10" target="_self" title="SCMRING2:th.10">Th12</a></span>
<br/>.= 
<font color="Maroon" title="c4">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E10:26"><span class="lab"><font color="Green" title="E25">A7</font></span></a>, <a class="txt" href="#E6:26"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="ami_3.html#T27" title="AMI_3:th.27">AMI_3:27</a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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