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

<span class="kw">set </span><font color="Maroon" title="c2">a2</font> =  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">a1</font> =  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a><br/>  for <font color="Olive" title="b2">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <br/>  for <font color="Olive" title="b3">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b2">f</font> <a href="scmfsa_7.html#K4" title="SCMFSA_7:func.4">:=</a> <font color="Olive" title="b3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">P</font> holds <br/><font color="Olive" title="b1">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">P</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> <br/>  for <font color="Olive" title="b2">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b1">f</font> <a href="scmfsa_7.html#K4" title="SCMFSA_7:func.4">:=</a> <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</font> holds <br/><font color="Maroon" title="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font></span><br/>



<a NAME="E1:10"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">D</font> =  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">f</font> be    <a href="scmfsa_2.html#M2" title="SCMFSA_2:mode.2">FinSeq-Location</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Maroon" title="c7">f</font> <a href="scmfsa_7.html#K4" title="SCMFSA_7:func.4">:=</a> <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</font> holds <br/><font color="Maroon" title="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">p</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <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="c7">f</font> <a href="scmfsa_7.html#K4" title="SCMFSA_7:func.4">:=</a> <font color="Maroon" title="c8">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</font> implies <font color="Maroon" title="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c9">q</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">q0</font> = <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:10"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
<font color="Maroon" title="c7">f</font> <a href="scmfsa_7.html#K4" title="SCMFSA_7:func.4">:=</a> <font color="Maroon" title="c8">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P</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="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c11">q</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E8">A3</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">i</font>, <font color="Maroon" title="c13">k</font> be    <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> ; <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="c12">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> implies <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <font color="Maroon" title="c12">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i</font> )</span><br/><span class="kw">assume </span><a NAME="E1:10_1"/>
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></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="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <font color="Maroon" title="c12">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i</font></span><br/><a NAME="E2:10_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A4</font></span>: 
<font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/><span class="kw">thus </span><a NAME="E3:10_1"/>
<font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <font color="Maroon" title="c12">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E2:10_1"><span class="lab"><font color="Green" title="E9">A4</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</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>
<span class="kw">consider </span><font color="Maroon" title="c12">pp</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <span class="kw"> such that </span><br/><a NAME="E5:10"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c12">pp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font> &amp; (  for <font color="Olive" title="b1">k</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="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c12">pp</font> holds <br/> ex <font color="Olive" title="b2">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c12">pp</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Olive" title="b2">i</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> ) ) )
 <span class="kw">and </span><br/><a NAME="E6:10"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
 <a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_7.html#D3" title="SCMFSA_7:def.3">SCMFSA_7:def 3</a></span>;<br/>
<a NAME="E7:10"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="afinsq_1.html#T75" title="AFINSQ_1:th.75">AFINSQ_1:75</a></span>;<br/>
<a NAME="E8:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A7</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>] <span class="kw">means </span>( $1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">pp</font> implies  ex <font color="Olive" title="b1">pp0</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  st <br/>( <font color="Olive" title="b1">pp0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; (  for <font color="Olive" title="b2">i</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="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Olive" title="b1">pp0</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b2">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">i</font> ) ) );<br/>
<a NAME="E9:10"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
 for <font color="Olive" title="b1">r</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a><br/>  for <font color="Olive" title="b2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c13">r</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">r</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>]</span><br/><span class="kw">let </span><font color="Maroon" title="c14">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">r</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>] )</span><br/>



<span class="kw">assume </span><a NAME="E1:10_2"/><span class="lab"><font color="Green" title="E13">A9</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c13">r</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">S<sub>1</sub></font>[<font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>]</span><br/>

<span class="kw">set </span><font color="Maroon" title="c15">r1</font> =  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font>;<br/>
<a NAME="E2:10_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T34" title="AFINSQ_1:th.34">AFINSQ_1:34</a></span>;<br/>
<a NAME="E3:10_2"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E4:10_2"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>;<br/>
<a NAME="E5:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A10</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/>
<span class="kw">assume </span><a NAME="E6:10_2"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
<font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">pp</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">pp0</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  st <br/>( <font color="Olive" title="b1">pp0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> &amp; (  for <font color="Olive" title="b2">i</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="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Olive" title="b1">pp0</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b2">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">i</font> ) )</span><br/>

