<?xml version="1.0"?>
<div class="add">

<b>thus </b><a NAME="E1:41_1_1"/>
 <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> is <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c2">I</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as   <a href="ami_1.html#NM4" title="AMI_1:NM.4">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> <b>by </b><i><a class="ref" href="scmring2.html#T3" target="_self" title="SCMRING2:th.3">Th3</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">I</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D9" title="AMI_1:def.9">AMI_1:def 9</a><br/>

<b>thus </b><a NAME="E2:41_1_1_1"/>
<font color="Maroon" title="c2">I</font> is <a href="ami_1.html#V3" title="AMI_1:attr.3">halting</a>
 <b>by </b><i><a class="ref" href="scmring2.html#T21" target="_self" title="SCMRING2:th.21">Th21</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:41_1_1"/>
 <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> is <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">l</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D14" title="AMI_1:def.14">AMI_1:def 14</a><br/>

<b>reconsider </b><font color="Maroon" title="c3">L</font> = <font color="Maroon" title="c2">l</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<b>thus </b> <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c2">l</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K2" title="SCMRING1:func.2">SCM-OK</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">L</font>
<b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>
<br/>.= 
 <a href="scmring1.html#K1" title="SCMRING1:func.1">SCM-Instr</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="ref" href="scmring1.html#T6" title="SCMRING1:th.6">SCMRING1:6</a></i>
<br/>.= 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</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>
<b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>
;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:41_1_1"/>
 <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font> is <a href="ami_1.html#V6" title="AMI_1:attr.6">steady-programmed</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">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>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D13" title="AMI_1:def.13">AMI_1:def 13</a><br/><b>let </b><font color="Maroon" title="c3">j</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">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>;<br/><b>let </b><font color="Maroon" title="c4">l</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Maroon" title="c1">R</font>;<br/>





