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<div class="add">

<span class="kw">thus </span><a NAME="E1:69_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is  <a href="compos_1.html#V6" title="COMPOS_1:attr.6">homogeneous</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is  <a href="amistd_2.html#V2" title="AMISTD_2:attr.2">with_explicit_jumps</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">J</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D12" title="COMPOS_1:def.12">COMPOS_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">J</font> or  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:69_1_1_1"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c2">J</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/>

<a NAME="E2:69_1_1_1"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1"/>
( <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_1"/>
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E2:69_1_1_1"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_2"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c4">b</font>
 ;<br/><a NAME="E4:69_1_1_1_1_2"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_2_1_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_2_1_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_2_1_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font>, <font color="Maroon" title="c6">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d1</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c6">d2</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="scmfsa10.html#T10" target="_self" title="SCMFSA10:th.10">Th18</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="ref" href="scmfsa10.html#T10" target="_self" title="SCMFSA10:th.10">Th18</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_2_1_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_2_1_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:69_1_1_1_1_2"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_3"/><span class="lab"><font color="Green" title="E48">A6</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>)
 ;<br/><a NAME="E4:69_1_1_1_1_3"/><span class="lab"><font color="Green" title="E49">A7</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_3"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_3_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_3_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_3_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_3_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_3"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_3_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_3_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font>, <font color="Maroon" title="c6">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_3_1_2"/><span class="lab"><font color="Green" title="E50">A8</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c5">d1</font>,<font color="Maroon" title="c6">d2</font>)
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_3"><span class="lab"><font color="Green" title="E48">A6</font></span></a>, <a class="ref" href="scmfsa10.html#T11" target="_self" title="SCMFSA10:th.11">Th19</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_3_1_2"><span class="lab"><font color="Green" title="E50">A8</font></span></a>, <a class="ref" href="scmfsa10.html#T11" target="_self" title="SCMFSA10:th.11">Th19</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_3_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_3_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_3_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_3"><span class="lab"><font color="Green" title="E49">A7</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_4"/><span class="lab"><font color="Green" title="E48">A9</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>)
 ;<br/><a NAME="E4:69_1_1_1_1_4"/><span class="lab"><font color="Green" title="E49">A10</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_4"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_4_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_4_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_4_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_4_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_4_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_4"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_4_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_4_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font>, <font color="Maroon" title="c6">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_4_1_2"/><span class="lab"><font color="Green" title="E50">A11</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c5">d1</font>,<font color="Maroon" title="c6">d2</font>)
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_4"><span class="lab"><font color="Green" title="E48">A9</font></span></a>, <a class="ref" href="scmfsa10.html#T12" target="_self" title="SCMFSA10:th.12">Th20</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_4_1_2"><span class="lab"><font color="Green" title="E50">A11</font></span></a>, <a class="ref" href="scmfsa10.html#T12" target="_self" title="SCMFSA10:th.12">Th20</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_4_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_4_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_4_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_4"><span class="lab"><font color="Green" title="E49">A10</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_5"/><span class="lab"><font color="Green" title="E48">A12</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>)
 ;<br/><a NAME="E4:69_1_1_1_1_5"/><span class="lab"><font color="Green" title="E49">A13</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_5"><span class="lab"><font color="Green" title="E48">A12</font></span></a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_5_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_5_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_5_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_5_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_5_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_5"><span class="lab"><font color="Green" title="E48">A12</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_5_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_5_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font>, <font color="Maroon" title="c6">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_5_1_2"/><span class="lab"><font color="Green" title="E50">A14</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c5">d1</font>,<font color="Maroon" title="c6">d2</font>)