<a NAME="E7:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A12</font></span>: 
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c12">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<a NAME="E8:10_2"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c12">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_2"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">pr1</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E10:10_2"/>
<font color="Maroon" title="c16">pr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E11:10_2"/><span class="lab"><font color="Green" title="E17">A13</font></span>: 
<font color="Maroon" title="c12">pp</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E9">A5</font></span></a></span>;<br/>
<a NAME="E12:10_2"/>
<font color="Maroon" title="c13">r</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">pp0</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <span class="kw"> such that </span><br/><a NAME="E14:10_2"/><span class="lab"><font color="Green" title="E18">A14</font></span>: 
<font color="Maroon" title="c17">pp0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">r</font>
 <span class="kw">and </span><br/><a NAME="E15:10_2"/><span class="lab"><font color="Green" title="E19">A15</font></span>: 
 for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E6:10_2"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">c2</font> =  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">c1</font> =  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span>;<br/>
<a NAME="E16:10_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:10_2"><span class="lab"><font color="Green" title="E19">A15</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c20">s1</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span>) as   <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D9" title="MEMSTR_0:def.9">MEMSTR_0:def 9</a></span>;<br/>
<span class="lab"><font color="Green" title="E20">A16</font></span>: <font color="Maroon" title="c14">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T36" title="AFINSQ_1:th.36">AFINSQ_1:36</a></span>
<br/>.= 
<font color="Maroon" title="c12">pp</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10_2"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E5:10_2"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
;<br/>
<a NAME="E19:10_2"/><span class="kw">then </span>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_2"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E7:10_2"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="funct_1.html#T102" title="FUNCT_1:th.102">FUNCT_1:102</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">pp1</font> = <font color="Maroon" title="c17">pp0</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> as   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c21">pp1</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="c21">pp1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> &amp; (  for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E21:10_2"/>
<font color="Maroon" title="c21">pp1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">r</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c14">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:10_2"><span class="lab"><font color="Green" title="E18">A14</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">  for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c22">x</font> = <font color="Maroon" title="c14">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_2"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E7:10_2"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E18:10_2"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="funct_1.html#T102" title="FUNCT_1:th.102">FUNCT_1:102</a></span>;<br/>
<span class="lab"><font color="Green" title="E21">A17</font></span>:  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font> = 
<span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><font color="Maroon" title="c22">x</font></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T75" title="AFINSQ_2:th.75">AFINSQ_2:75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T73" title="AFINSQ_2:th.73">AFINSQ_2:73</a></span>
;<br/>
<span class="kw">set </span><font color="Maroon" title="c23">s2</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span>);<br/>
<a NAME="E24:10_2"/><span class="lab"><font color="Green" title="E22">A18</font></span>: 
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10_2"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E18:10_2"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E23">A19</font></span>: <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:10_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="scmfsa7b.html#E5"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T34" title="AFINSQ_1:th.34">AFINSQ_1:34</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1

;<br/>
<a NAME="E26:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A20</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E27:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A21</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E28:10_2"/><span class="lab"><font color="Green" title="E26">A22</font></span>: 
 <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10_2"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E14:10_2"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="afinsq_2.html#T82" title="AFINSQ_2:th.82">AFINSQ_2:82</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E27">A23</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">p</font> be   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</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="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c22">x</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> )</span><br/><span class="kw">assume </span><a NAME="E1:10_2_4"/>
<font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c22">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span><br/><a NAME="E2:10_2_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T81" title="AFINSQ_2:th.81">AFINSQ_2:81</a></span>;<br/><a NAME="E3:10_2_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:10_2"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="txt" href="#E23:10_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E4:10_2_4"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T81" title="AFINSQ_2:th.81">AFINSQ_2:81</a></span>;<br/><a NAME="E5:10_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A24</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>;<br/><a NAME="E6:10_2_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/><span class="kw">hence </span><a NAME="E7:10_2_4"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c24">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_2_4"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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>
<a NAME="E30:10_2"/><span class="lab"><font color="Green" title="E28">A25</font></span>: 
 for <font color="Olive" title="b1">c</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="Olive" title="b1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">c</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c24">c</font> be    <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> ; <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="c24">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> implies <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c24">c</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:10_2_5"/>
<font color="Maroon" title="c24">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c24">c</font></span>)</span></span><br/>

