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

<b>let </b><font color="Maroon">I1</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I2</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I3</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I4</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I5</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I6</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I7</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I8</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I9</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">i2</font> be   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">i3</font> be   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">i4</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">il</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>







<b>assume </b><a NAME="E1:28"/><i><font color="Green">E23</font></i>: 
(  <a href="ami_1.html#K6">IC</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> <font color="Maroon">il</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I1</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I2</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I3</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I4</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I5</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 5</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I6</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 6</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I7</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 7</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I8</font> &amp; <font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> 8</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I9</font> &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i3</font> &amp; <font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i4</font> )
 ;<br/>

<b>set </b><font color="Maroon">I</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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I2</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I6</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I7</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I8</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I9</font></span><a href="finseq_1.html#K12">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">D</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i3</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i4</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span>;<br/>
<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I2</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I6</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I7</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I8</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I9</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:28_1"/>
(  <a href="finseq_1.html#K3">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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I2</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I6</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I7</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I8</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I9</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> 9 &amp; 9 <a href="hidden.html#R1">=</a> 8 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="finseq_1.html#T92">FINSEQ_1:92</a></i>;<br/><a NAME="E3:28_1"/><b>then </b>
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 8 &amp; 8 <a href="hidden.html#R1">=</a> 7 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 7 <a href="hidden.html#R1">=</a> 6 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E5:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 6 <a href="hidden.html#R1">=</a> 5 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E6:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 5 <a href="hidden.html#R1">=</a> 4 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E7:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 4 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 4 <a href="hidden.html#R1">=</a> 3 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E8:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 3 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 3 <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E9:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 2 <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E10:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 1 <a href="hidden.html#R1">=</a> 0 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E11:28_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 ) &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E12:28_1"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 4 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 5 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 6 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 7 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 8 )
 ;<br/><b>hence </b><a NAME="E13:28_1"/>
<font color="Maroon">s</font> <a href="ami_1.html#K13">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K16">il.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I2</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I6</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I7</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I8</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I9</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="scm_1.html#T7" target="_self">Th7</a>, <a class="ref" href="finseq_1.html#T92">FINSEQ_1:92</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:28_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i3</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i4</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span>
 ;<br/><a NAME="E2:28_2"/>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i3</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i4</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> 4 &amp; 4 <a href="hidden.html#R1">=</a> 3 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="finseq_1.html#T87">FINSEQ_1:87</a></i>;<br/><a NAME="E3:28_2"/><b>then </b>
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 3 &amp; 3 <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:28_2"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 ) &amp; 2 <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E5:28_2"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 ) &amp; 1 <a href="hidden.html#R1">=</a> 0 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E6:28_2"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 0 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 ) &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/><a NAME="E7:28_2"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/><b>hence </b><a NAME="E8:28_2"/>
<font color="Maroon">s</font> <a href="ami_3.html#K2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> <span class="p2">(<span class="default">0 <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i3</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i4</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="scm_1.html#T7" target="_self">Th7</a>, <a class="ref" href="finseq_1.html#T87">FINSEQ_1:87</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:28"/>
<font color="Maroon">s</font> is    <a href="scm_1.html#M1" target="_self">State-consisting</a> of <font color="Maroon">il</font>,0,0,<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"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I1</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I2</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I3</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I6</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I7</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I8</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">I9</font></span><a href="finseq_1.html#K12">*&gt;</a></span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i1</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i2</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i3</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="scm_1.html#K1" target="_self">&lt;*</a><span class="default"><font color="Maroon">i4</font></span><a href="scm_1.html#K1" target="_self">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="scm_1.html#T7" target="_self">Th7</a>, , </i>;<br/>


</div>
