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

<span class="kw">let </span><font color="Maroon" title="c1">i1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <br/> for <font color="Olive" title="b2">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds   <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span>,<font color="Olive" title="b1">k</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> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">k</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a>  holds   <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <font color="Maroon" title="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="scmfsa_2.html#K13" title="SCMFSA_2:func.13">&gt;0_goto</a> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be    <a href="scmfsa_2.html#M1" title="SCMFSA_2:mode.1">Int-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</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> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span><br/>





<span class="lab"><font color="Green" title="E94">A1</font></span>:  <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p2">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span> = 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</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="c1">i1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D14" title="AMISTD_2:def.14">AMISTD_2:def 14</a></span>
<br/>.= 
8
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T49" title="SCMFSA_2:th.49">SCMFSA_2:49</a></span>
<br/>.= 
 <a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</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> <span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T49" title="SCMFSA_2:th.49">SCMFSA_2:49</a></span>
;<br/>
<a NAME="E2:122"/><span class="lab"><font color="Green" title="E95">A2</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></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="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="amistd_2.html#D14" title="AMISTD_2:def.14">AMISTD_2:def 14</a></span>;<br/>
<a NAME="E3:122"/><span class="lab"><font color="Green" title="E96">A3</font></span>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">x</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="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:122_2"/><span class="lab"><font color="Green" title="E97">A4</font></span>: 
<font color="Maroon" title="c4">x</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="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span><br/>

<a NAME="E2:122_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E98">A5</font></span>: 
<font color="Maroon" title="c4">x</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"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_2_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="E1:122_2_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:122_2"><span class="lab"><font color="Green" title="E98">A5</font></span></a>, <a class="txt" href="scmfsa10.html#E18"><span class="lab"><font color="Green" title="E15">Lm2</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:122_2_1_1"/><span class="lab"><font color="Green" title="E99">A6</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span><br/><div class="add"><a NAME="E2:122_2_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<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="c1">i1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T56" target="_self" title="SCMFSA10:th.56">Th56</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">f</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E4:122_2_1_1"/><span class="lab"><font color="Green" title="E100">A7</font></span>: 
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E5:122_2_1_1"/><span class="lab"><font color="Green" title="E101">A8</font></span>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c5">f</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122_2"><span class="lab"><font color="Green" title="E97">A4</font></span></a>, <a class="ref" href="amistd_2.html#D14" title="AMISTD_2:def.14">AMISTD_2:def 14</a></span>;<br/><font color="Maroon" title="c5">f</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:122_2_1_1"><span class="lab"><font color="Green" title="E100">A7</font></span></a>, <a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>
<br/>.= 
<font color="Maroon" title="c1">i1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122_2_1_1"><span class="lab"><font color="Green" title="E99">A6</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122_2_1_1"><span class="lab"><font color="Green" title="E99">A6</font></span></a>, <a class="txt" href="#E5:122_2_1_1"><span class="lab"><font color="Green" title="E101">A8</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="122_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:122_2_1_2"/><span class="lab"><font color="Green" title="E99">A9</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font></span><br/><div class="add"><a NAME="E2:122_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="card_3.html#K10" title="CARD_3:func.10">product"</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K4" title="AMISTD_2:func.4">AddressParts</a> <span class="p3">(<span class="default"><a href="ami_1.html#K21" title="AMI_1:func.21">InsCode</a> <span class="p4">(<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="c1">i1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T5" target="_self" title="SCMFSA10:th.5">Th5</a>, <a class="ref" href="scmfsa10.html#T57" target="_self" title="SCMFSA10:th.57">Th57</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<span class="default"><a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</a> <span class="p3">(<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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122_2"><span class="lab"><font color="Green" title="E97">A4</font></span></a>, <a class="ref" href="amistd_2.html#D14" title="AMISTD_2:def.14">AMISTD_2:def 14</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>
<br/>.= 
<font color="Maroon" title="c3">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122_2_1_2"><span class="lab"><font color="Green" title="E99">A9</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122_2_1_2"><span class="lab"><font color="Green" title="E99">A9</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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> <span class="p3">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>
<br/>.= 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c3">a</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" title="FINSEQ_3:th.29">FINSEQ_3:29</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K3" title="AMISTD_2:func.3">AddressPart</a> <span class="p2">(<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="c1">i1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa10.html#T25" target="_self" title="SCMFSA10:th.25">Th25</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:122"/>
 <a href="amistd_2.html#K7" title="AMISTD_2:func.7">IncAddr</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="c1">i1</font></span>)</span>,<font color="Maroon" title="c2">k</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> <span class="p1">(<span class="default"><a href="amistd_1.html#K5" title="AMISTD_1:func.5">il.</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="amistd_1.html#K7" title="AMISTD_1:func.7">locnum</a> <font color="Maroon" title="c1">i1</font>,<a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:122"><span class="lab"><font color="Green" title="E94">A1</font></span></a>, <a class="txt" href="#E2:122"><span class="lab"><font color="Green" title="E95">A2</font></span></a>, <a class="txt" href="#E3:122"><span class="lab"><font color="Green" title="E96">A3</font></span></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a>, <a class="ref" href="mcart_1.html#T95" title="MCART_1:th.95">MCART_1:95</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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