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_5"><span class="lab"><font color="Green" title="E48">A12</font></span></a>, <a class="ref" href="scmfsa10.html#T13" target="_self" title="SCMFSA10:th.13">Th21</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_5_1_2"><span class="lab"><font color="Green" title="E50">A14</font></span></a>, <a class="ref" href="scmfsa10.html#T13" target="_self" title="SCMFSA10:th.13">Th21</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_5_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_5_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_5_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_5"><span class="lab"><font color="Green" title="E49">A13</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_6"/><span class="lab"><font color="Green" title="E48">A15</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>)
 ;<br/><a NAME="E4:69_1_1_1_1_6"/><span class="lab"><font color="Green" title="E49">A16</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_6"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_6_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_6_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_6_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_6_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_6_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_6"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_6_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_6_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font>, <font color="Maroon" title="c6">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_6_1_2"/><span class="lab"><font color="Green" title="E50">A17</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c5">d1</font>,<font color="Maroon" title="c6">d2</font>)
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_6"><span class="lab"><font color="Green" title="E48">A15</font></span></a>, <a class="ref" href="scmfsa10.html#T14" target="_self" title="SCMFSA10:th.14">Th22</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_6_1_2"><span class="lab"><font color="Green" title="E50">A17</font></span></a>, <a class="ref" href="scmfsa10.html#T14" target="_self" title="SCMFSA10:th.14">Th22</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_6_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_6_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_6_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_6"><span class="lab"><font color="Green" title="E49">A16</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_7"/>
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_7"/><span class="lab"><font color="Green" title="E48">A18</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">i1</font>
 ;<br/><a NAME="E4:69_1_1_1_1_7"/><span class="lab"><font color="Green" title="E49">A19</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_7"><span class="lab"><font color="Green" title="E48">A18</font></span></a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_7_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_7_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_7_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_7_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_7_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_7"><span class="lab"><font color="Green" title="E48">A18</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_7_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_7_1_2"/>
 ex <font color="Olive" title="b1">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_7_1_2"/><span class="lab"><font color="Green" title="E50">A20</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c4">i2</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_7"><span class="lab"><font color="Green" title="E48">A18</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_7_1_2"><span class="lab"><font color="Green" title="E50">A20</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_7_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_7_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_7_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_7"><span class="lab"><font color="Green" title="E49">A19</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_8"/>
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_8"/><span class="lab"><font color="Green" title="E48">A21</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c4">i1</font>
 ;<br/><a NAME="E4:69_1_1_1_1_8"/><span class="lab"><font color="Green" title="E49">A22</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_8"><span class="lab"><font color="Green" title="E48">A21</font></span></a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_8_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_8_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d1</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_8_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_8_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_8_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_8"><span class="lab"><font color="Green" title="E48">A21</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_8_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_8_1_2"/>
 ex <font color="Olive" title="b1">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d1</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_8_1_2"/><span class="lab"><font color="Green" title="E50">A23</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d1</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c6">i2</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_8"><span class="lab"><font color="Green" title="E48">A21</font></span></a>, <a class="ref" href="scmfsa10.html#T15" target="_self" title="SCMFSA10:th.15">Th24</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">i2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_8_1_2"><span class="lab"><font color="Green" title="E50">A23</font></span></a>, <a class="ref" href="scmfsa10.html#T15" target="_self" title="SCMFSA10:th.15">Th24</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_8_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_8_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_8_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_8"><span class="lab"><font color="Green" title="E49">A22</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_9"/>