<a NAME="E2:10_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A26</font></span>: 
<font color="Maroon" title="c24">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<a NAME="E3:10_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A27</font></span>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c24">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T23" title="AFINSQ_1:th.23">AFINSQ_1:23</a></span>;<br/>
<a NAME="E4:10_2_5"/><span class="lab"><font color="Green" title="E31">A28</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:10_2"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E29:10_2"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/>
<a NAME="E5:10_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A29</font></span>: 
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c24">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2_5"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="ref" href="afinsq_1.html#D3" title="AFINSQ_1:def.3">AFINSQ_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c24">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10_2_5"><span class="lab"><font color="Green" title="E31">A28</font></span></a>, <a class="txt" href="#E3:10_2_5"><span class="lab"><font color="Green" title="E30">A27</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c24">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E5:10_2_5"><span class="lab"><font color="Green" title="E32">A29</font></span></a>, <a class="txt" href="#E3:10_2_5"><span class="lab"><font color="Green" title="E30">A27</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</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>
<span class="kw">set </span><font color="Maroon" title="c24">c3</font> =  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span>;<br/>
<a NAME="E31:10_2"/><span class="lab"><font color="Green" title="E29">A30</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E32:10_2"/><span class="lab"><font color="Green" title="E30">A31</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:10_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>;<br/>
<a NAME="E33:10_2"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:10_2"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="ref" href="nat_1.html#T43" title="NAT_1:th.43">NAT_1:43</a></span>;<br/>
<a NAME="E34:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A32</font></span>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:10_2"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E35:10_2"/><span class="lab"><font color="Green" title="E32">A33</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E36:10_2"/><span class="lab"><font color="Green" title="E33">A34</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c20">s1</font>,<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:10_2"><span class="lab"><font color="Green" title="E29">A30</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/>
<a NAME="E37:10_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:10_2"><span class="lab"><font color="Green" title="E29">A30</font></span></a>, <a class="txt" href="#E36:10_2"><span class="lab"><font color="Green" title="E33">A34</font></span></a>, <a class="txt" href="#E30:10_2"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="scmfsa7b.html#E6"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c25">s2</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span>) as   <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D9" title="MEMSTR_0:def.9">MEMSTR_0:def 9</a></span>;<br/>
<a NAME="E39:10_2"/><span class="lab"><font color="Green" title="E34">A35</font></span>: 
 for <font color="Olive" title="b1">c</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="Olive" title="b1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> holds <br/><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Olive" title="b1">c</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c26">c</font> be    <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> ; <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="c26">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">c</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:10_2_6"/>
<font color="Maroon" title="c26">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">c</font></span>)</span></span><br/>

<a NAME="E2:10_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A36</font></span>: 
<font color="Maroon" title="c26">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<a NAME="E3:10_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A37</font></span>: 
<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T23" title="AFINSQ_1:th.23">AFINSQ_1:23</a></span>;<br/>
<a NAME="E4:10_2_6"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10_2"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E18:10_2"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E29:10_2"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/>
<a NAME="E5:10_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A38</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>;<br/>
<a NAME="E6:10_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A39</font></span>: 
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c26">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2_6"><span class="lab"><font color="Green" title="E35">A36</font></span></a>, <a class="ref" href="afinsq_1.html#D3" title="AFINSQ_1:def.3">AFINSQ_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_2_6"><span class="lab"><font color="Green" title="E36">A37</font></span></a>, <a class="txt" href="#E5:10_2_6"><span class="lab"><font color="Green" title="E37">A38</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E6:10_2_6"><span class="lab"><font color="Green" title="E38">A39</font></span></a>, <a class="txt" href="#E3:10_2_6"><span class="lab"><font color="Green" title="E36">A37</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</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><span class="lab"><font color="Green" title="E35">A40</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_7"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c26">i</font> be    <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> ; <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="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span> implies <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font></span>)</span>)</span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:10_2_7"/>
<font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font></span>)</span>)</span>)</span></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c26">i</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:10_2"><span class="lab"><font color="Green" title="E34">A35</font></span></a>, <a class="txt" href="scmfsa7b.html#E6"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
;<br/> <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="lab"><font color="Green" title="E36">A41</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_8"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c26">i</font> be    <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> ; <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="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> implies <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font></span>)</span>)</span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:10_2_8"/>
<font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font></span>)</span>)</span>)</span></span><br/><span class="kw">hence </span><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c20">s1</font>,<font color="Maroon" title="c26">i</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:10_2"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="scmfsa7b.html#E6"><span class="lab"><font color="Green" title="E3">Lm3</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">i</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
;<br/> <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>
<a NAME="E42:10_2"/><span class="lab"><font color="Green" title="E37">A42</font></span>: 
 for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c26">i</font> be    <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> ; <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="c26">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> implies  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:10_2_9"/><span class="lab"><font color="Green" title="E38">A43</font></span>: 
<font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">i</font></span><br/>