<b>reconsider </b><font color="Maroon" title="c5">c</font> = <font color="Maroon" title="c3">j</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> <b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>;<br/>
<a NAME="E2:41_1_1_3"/>
( <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">{<span class="default"> <span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I</font>,<span class="p5"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">6,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Olive" title="b2">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p3"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b2">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> : verum </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:41_1_1_3"/><b>then </b>
( <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I</font>,<span class="p4"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">6,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Olive" title="b2">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p3"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b2">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> : verum </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:41_1_1_3"/><b>then </b><i><font color="Green" title="E28">A1</font></i>: 
( <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I</font>,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">6,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Olive" title="b2">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p3"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b2">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> : verum </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">S</font> = <font color="Maroon" title="c2">s</font> as   <a href="scmring1.html#NM1" title="SCMRING1:NM.1">SCM-State</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">l'</font> = <font color="Maroon" title="c4">l</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<i><font color="Green" title="E29">A2</font></i>:  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c2">s</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmring1.html#K16" title="SCMRING1:func.16">SCM-Exec</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">S</font>
<b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>
<br/>.= 
 <a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font>
<b>by </b><i><a class="ref" href="scmring1.html#D15" title="SCMRING1:def.15">SCMRING1:def 15</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_3_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_3_2_1"/>
( <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">6,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Olive" title="b2">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I</font>,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p3"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b2">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> : verum </span>}</span>  )
 </span><b>by </b><i><a class="txt" href="scmring2.html#E4:41_1_1_3"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_1"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_1"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:41_1_1_3_2_1_1"/><b>then </b>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:41_1_1_3_2_1_1"/><b>then </b>
<font color="Maroon" title="c5">c</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><a NAME="E4:41_1_1_3_2_1_1"/><b>then </b>
( ( for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   holds not <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,<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="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp; ( for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   holds not <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,<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="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp; ( for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   holds not <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,<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="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp; ( for <font color="Olive" title="b1">mk</font>, <font color="Olive" title="b2">ml</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   holds not <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">4,<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="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp; ( for <font color="Olive" title="b1">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   holds not <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</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></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp; ( for <font color="Olive" title="b1">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b2">ml</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   holds not <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<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="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) &amp; ( for <font color="Olive" title="b1">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</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="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p2"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">mk</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/><b>hence </b><a NAME="E5:41_1_1_3_2_1_1"/>
<span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
 <b>by </b><i><a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_2"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_2"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">6,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  : verum </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c8">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:41_1_1_3_2_1_2"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</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="Maroon" title="c8">i</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:41_1_1_3_2_1_2"/>
verum
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K9" title="SCMRING1:func.9">jump_address</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_2"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_3"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_3"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">i</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Olive" title="b2">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c8">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Maroon" title="c9">a</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:41_1_1_3_2_1_3"/><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">7,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">i</font>,<font color="Maroon" title="c9">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:41_1_1_3_2_1_3"/>
verum
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><a href="funcop_1.html#K15" title="FUNCOP_1:func.15">IFEQ</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K11" title="SCMRING1:func.11">cond_address</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K10" title="SCMRING1:func.10">cjump_address</a> </span>)</span>,<span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p4">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c6">S</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_3"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_4"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_4"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">I</font>,<span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">I</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c8">I</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 8, <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c10">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:41_1_1_3_2_1_4"/><i><font color="Green" title="E30">A5</font></i>: 
( <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">I</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c8">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_3_2_1_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_1_1_3_2_1_4_1_1"/>
( <font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 )
 </span><b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_4"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_4_1_1_1"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_4_1_1_1"/>
<font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c6">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_4"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T16" title="SCMRING1:th.16">SCMRING1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_4_1_1_2"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_4_1_1_2"/>
<font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c6">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_4"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T16" title="SCMRING1:th.16">SCMRING1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_4_1_1_3"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_4_1_1_3"/>
<font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c6">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_4"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T16" title="SCMRING1:th.16">SCMRING1:16</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_4_1_1_4"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_4_1_1_4"/>
<font color="Maroon" title="c8">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c6">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_4"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K7" title="SCMRING1:func.7">address_1</a> </span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">S</font> <a href="scmring1.html#K6" title="SCMRING1:func.6">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K8" title="SCMRING1:func.8">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T16" title="SCMRING1:th.16">SCMRING1:16</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:41_1_1_3_2_1_4"/>
<span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_3_2_1_5"><b>case </b></a><a NAME="E1:41_1_1_3_2_1_5"/>
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p3"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b2">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> : verum </span>}</span> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c8">a</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c9">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E3:41_1_1_3_2_1_5"/><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">5,<span class="p2"><a href="scmring1.html#K12" title="SCMRING1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">r</font></span><a href="scmring1.html#K12" title="SCMRING1:func.12">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>and </b><br/><a NAME="E4:41_1_1_3_2_1_5"/>
verum
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmring1.html#K15" title="SCMRING1:func.15">SCM-Exec-Res</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font> = 
<span class="p1">(<span class="default"><a href="scmring1.html#K4" title="SCMRING1:func.4">SCM-Chg</a> <span class="p2">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K14" title="SCMRING1:func.14">const_value</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">succ</a> <span class="p3">(<span class="default"><a href="scmring1.html#K3" title="SCMRING1:func.3">IC</a> <font color="Maroon" title="c6">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="txt" href="scmring2.html#E3:41_1_1_3_2_1_5"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="scmring1.html#D14" title="SCMRING1:def.14">SCMRING1:def 14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmring1.html#K5" title="SCMRING1:func.5">SCM-Chg</a> <font color="Maroon" title="c6">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K13" title="SCMRING1:func.13">const_address</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="scmring1.html#K14" title="SCMRING1:func.14">const_value</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T12" title="SCMRING1:th.12">SCMRING1:12</a></i>
<br/>.= 
<font color="Maroon" title="c6">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">l'</font>
<b>by </b><i><a class="ref" href="scmring1.html#T16" title="SCMRING1:th.16">SCMRING1:16</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E9:41_1_1_3"/>
<font color="Maroon" title="c2">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c2">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">l</font>
 <b>by </b><i><a class="txt" href="scmring2.html#E7:41_1_1_3"><i><font color="Green" title="E29">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>

<a NAME="E4:41_1_1"/><i><font color="Green" title="E28">A7</font></i>: 
the <a href="ami_1.html#U1" title="AMI_1:sel.1">Instruction-Counter</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="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="scmring2.html#D1" target="_self" title="SCMRING2:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E5:41_1_1"/>
the <a href="ami_1.html#U1" title="AMI_1:sel.1">Instruction-Counter</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="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D21" title="AMI_1:def.21">AMI_1:def 21</a><br/>

<b>hence </b><a NAME="E6:41_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="scmring2.html#E4:41_1_1"><i><font color="Green" title="E28">A7</font></i></a></i>;<br/>


</div>