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_9"/><span class="lab"><font color="Green" title="E48">A24</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c4">i1</font>
 ;<br/><a NAME="E4:69_1_1_1_1_9"/><span class="lab"><font color="Green" title="E49">A25</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_9"><span class="lab"><font color="Green" title="E48">A24</font></span></a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_9_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_9_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d1</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i2</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_9_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_9_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_9_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_9"><span class="lab"><font color="Green" title="E48">A24</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a>, <a class="ref" href="scmfsa_2.html#T97" title="SCMFSA_2:th.97">SCMFSA_2:97</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_9_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_9_1_2"/>
 ex <font color="Olive" title="b1">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">d1</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">i2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_9_1_2"/><span class="lab"><font color="Green" title="E50">A26</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d1</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c6">i2</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_9"><span class="lab"><font color="Green" title="E48">A24</font></span></a>, <a class="ref" href="scmfsa10.html#T16" target="_self" title="SCMFSA10:th.16">Th25</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c6">i2</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" title="FINSEQ_1:th.38">FINSEQ_1:38</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_9_1_2"><span class="lab"><font color="Green" title="E50">A26</font></span></a>, <a class="ref" href="scmfsa10.html#T16" target="_self" title="SCMFSA10:th.16">Th25</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_9_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_9_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_9_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_9"><span class="lab"><font color="Green" title="E49">A25</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_10"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_10"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_10"/><span class="lab"><font color="Green" title="E48">A27</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c3">a</font>)
 ;<br/><a NAME="E4:69_1_1_1_1_10"/><span class="lab"><font color="Green" title="E49">A28</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_10"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_10_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_10_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_10_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_10_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_10_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_10"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_10_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_10_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">d1</font>, <font color="Maroon" title="c7">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c8">f1</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_10_1_2"/><span class="lab"><font color="Green" title="E50">A29</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">d2</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c8">f1</font>,<font color="Maroon" title="c6">d1</font>)
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_10"><span class="lab"><font color="Green" title="E48">A27</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_10_1_2"><span class="lab"><font color="Green" title="E50">A29</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_10_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_10_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_10_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_10"><span class="lab"><font color="Green" title="E49">A28</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_11"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_11"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_11"/><span class="lab"><font color="Green" title="E48">A30</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c3">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c4">b</font>
 ;<br/><a NAME="E4:69_1_1_1_1_11"/><span class="lab"><font color="Green" title="E49">A31</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_11"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_11_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_11_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_11_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_11_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_11_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_11"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_11_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_11_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">d1</font>, <font color="Maroon" title="c7">d2</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c8">f1</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_11_1_2"/><span class="lab"><font color="Green" title="E50">A32</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c8">f1</font>,<font color="Maroon" title="c6">d1</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c7">d2</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_11"><span class="lab"><font color="Green" title="E48">A30</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_11_1_2"><span class="lab"><font color="Green" title="E50">A32</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_11_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_11_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_11_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_11"><span class="lab"><font color="Green" title="E49">A31</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_12"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_12"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_12"/><span class="lab"><font color="Green" title="E48">A33</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c4">f</font>