<div><span class="lab"><font color="Green" title="E39">A44</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_9_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:10_2_9_1"/><span class="lab"><font color="Green" title="E40">A45</font></span>: 
<font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_9"><span class="lab"><font color="Green" title="E38">A43</font></span></a>, <a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/><span class="kw">assume </span><a NAME="E2:10_2_9_1"/><span class="lab"><font color="Green" title="E41">A46</font></span>: 
 not <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  not <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> or  not <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> ) implies ( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> ) )</span><br/><span class="kw">assume </span><a NAME="E3:10_2_9_1"/>
(  not <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> or  not <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> )</span><br/><span class="kw">hence </span><a NAME="E4:10_2_9_1"/>
( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:10_2"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="txt" href="#E2:10_2_9_1"><span class="lab"><font color="Green" title="E41">A46</font></span></a>, <a class="txt" href="#E1:10_2_9_1"><span class="lab"><font color="Green" title="E40">A45</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</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="10_2_9_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="E1:10_2_9_2"/>
( <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> or ( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> ) or ( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2_9"><span class="lab"><font color="Green" title="E39">A44</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_9_2_1"><span class="kw">suppose </span></a><a NAME="E1:10_2_9_2_1"/>
<font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">i</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:10_2_9_2_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:10_2"><span class="lab"><font color="Green" title="E19">A15</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="10_2_9_2_2"><span class="kw">suppose </span></a><a NAME="E1:10_2_9_2_2"/><span class="lab"><font color="Green" title="E40">A47</font></span>: 
( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">i</font></span><br/><div class="add"><a NAME="E2:10_2_9_2_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">ii</font> = <font color="Maroon" title="c26">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> as    <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">by</span> <span class="lab"><a class="ref" href="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/><a NAME="E4:10_2_9_2_2"/>
<font color="Maroon" title="c26">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_9_2_2"><span class="lab"><font color="Green" title="E40">A47</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c26">i</font> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">ii</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:10_2"><span class="lab"><font color="Green" title="E29">A30</font></span></a>, <a class="txt" href="#E41:10_2"><span class="lab"><font color="Green" title="E36">A41</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span>

;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/><span class="kw">thus </span><a NAME="E6:10_2_9_2_2"/>
verum
 ; <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="10_2_9_2_3"><span class="kw">suppose </span></a><a NAME="E1:10_2_9_2_3"/><span class="lab"><font color="Green" title="E40">A48</font></span>: 
( <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> &amp; <font color="Maroon" title="c26">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">i</font></span><br/><div class="add"><a NAME="E2:10_2_9_2_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">ii</font> = <font color="Maroon" title="c26">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> as    <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">by</span> <span class="lab"><a class="ref" href="int_1.html#T3" title="INT_1:th.3">INT_1:3</a></span>;<br/><a NAME="E4:10_2_9_2_3"/>
<font color="Maroon" title="c26">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_9_2_3"><span class="lab"><font color="Green" title="E40">A48</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c26">i</font> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c27">ii</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:10_2"><span class="lab"><font color="Green" title="E35">A40</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c26">i</font>)</span>)</span>

