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

<span class="kw">let </span><font color="Maroon" title="c1">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <br/> for <font color="Olive" title="b2">l</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  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b2">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</font> be   <a href="ami_1.html#NM2" title="AMI_1:NM.2">Instruction</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">l</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  <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Olive" title="b1">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c3">l</font></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">c</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="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">S</font> = <font color="Maroon" title="c1">s</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <a href="ami_2.html#K7" title="AMI_2:func.7">SCM-OK</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T155" title="PBOOLE:th.155">PBOOLE:155</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">l9</font> = <font color="Maroon" title="c3">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>  ;<br/>
<a NAME="E4:36"/>
( <font color="Maroon" title="c4">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="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</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">Y</font>,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a2</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">Y</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> 9, <font color="Olive" title="b2">a2</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="b1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </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"><font color="Olive" title="b1">K</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">a1</font>,<font color="Olive" title="b3">b1</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">K</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> 9, <font color="Olive" title="b2">a1</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="b3">b1</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">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c4">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">T</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">b2</font>,<font color="Olive" title="b3">c1</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">T</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> 9, <font color="Olive" title="b2">b2</font>, <font color="Olive" title="b3">c1</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">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E5:36"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A1</font></span>: 
( <font color="Maroon" title="c4">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="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</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">Y</font>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a2</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">Y</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> 9, <font color="Olive" title="b2">a2</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="b1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span>  or <font color="Maroon" title="c4">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">K</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">a1</font>,<font color="Olive" title="b3">b1</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">K</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> 9, <font color="Olive" title="b2">a1</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="b3">b1</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">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c4">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">T</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">b2</font>,<font color="Olive" title="b3">c1</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">T</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> 9, <font color="Olive" title="b2">b2</font>, <font color="Olive" title="b3">c1</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">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1"/>
( <font color="Maroon" title="c4">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="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</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="c4">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">Y</font>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a2</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">Y</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> 9, <font color="Olive" title="b2">a2</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="b1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span>  or <font color="Maroon" title="c4">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">K</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">a1</font>,<font color="Olive" title="b3">b1</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">K</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> 9, <font color="Olive" title="b2">a1</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="b3">b1</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">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c4">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">T</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">b2</font>,<font color="Olive" title="b3">c1</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">T</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> 9, <font color="Olive" title="b2">b2</font>, <font color="Olive" title="b3">c1</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">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1"><span class="kw">case </span></a><a NAME="E1:36_1_1_1"/>
<font color="Maroon" title="c4">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="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><a NAME="E2:36_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">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="ami_2.html#K1" title="AMI_2:func.1">SCM-Halt</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 class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:36_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c4">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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E4:36_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A3</font></span>: 
( ( 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="c4">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="c4">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> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E5:36_1_1_1"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
( ( 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="c4">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#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="c4">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">8,<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> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E6:36_1_1_1"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
( ( 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="c4">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="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="c4">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> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E7:36_1_1_1"/>
( ( 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="c4">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="c4">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> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E8:36_1_1_1"/>
<span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_1"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E6:36_1_1_1"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E5:36_1_1_1"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_2"><span class="kw">case </span></a><a NAME="E1:36_1_1_2"/>