 ;<br/><a NAME="E4:69_1_1_1_1_12"/><span class="lab"><font color="Green" title="E49">A34</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_12"><span class="lab"><font color="Green" title="E48">A33</font></span></a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_12_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_12_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_12_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_12_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_12_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_12"><span class="lab"><font color="Green" title="E48">A33</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_12_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_12_1_2"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">f1</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_12_1_2"/><span class="lab"><font color="Green" title="E50">A35</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d1</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c6">f1</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_12"><span class="lab"><font color="Green" title="E48">A33</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_12_1_2"><span class="lab"><font color="Green" title="E50">A35</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_12_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_12_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_12_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_12"><span class="lab"><font color="Green" title="E49">A34</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_13"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_13"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_13"/><span class="lab"><font color="Green" title="E48">A36</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c3">a</font>
 ;<br/><a NAME="E4:69_1_1_1_1_13"/><span class="lab"><font color="Green" title="E49">A37</font></span>: 
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_13"><span class="lab"><font color="Green" title="E48">A36</font></span></a>, <a class="ref" href="scmfsa_2.html#T29" title="SCMFSA_2:th.29">SCMFSA_2:29</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_13_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_1_1_13_1"/>
( <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_13_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_13_1_1"/>
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_13_1_1"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E3:69_1_1_1_1_13"><span class="lab"><font color="Green" title="E48">A36</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_13_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_13_1_2"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">d1</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">f1</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_1_1_13_1_2"/><span class="lab"><font color="Green" title="E50">A38</font></span>: 
<font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c5">d1</font>
 ;<br/><span class="kw">thus </span> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_13"><span class="lab"><font color="Green" title="E48">A36</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c2">J</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_1_1_13_1_2"><span class="lab"><font color="Green" title="E50">A38</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1_1_13_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_1_1_13_1_3"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c2">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_1_1_13_1_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">J</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_1"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E4:69_1_1_1_1_13"><span class="lab"><font color="Green" title="E49">A37</font></span></a>, <a class="ref" href="scmfsa_2.html#T18" title="SCMFSA_2:th.18">SCMFSA_2:18</a>, <a class="ref" href="scmfsa_2.html#T19" title="SCMFSA_2:th.19">SCMFSA_2:19</a>, <a class="ref" href="scmfsa_2.html#T20" title="SCMFSA_2:th.20">SCMFSA_2:20</a>, <a class="ref" href="scmfsa_2.html#T21" title="SCMFSA_2:th.21">SCMFSA_2:21</a>, <a class="ref" href="scmfsa_2.html#T22" title="SCMFSA_2:th.22">SCMFSA_2:22</a>, <a class="ref" href="scmfsa_2.html#T23" title="SCMFSA_2:th.23">SCMFSA_2:23</a>, <a class="ref" href="scmfsa_2.html#T24" title="SCMFSA_2:th.24">SCMFSA_2:24</a>, <a class="ref" href="scmfsa_2.html#T25" title="SCMFSA_2:th.25">SCMFSA_2:25</a>, <a class="ref" href="scmfsa_2.html#T26" title="SCMFSA_2:th.26">SCMFSA_2:26</a>, <a class="ref" href="scmfsa_2.html#T27" title="SCMFSA_2:th.27">SCMFSA_2:27</a>, <a class="ref" href="scmfsa_2.html#T28" title="SCMFSA_2:th.28">SCMFSA_2:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:69_1_1"/>
 <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  is  <a href="amistd_2.html#V2" title="AMISTD_2:attr.2">with_explicit_jumps</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_2.html#D2" title="AMISTD_2:def.2">AMISTD_2:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">I</font> is  <a href="amistd_2.html#V1" title="AMISTD_2:attr.1">with_explicit_jumps</a> </span><br/>

<span class="kw">thus </span><a NAME="E1:69_1_1_2"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="amistd_2.html#D1" title="AMISTD_2:def.1">AMISTD_2:def 1</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> or <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:69_1_1_2_1"/><span class="lab"><font color="Green" title="E46">A39</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_2_1_1"/>
( <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_1"/>