;<br/> <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>
<a NAME="E43:10_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:10_2"><span class="lab"><font color="Green" title="E27">A23</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">rq</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <span class="kw"> such that </span><br/><a NAME="E45:10_2"/><span class="lab"><font color="Green" title="E38">A49</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c26">rq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T80" title="AFINSQ_2:th.80">AFINSQ_2:80</a></span>;<br/>
<a NAME="E46:10_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:10_2"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E47:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A50</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E48:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A51</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:10_2"><span class="lab"><font color="Green" title="E30">A31</font></span></a>, <a class="txt" href="#E35:10_2"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<a NAME="E49:10_2"/>
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T33" title="AFINSQ_1:th.33">AFINSQ_1:33</a></span>;<br/>
<a NAME="E50:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A52</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T49" title="CARD_1:th.49">CARD_1:49</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E51:10_2"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T34" title="AFINSQ_1:th.34">AFINSQ_1:34</a></span>;<br/>
<a NAME="E52:10_2"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E53:10_2"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>;<br/>
<a NAME="E54:10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A53</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<a NAME="E55:10_2"/><span class="lab"><font color="Green" title="E43">A54</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:10_2"><span class="lab"><font color="Green" title="E29">A30</font></span></a>, <a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E56:10_2"/><span class="lab"><font color="Green" title="E44">A55</font></span>: 
<font color="Maroon" title="c5">P</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c5">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>) = 
<font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:10_2"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="txt" href="#E42:10_2"><span class="lab"><font color="Green" title="E37">A42</font></span></a>, <a class="txt" href="#E56:10_2"><span class="lab"><font color="Green" title="E44">A55</font></span></a>, <a class="txt" href="#E47:10_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="txt" href="#E35:10_2"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="txt" href="#E34:10_2"><span class="lab"><font color="Green" title="E31">A32</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:10_2"><span class="lab"><font color="Green" title="E43">A54</font></span></a>, <a class="txt" href="#E48:10_2"><span class="lab"><font color="Green" title="E40">A51</font></span></a>, <a class="txt" href="#E45:10_2"><span class="lab"><font color="Green" title="E38">A49</font></span></a>, <a class="ref" href="afinsq_1.html#D3" title="AFINSQ_1:def.3">AFINSQ_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="afinsq_1.html#K15" title="AFINSQ_1:func.15">^</a> <font color="Maroon" title="c22">x</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E45">A56</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c5">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:10_2"><span class="lab"><font color="Green" title="E42">A53</font></span></a>, <a class="txt" href="#E11:10_2"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E18:10_2"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="afinsq_1.html#D3" title="AFINSQ_1:def.3">AFINSQ_1:def 3</a></span>
<br/>.= 
<span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:10_2"><span class="lab"><font color="Green" title="E41">A52</font></span></a>, <a class="ref" href="afinsq_1.html#D3" title="AFINSQ_1:def.3">AFINSQ_1:def 3</a></span>
<br/>.= 
(<font color="Maroon" title="c7">f</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T34" title="AFINSQ_1:th.34">AFINSQ_1:34</a></span>
;<br/>
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c5">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p0">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:10_2"><span class="lab"><font color="Green" title="E45">A56</font></span></a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E46">A57</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span></span>)</span>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p2">(<span class="default">(<font color="Maroon" title="c7">f</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>) <a href="scmfsa_2.html#K15" title="SCMFSA_2:func.15">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:10_2"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>
<br/>.= 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_2.html#T73" title="SCMFSA_2:th.73">SCMFSA_2:73</a></span>
<br/>.= 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p0"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p5">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c17">pp0</font></span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c13">r</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 2</span>)</span>,<font color="Maroon" title="c16">pr1</font>)</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:10_2"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="txt" href="#E42:10_2"><span class="lab"><font color="Green" title="E37">A42</font></span></a>, <a class="txt" href="#E27:10_2"><span class="lab"><font color="Green" title="E25">A21</font></span></a></span>
;<br/>
<span class="kw">thus </span><a NAME="E61:10_2"/>
 for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_14"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c27">i</font> be    <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> ; <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="c27">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> implies  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c27">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:10_2_14"/><span class="lab"><font color="Green" title="E47">A58</font></span>: 
<font color="Maroon" title="c27">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c27">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">i</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_14_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="E1:10_2_14_1"/>
( <font color="Maroon" title="c27">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> or <font color="Maroon" title="c27">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_14"><span class="lab"><font color="Green" title="E47">A58</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_14_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_2_14_1_1"/>
<font color="Maroon" title="c27">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c27">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">i</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:10_2_14_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c27">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:10_2"><span class="lab"><font color="Green" title="E37">A42</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="10_2_14_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_2_14_1_2"/>
<font color="Maroon" title="c27">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c21">pp1</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c27">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">i</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:10_2_14_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c27">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:10_2"><span class="lab"><font color="Green" title="E32">A33</font></span></a>, <a class="txt" href="#E26:10_2"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="txt" href="#E60:10_2"><span class="lab"><font color="Green" title="E46">A57</font></span></a>, <a class="ref" href="nat_1.html#T38" title="NAT_1:th.38">NAT_1:38</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>
<span class="kw">set </span><font color="Maroon" title="c13">k</font> =  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span>;<br/>
<a NAME="E10:10"/><span class="lab"><font color="Green" title="E13">A59</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T75" title="AFINSQ_1:th.75">AFINSQ_1:75</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>
;<br/>
<a NAME="E12:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A60</font></span>: 
 <a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">f</font> <a href="scmfsa_7.html#K4" title="SCMFSA_7:func.4">:=</a> <font color="Maroon" title="c8">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/>
<a NAME="E13:10"/><span class="lab"><font color="Green" title="E15">A61</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_4"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">pp</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">pp0</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  st <br/>( <font color="Olive" title="b1">pp0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; (  for <font color="Olive" title="b2">i</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="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Olive" title="b1">pp0</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b2">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">i</font> ) )</span><br/>

