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<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">k</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Olive" title="b2">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) &amp; (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; ( not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> ) )</span>
<div class="add"><b>assume </b><a NAME="E1:42_1_1_1"/>
 <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">x'</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  ex <font color="Olive" title="b3">s'</font> being  <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a> st <br/>( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x'</font> &amp; <font color="Olive" title="b3">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Olive" title="b2">x'</font></span>)</span> &amp; <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Olive" title="b2">x'</font>,<font color="Olive" title="b3">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> )</span><br/><b>then reconsider </b><font color="Maroon" title="c3">x'</font> = <font color="Maroon" title="c1">x</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <b>by </b><i><a class="ref" href="scmfsa_1.html#T3" target="_self" title="SCMFSA_1:th.3">Th3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c4">s'</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c3">x'</font></span>)</span> as   <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a> <b>by </b><i><a class="ref" href="scmfsa_1.html#T18" target="_self" title="SCMFSA_1:th.18">Th18</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">s1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c3">x'</font>,<font color="Maroon" title="c4">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> as   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> <b>by </b><i><a class="ref" href="scmfsa_1.html#T19" target="_self" title="SCMFSA_1:th.19">Th19</a></i>;<br/><b>take </b><font color="Maroon" title="c6">s1</font> = <font color="Maroon" title="c5">s1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">x'</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  ex <font color="Olive" title="b2">s'</font> being  <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a> st <br/>( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x'</font> &amp; <font color="Olive" title="b2">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Olive" title="b1">x'</font></span>)</span> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Olive" title="b1">x'</font>,<font color="Olive" title="b2">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c7">x'</font> = <font color="Maroon" title="c3">x'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s'</font> being  <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a> st <br/>( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x'</font> &amp; <font color="Olive" title="b1">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c7">x'</font></span>)</span> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c7">x'</font>,<font color="Olive" title="b1">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c8">s'</font> = <font color="Maroon" title="c4">s'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x'</font> &amp; <font color="Maroon" title="c8">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c7">x'</font></span>)</span> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c7">x'</font>,<font color="Maroon" title="c8">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> )</span><br/><b>thus </b><a NAME="E5:42_1_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c7">x'</font></span>)</span> &amp; <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c7">x'</font>,<font color="Maroon" title="c8">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span> )</span><br/><b>thus </b><a NAME="E6:42_1_1_1"/>
<font color="Maroon" title="c8">s'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <font color="Maroon" title="c7">x'</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c7">x'</font>,<font color="Maroon" title="c8">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span></span><br/><b>thus </b><a NAME="E7:42_1_1_1"/>
<font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="ami_2.html#K16" title="AMI_2:func.16">SCM-Exec-Res</a> <font color="Maroon" title="c7">x'</font>,<font color="Maroon" title="c8">s'</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) &amp; (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; ( not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> ) )</span>
<div class="add"><b>assume </b><a NAME="E1:42_1_1_2"/>
 <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ex <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">k</font> &amp; <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Olive" title="b2">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>reconsider </b><font color="Maroon" title="c3">k</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  ;<br/><b>reconsider </b><font color="Maroon" title="c4">i</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c3">k</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/><b>take </b><font color="Maroon" title="c5">s1</font> =  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Maroon" title="c4">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">i</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ex <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">k</font> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Olive" title="b1">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c6">i</font> = <font color="Maroon" title="c4">i</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k</font> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Maroon" title="c6">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c7">k</font> = <font color="Maroon" title="c3">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Maroon" title="c6">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>thus </b><a NAME="E4:42_1_1_2"/>
( <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c7">k</font> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span>,<font color="Maroon" title="c6">i</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) &amp; (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; ( not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> ) )</span>
<div class="add"><b>assume </b><a NAME="E1:42_1_1_3"/>
 <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>reconsider </b><font color="Maroon" title="c3">k</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1_1_3_1"/>
( <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> or  not <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_3_1_1"><b>suppose </b></a><a NAME="E1:42_1_1_3_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><div class="add"><a NAME="E2:42_1_1_3_1_1"/><b>then </b><i><font color="Green" title="E18">A2</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/><b>set </b><font color="Maroon" title="c4">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span>;<br/> <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">k</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmfsa_1.html#E2:42_1_1_3_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>