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a>, <a class="ref" href="ami_3.html#T26" title="AMI_3:th.26">AMI_3:26</a>, <a class="ref" href="scmfsa_2.html#T96" title="SCMFSA_2:th.96">SCMFSA_2:96</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_3"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_4"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_5"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_6"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_7"/><span class="lab"><font color="Green" title="E47">A40</font></span>: 
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_1_1_7"/><span class="lab"><font color="Green" title="E48">A41</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1_1_7"><span class="lab"><font color="Green" title="E47">A40</font></span></a></span>;<br/><a NAME="E4:69_1_1_2_1_1_7"/><span class="lab"><font color="Green" title="E49">A42</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c3">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><a NAME="E5:69_1_1_2_1_1_7"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></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"><font color="Maroon" title="c3">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" title="FINSEQ_1:th.39">FINSEQ_1:39</a></span>;<br/><span class="kw">hence </span><a NAME="E6:69_1_1_2_1_1_7"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a>, <a class="txt" href="#E3:69_1_1_2_1_1_7"><span class="lab"><font color="Green" title="E48">A41</font></span></a>, <a class="txt" href="#E4:69_1_1_2_1_1_7"><span class="lab"><font color="Green" title="E49">A42</font></span></a>, <a class="ref" href="scmfsa10.html#T34" target="_self" title="SCMFSA10:th.34">Th75</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_8"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_8"/><span class="lab"><font color="Green" title="E47">A44</font></span>: 
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_1_1_8"/><span class="lab"><font color="Green" title="E48">A45</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c4">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1_1_8"><span class="lab"><font color="Green" title="E47">A44</font></span></a></span>;<br/><a NAME="E4:69_1_1_2_1_1_8"/><span class="lab"><font color="Green" title="E49">A46</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c4">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T15" target="_self" title="SCMFSA10:th.15">Th24</a></span>;<br/><a NAME="E5:69_1_1_2_1_1_8"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></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"><font color="Maroon" title="c4">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" title="FINSEQ_1:th.39">FINSEQ_1:39</a></span>;<br/><span class="kw">hence </span><a NAME="E6:69_1_1_2_1_1_8"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a>, <a class="txt" href="#E3:69_1_1_2_1_1_8"><span class="lab"><font color="Green" title="E48">A45</font></span></a>, <a class="txt" href="#E4:69_1_1_2_1_1_8"><span class="lab"><font color="Green" title="E49">A46</font></span></a>, <a class="ref" href="scmfsa10.html#T36" target="_self" title="SCMFSA10:th.36">Th77</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_9"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_9"/><span class="lab"><font color="Green" title="E47">A48</font></span>: 
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c4">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_1_1_9"/><span class="lab"><font color="Green" title="E48">A49</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c4">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1_1_9"><span class="lab"><font color="Green" title="E47">A48</font></span></a></span>;<br/><a NAME="E4:69_1_1_2_1_1_9"/><span class="lab"><font color="Green" title="E49">A50</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c4">i1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T16" target="_self" title="SCMFSA10:th.16">Th25</a></span>;<br/><a NAME="E5:69_1_1_2_1_1_9"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></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"><font color="Maroon" title="c4">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T39" title="FINSEQ_1:th.39">FINSEQ_1:39</a></span>;<br/><span class="kw">hence </span><a NAME="E6:69_1_1_2_1_1_9"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a>, <a class="txt" href="#E3:69_1_1_2_1_1_9"><span class="lab"><font color="Green" title="E48">A49</font></span></a>, <a class="txt" href="#E4:69_1_1_2_1_1_9"><span class="lab"><font color="Green" title="E49">A50</font></span></a>, <a class="ref" href="scmfsa10.html#T38" target="_self" title="SCMFSA10:th.38">Th79</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_10"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_10"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_10"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_11"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_11"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_11"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_12"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_12"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_12"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_1_1_13"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_1_1_13"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:69_1_1_2_1_1_13"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69_1_1_2_1"><span class="lab"><font color="Green" title="E46">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="recdef_2.html#K2" title="RECDEF_2:func.2">`2_3</a></span>)</span> or <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:69_1_1_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">k</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:69_1_1_2"/><span class="lab"><font color="Green" title="E46">A52</font></span>: 
<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"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:69_1_1_2"/><span class="lab"><font color="Green" title="E47">A53</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" title="FUNCT_1:def.3">FUNCT_1:def 3</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:69_1_1_2_2"/>
( <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>) or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font> or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) or  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font> or  ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T93" title="SCMFSA_2:th.93">SCMFSA_2:93</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_1"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_1"/>