<span class="kw">take </span>
 <a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p1">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p1">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; (  for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <span class="p3">(<span class="default"><a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p4">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span></span>)</span></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E2:10_4"/>
 <a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p1">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <span class="p3">(<span class="default"><a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p4">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span></span>)</span></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font></span><br/>

<a NAME="E3:10_4"/><span class="lab"><font color="Green" title="E16">A62</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T27" title="AFINSQ_1:th.27">AFINSQ_1:27</a></span>;<br/>
<a NAME="E4:10_4"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T17" title="AFINSQ_1:th.17">AFINSQ_1:17</a></span>;<br/>
<a NAME="E5:10_4"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/>
<a NAME="E6:10_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A63</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A59</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E18">A64</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">i</font> be    <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> ; <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="c14">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> implies  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c14">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i</font> )</span><br/><span class="kw">assume </span><a NAME="E1:10_4_1"/>
<font color="Maroon" title="c14">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c14">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i</font></span><br/><a NAME="E2:10_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A59</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><span class="kw">hence </span><a NAME="E3:10_4_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c14">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E14">A60</font></span></a>, <a class="txt" href="scmfsa7b.html#E7"><span class="lab"><font color="Green" title="E4">Lm4</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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>
<a NAME="E8:10_4"/><span class="lab"><font color="Green" title="E19">A65</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A59</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E9:10_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A66</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/>
<a NAME="E10:10_4"/><span class="lab"><font color="Green" title="E21">A67</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_4"><span class="lab"><font color="Green" title="E18">A64</font></span></a>, <a class="txt" href="#E8:10_4"><span class="lab"><font color="Green" title="E19">A65</font></span></a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E22">A68</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c5">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>)</span>)</span>) = 
<font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="txt" href="#E6:10_4"><span class="lab"><font color="Green" title="E17">A63</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_4"><span class="lab"><font color="Green" title="E16">A62</font></span></a>, <a class="txt" href="#E9:10_4"><span class="lab"><font color="Green" title="E20">A66</font></span></a>, <a class="ref" href="afinsq_1.html#D3" title="AFINSQ_1:def.3">AFINSQ_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T36" title="AFINSQ_1:th.36">AFINSQ_1:36</a></span>
;<br/>
<span class="lab"><font color="Green" title="E23">A69</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c5">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A59</font></span></a>, <a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10_4"><span class="lab"><font color="Green" title="E22">A68</font></span></a></span>
;<br/>
<span class="lab"><font color="Green" title="E24">A70</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span></span>)</span>)</span>)</span> = 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p3">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span></span>)</span>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:10_4"><span class="lab"><font color="Green" title="E23">A69</font></span></a>, <a class="ref" href="scmfsa_2.html#T75" title="SCMFSA_2:th.75">SCMFSA_2:75</a></span>