;<br/><b>then reconsider </b><font color="Maroon" title="c5">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2" title="FINSEQ_1:def.2">FINSEQ_1:def 2</a></i>;<br/><a NAME="E5:42_1_1_3_1_1"/><i><font color="Green" title="E19">A3</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">FUNCT_4:18</a></i>;<br/><a NAME="E6:42_1_1_3_1_1"/><i><font color="Green" title="E20">A4</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/><a NAME="E7:42_1_1_3_1_1"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/><a NAME="E8:42_1_1_3_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a></i>;<br/><a NAME="E9:42_1_1_3_1_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E7:42_1_1_3_1_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/><a NAME="E10:42_1_1_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E6:42_1_1_3_1_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/><a NAME="E11:42_1_1_3_1_1"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c5">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E5:42_1_1_3_1_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c5">f</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/><b>take </b><font color="Maroon" title="c7">s1</font> =  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b2">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c8">f</font> = <font color="Maroon" title="c6">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b1">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c8">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c9">k</font> = <font color="Maroon" title="c3">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c9">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c8">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>thus </b><a NAME="E13:42_1_1_3_1_1"/>
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c9">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c8">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>thus </b><a NAME="E14:42_1_1_3_1_1"/>
<font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c9">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:42_1_1_3_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c8">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span><br/><b>thus </b><a NAME="E15:42_1_1_3_1_1"/>
<font color="Maroon" title="c7">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c8">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_3_1_2"><b>suppose </b></a><a NAME="E1:42_1_1_3_1_2"/><i><font color="Green" title="E17">A6</font></i>: 
not <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><div class="add"><b>reconsider </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ;<br/><b>take </b><font color="Maroon" title="c5">s1</font> =  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b2">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Olive" title="b1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c4">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Olive" title="b1">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c7">k</font> = <font color="Maroon" title="c3">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c7">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>thus </b><a NAME="E3:42_1_1_3_1_2"/>
<font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K14" title="SCMFSA_1:func.14">int_addr2</a> </span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c7">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>thus </b><a NAME="E4:42_1_1_3_1_2"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span></span>)</span> <a href="funct_7.html#K2" title="FUNCT_7:func.2">+*</a> <font color="Maroon" title="c7">k</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K13" title="SCMFSA_1:func.13">int_addr1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:42_1_1_3_1_2"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span><br/><b>thus </b><a NAME="E5:42_1_1_3_1_2"/>
<font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K15" title="SCMFSA_1:func.15">coll_addr1</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>thus </b><a NAME="E4:42_1_1"/>
(  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 implies  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</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="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> ) ) &amp; ( not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:42_1_1_4"/>
 <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">s1</font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> ex <font color="Olive" title="b2">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Olive" title="b2">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>reconsider </b><font color="Maroon" title="c3">k</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  ;<br/><a NAME="E3:42_1_1_4"/>
<font color="Maroon" title="c3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="finseq_2.html#D2" title="FINSEQ_2:def.2">FINSEQ_2:def 2</a></i>;<br/><a NAME="E4:42_1_1_4"/><b>then </b><i><font color="Green" title="E17">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E5:42_1_1_4"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/><a NAME="E6:42_1_1_4"/><b>then </b>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/><a NAME="E7:42_1_1_4"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E4:42_1_1_4"><i><font color="Green" title="E17">A7</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c3">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/><b>take </b><font color="Maroon" title="c5">s1</font> =  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Maroon" title="c4">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ex <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Olive" title="b1">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c4">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>take </b><font color="Maroon" title="c7">k</font> = <font color="Maroon" title="c3">k</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )</span><br/><b>thus </b><a NAME="E9:42_1_1_4"/>
( <font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">s</font> <a href="scmfsa_1.html#K11" title="SCMFSA_1:func.11">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K16" title="SCMFSA_1:func.16">int_addr3</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">k</font> <a href="finsop_1.html#K1" title="FINSOP_1:func.1">|-&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c5">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K8" title="SCMFSA_1:func.8">SCM+FSA-Chg</a> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-Chg</a> <font color="Maroon" title="c2">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="scmfsa_1.html#K17" title="SCMFSA_1:func.17">coll_addr2</a> </span>)</span>,<font color="Maroon" title="c6">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p2">(<span class="default"><a href="scmfsa_1.html#K18" title="SCMFSA_1:func.18">IC</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E6:42_1_1"/>
( not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 8 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 &amp; not  <a href="ami_1.html#NK20" title="AMI_1:NK.20">InsCode</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 implies  ex <font color="Olive">b<sub>1</sub></font> being  <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