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><a NAME="E2:69_1_1_2_2_1"/><span class="kw">then </span>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:69_1_1_2_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_2"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_2"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_2"/><span class="lab"><font color="Green" title="E48">A54</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">:=</a> <font color="Maroon" title="c5">b</font>
 ;<br/><a NAME="E4:69_1_1_2_2_2"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_2"><span class="lab"><font color="Green" title="E48">A54</font></span></a>, <a class="ref" href="scmfsa10.html#T10" target="_self" title="SCMFSA10:th.10">Th18</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_3"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_3"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_3"/><span class="lab"><font color="Green" title="E48">A55</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K7" title="SCMFSA_2:func.7">AddTo</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:69_1_1_2_2_3"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_3"><span class="lab"><font color="Green" title="E48">A55</font></span></a>, <a class="ref" href="scmfsa10.html#T11" target="_self" title="SCMFSA10:th.11">Th19</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_3"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_4"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_4"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_4"/><span class="lab"><font color="Green" title="E48">A56</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K8" title="SCMFSA_2:func.8">SubFrom</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:69_1_1_2_2_4"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_4"><span class="lab"><font color="Green" title="E48">A56</font></span></a>, <a class="ref" href="scmfsa10.html#T12" target="_self" title="SCMFSA10:th.12">Th20</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_4"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_5"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_5"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_5"/><span class="lab"><font color="Green" title="E48">A57</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K9" title="SCMFSA_2:func.9">MultBy</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:69_1_1_2_2_5"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_5"><span class="lab"><font color="Green" title="E48">A57</font></span></a>, <a class="ref" href="scmfsa10.html#T13" target="_self" title="SCMFSA10:th.13">Th21</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_5"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_6"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_6"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_6"/><span class="lab"><font color="Green" title="E48">A58</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K10" title="SCMFSA_2:func.10">Divide</a> (<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>)
 ;<br/><a NAME="E4:69_1_1_2_2_6"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_6"><span class="lab"><font color="Green" title="E48">A58</font></span></a>, <a class="ref" href="scmfsa10.html#T14" target="_self" title="SCMFSA10:th.14">Th22</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_6"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_7"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_7"/>
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_7"/><span class="lab"><font color="Green" title="E48">A59</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K11" title="SCMFSA_2:func.11">goto</a> <font color="Maroon" title="c4">i1</font>
 ;<br/><a NAME="E4:69_1_1_2_2_7"/><span class="lab"><font color="Green" title="E49">A60</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_2_2_7"><span class="lab"><font color="Green" title="E48">A59</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><a NAME="E5:69_1_1_2_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="ref" href="finseq_1.html#T90" title="FINSEQ_1:th.90">FINSEQ_1:90</a></span>;<br/><a NAME="E6:69_1_1_2_2_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A61</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2_2_7"><span class="lab"><font color="Green" title="E49">A60</font></span></a>, <a class="txt" href="#E5:69_1_1_2"><span class="lab"><font color="Green" title="E47">A53</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E7:69_1_1_2_2_7"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> <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"><font color="Maroon" title="c4">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_2_2_7"><span class="lab"><font color="Green" title="E48">A59</font></span></a>, <a class="ref" href="scmfsa10.html#T34" target="_self" title="SCMFSA10:th.34">Th75</a></span>;<br/><span class="kw">hence </span><a NAME="E8:69_1_1_2_2_7"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:69_1_1_2_2_7"><span class="lab"><font color="Green" title="E50">A61</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_8"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_8"/>
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_8"/><span class="lab"><font color="Green" title="E48">A62</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K12" title="SCMFSA_2:func.12">=0_goto</a> <font color="Maroon" title="c5">i1</font>
 ;<br/><a NAME="E4:69_1_1_2_2_8"/><span class="lab"><font color="Green" title="E49">A63</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_2_2_8"><span class="lab"><font color="Green" title="E48">A62</font></span></a>, <a class="ref" href="scmfsa10.html#T15" target="_self" title="SCMFSA10:th.15">Th24</a></span>;<br/><a NAME="E5:69_1_1_2_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="ref" href="finseq_1.html#T90" title="FINSEQ_1:th.90">FINSEQ_1:90</a></span>;<br/><a NAME="E6:69_1_1_2_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A64</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2_2_8"><span class="lab"><font color="Green" title="E49">A63</font></span></a>, <a class="txt" href="#E5:69_1_1_2"><span class="lab"><font color="Green" title="E47">A53</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E7:69_1_1_2_2_8"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> <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"><font color="Maroon" title="c5">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_2_2_8"><span class="lab"><font color="Green" title="E48">A62</font></span></a>, <a class="ref" href="scmfsa10.html#T36" target="_self" title="SCMFSA10:th.36">Th77</a></span>;<br/><span class="kw">hence </span><a NAME="E8:69_1_1_2_2_8"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:69_1_1_2_2_8"><span class="lab"><font color="Green" title="E50">A64</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_9"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_9"/>