<font color="Maroon" title="c4">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">Y</font>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a2</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">Y</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> 9, <font color="Olive" title="b2">a2</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="b1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><a NAME="E2:36_1_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">Y</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> 9 ex <font color="Olive" title="b2">a2</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>  st <br/>( <font color="Maroon" title="c4">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="Olive" title="b1">Y</font>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a2</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; <font color="Olive" title="b1">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 )
 ;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K13" title="AMI_2:func.13">jump_address</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3"><span class="kw">case </span></a><a NAME="E1:36_1_1_3"/>
<font color="Maroon" title="c4">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">K</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">a1</font>,<font color="Olive" title="b3">b1</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">K</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> 9, <font color="Olive" title="b2">a1</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="b3">b1</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">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">K</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> 9, <font color="Maroon" title="c8">a1</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">b1</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> <span class="kw"> such that </span><br/><a NAME="E3:36_1_1_3"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<font color="Maroon" title="c4">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="c7">K</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">a1</font>,<font color="Maroon" title="c9">b1</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>
 <span class="kw">and </span><br/><a NAME="E4:36_1_1_3"/><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<font color="Maroon" title="c7">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">7,8</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_3_1_1"/>
( <font color="Maroon" title="c7">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or <font color="Maroon" title="c7">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_3"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_1_1"><span class="kw">case </span></a><a NAME="E1:36_1_1_3_1_1_1"/>
<font color="Maroon" title="c7">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <font color="Maroon" title="c5">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="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K15" title="AMI_2:func.15">cond_address</a> </span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K14" title="AMI_2:func.14">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_3"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_3_1_1_2"><span class="kw">case </span></a><a NAME="E1:36_1_1_3_1_1_2"/>
<font color="Maroon" title="c7">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><a href="xxreal_0.html#K5" title="XXREAL_0:func.5">IFGT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K15" title="AMI_2:func.15">cond_address</a> </span>)</span></span>)</span>,<a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> ,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K14" title="AMI_2:func.14">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_3"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:36_1_1_3"/>
<span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4"><span class="kw">case </span></a><a NAME="E1:36_1_1_4"/>
<font color="Maroon" title="c4">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">T</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">b2</font>,<font color="Olive" title="b3">c1</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">T</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> 9, <font color="Olive" title="b2">b2</font>, <font color="Olive" title="b3">c1</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">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">T</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> 9, <font color="Maroon" title="c8">b2</font>, <font color="Maroon" title="c9">c1</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> <span class="kw"> such that </span><br/><a NAME="E3:36_1_1_4"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c4">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="c7">T</font>,<span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">c1</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>
 <span class="kw">and </span><br/><a NAME="E4:36_1_1_4"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
<font color="Maroon" title="c7">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">1,2,3,4,5</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_1_4_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_4_1_1"/>
( <font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_4"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4_1_1_1"><span class="kw">case </span></a><a NAME="E1:36_1_1_4_1_1_1"/>
<font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <span class="p2">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_4"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T22" title="AMI_2:th.22">AMI_2:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4_1_1_2"><span class="kw">case </span></a><a NAME="E1:36_1_1_4_1_1_2"/>
<font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <span class="p2">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_4"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T22" title="AMI_2:th.22">AMI_2:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4_1_1_3"><span class="kw">case </span></a><a NAME="E1:36_1_1_4_1_1_3"/>
<font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <span class="p2">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_4"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T22" title="AMI_2:th.22">AMI_2:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4_1_1_4"><span class="kw">case </span></a><a NAME="E1:36_1_1_4_1_1_4"/>
<font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <span class="p2">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_4"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T22" title="AMI_2:th.22">AMI_2:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_4_1_1_5"><span class="kw">case </span></a><a NAME="E1:36_1_1_4_1_1_5"/>
<font color="Maroon" title="c7">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font></span><br/><div class="add"><span class="kw">hence </span><span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> = 
<span class="p1">(<span class="default"><a href="ami_2.html#K9" title="AMI_2:func.9">SCM-Chg</a> <span class="p2">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <span class="p3">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">address_2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="ami_2.html#K8" title="AMI_2:func.8">IC</a> <font color="Maroon" title="c5">S</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_4"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_2.html#D16" title="AMI_2:def.16">AMI_2:def 16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <span class="p2">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">address_2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">address_2</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T18" title="AMI_2:th.18">AMI_2:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c5">S</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K11" title="AMI_2:func.11">address_1</a> </span>)</span></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="ami_2.html#K12" title="AMI_2:func.12">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="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T22" title="AMI_2:th.22">AMI_2:22</a></span>
<br/>.= 
<font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#T22" title="AMI_2:th.22">AMI_2:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:36_1_1_4"/>
<span class="p1">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">l9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:36"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c1">s</font></span>)</span> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <font color="Maroon" title="c3">l</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ami_2.html#D17" title="AMI_2:def.17">AMI_2:def 17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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