<br/>.= 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E13">A59</font></span></a>, <a class="txt" href="#E10:10_4"><span class="lab"><font color="Green" title="E21">A67</font></span></a>, <a class="ref" href="nat_1.html#T38" title="NAT_1:th.38">NAT_1:38</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E25">A71</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_4_5"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">i</font> be    <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> ; <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="c14">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> implies  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c14">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i</font> )</span><br/><span class="kw">assume </span><a NAME="E1:10_4_5"/>
<font color="Maroon" title="c14">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c14">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i</font></span><br/><a NAME="E2:10_4_5"/><span class="kw">then </span>
( <font color="Maroon" title="c14">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> or <font color="Maroon" title="c14">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:10_4_5"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c14">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10_4"><span class="lab"><font color="Green" title="E18">A64</font></span></a>, <a class="txt" href="#E13:10_4"><span class="lab"><font color="Green" title="E24">A70</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>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p1">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <span class="p2">(<span class="default"><a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p3">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_2.html#T74" title="AFINSQ_2:th.74">AFINSQ_2:74</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T29" title="AFINSQ_1:th.29">AFINSQ_1:29</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E16:10_4"/>
 for <font color="Olive" title="b1">i</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="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <span class="p3">(<span class="default"><a href="afinsq_1.html#K4" title="AFINSQ_1:func.4">&lt;%&gt;</a> <span class="p4">(<span class="default"> the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span></span>)</span></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:10_4"><span class="lab"><font color="Green" title="E25">A71</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>
<a NAME="E14:10"/>
 for <font color="Olive" title="b1">r</font> being   <a href="afinsq_1.html#NM1" title="AFINSQ_1:NM.1">XFinSequence</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="afinsq_1.html#S3" title="AFINSQ_1:sch.3">AFINSQ_1:sch 3</a>(<a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E15">A61</font></span></a>, <a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E12">A8</font></span></a>);<br/></span>
<a NAME="E15:10"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">pp0</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  st <br/>( <font color="Olive" title="b1">pp0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">pp</font> &amp; (  for <font color="Olive" title="b2">i</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="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Olive" title="b1">pp0</font></span>)</span></span>)</span> holds <br/> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<font color="Olive" title="b2">i</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">i</font> ) )
 
;<br/>
<a NAME="E16:10"/><span class="kw">then </span>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p4">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p2">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span>
 
;<br/>
<span class="kw">then </span> <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c5">P</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p5"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p4">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span></span>)</span>)</span>)</span>) = 
<font color="Maroon" title="c5">P</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p3">(<span class="default"><a href="scmfsa_7.html#K3" title="SCMFSA_7:func.3">aSeq</a> (<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmfsa_7.html#K2" title="SCMFSA_7:func.2">aSeq</a> (<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">p</font></span>)</span>)</span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p4"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c7">f</font> <a href="scmfsa_2.html#K17" title="SCMFSA_2:func.17">:=&lt;0,...,0&gt;</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> 1</span>)</span></span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="afinsq_1.html#K14" title="AFINSQ_1:func.14">^</a> <span class="p3">(<span class="default"><a href="afinsq_2.html#K8" title="AFINSQ_2:func.8">FlattenSeq</a> <font color="Maroon" title="c12">pp</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E11">A7</font></span></a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="ref" href="afinsq_1.html#T36" title="AFINSQ_1:th.36">AFINSQ_1:36</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E18:10"/>
<font color="Maroon" title="c5">P</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T29" title="EXTPRO_1:th.29">EXTPRO_1:29</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>