 ex <font color="Olive" title="b1">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b2">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Olive" title="b1">i1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">i1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_9"/><span class="lab"><font color="Green" title="E48">A65</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c5">i1</font>
 ;<br/><a NAME="E4:69_1_1_2_2_9"/><span class="lab"><font color="Green" title="E49">A66</font></span>: 
 <a href="compos_1.html#NK5" title="COMPOS_1:NK.5">JumpPart</a> <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c5">i1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_2_2_9"><span class="lab"><font color="Green" title="E48">A65</font></span></a>, <a class="ref" href="scmfsa10.html#T16" target="_self" title="SCMFSA10:th.16">Th25</a></span>;<br/><a NAME="E5:69_1_1_2_2_9"/><span class="kw">then </span>
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="ref" href="finseq_1.html#T90" title="FINSEQ_1:th.90">FINSEQ_1:90</a></span>;<br/><a NAME="E6:69_1_1_2_2_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A67</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">i1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2_2_9"><span class="lab"><font color="Green" title="E49">A66</font></span></a>, <a class="txt" href="#E5:69_1_1_2"><span class="lab"><font color="Green" title="E47">A53</font></span></a>, <a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></span>;<br/><a NAME="E7:69_1_1_2_2_9"/>
 <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font> <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"><font color="Maroon" title="c5">i1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:69_1_1_2_2_9"><span class="lab"><font color="Green" title="E48">A65</font></span></a>, <a class="ref" href="scmfsa10.html#T38" target="_self" title="SCMFSA10:th.38">Th79</a></span>;<br/><span class="kw">hence </span><a NAME="E8:69_1_1_2_2_9"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:69_1_1_2_2_9"><span class="lab"><font color="Green" title="E50">A67</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_10"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_10"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_10"/><span class="lab"><font color="Green" title="E48">A68</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> <a href="scmfsa_2.html#K14" title="SCMFSA_2:func.14">:=</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">a</font>)
 ;<br/><a NAME="E4:69_1_1_2_2_10"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_10"><span class="lab"><font color="Green" title="E48">A68</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_10"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_11"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_11"/>
 ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b3">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b1">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Olive" title="b2">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c6">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_11"/><span class="lab"><font color="Green" title="E48">A69</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c4">a</font>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <font color="Maroon" title="c5">b</font>
 ;<br/><a NAME="E4:69_1_1_2_2_11"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_11"><span class="lab"><font color="Green" title="E48">A69</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_11"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_12"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_12"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Olive" title="b2">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_12"/><span class="lab"><font color="Green" title="E48">A70</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="scmfsa_2.html#K16" title="SCMFSA_2:func.16">:=len</a> <font color="Maroon" title="c5">f</font>
 ;<br/><a NAME="E4:69_1_1_2_2_12"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_12"><span class="lab"><font color="Green" title="E48">A70</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_12"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2_2_13"><span class="kw">suppose </span></a><a NAME="E1:69_1_1_2_2_13"/>
 ex <font color="Olive" title="b1">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  ex <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a>  st <font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Olive" title="b1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">a</font> being    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> , <font color="Maroon" title="c5">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <span class="kw"> such that </span><br/><a NAME="E3:69_1_1_2_2_13"/><span class="lab"><font color="Green" title="E48">A71</font></span>: 
<font color="Maroon" title="c1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <font color="Maroon" title="c4">a</font>
 ;<br/><a NAME="E4:69_1_1_2_2_13"/>
<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> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:69_1_1_2"><span class="lab"><font color="Green" title="E46">A52</font></span></a>, <a class="txt" href="#E3:69_1_1_2_2_13"><span class="lab"><font color="Green" title="E48">A71</font></span></a>, <a class="ref" href="recdef_2.html#D2" title="RECDEF_2:def.2">RECDEF_2:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:69_1_1_2_2_13"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K2" title="AMISTD_1:func.2">JUMP</a> <font color="Maroon" title="c1">I</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>


</div>
