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<b>let </b><font color="Maroon">I1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a> , <font color="Maroon">I2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</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> , <font color="Maroon">ps</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">ds</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">il1</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="scm_1.html#M1">State-consisting</a> of <font color="Maroon">il</font>,<font color="Maroon">ps</font>,<font color="Maroon">ds</font>,<font color="Maroon">I1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">I2</font>, <a href="lang1.html#K2">&lt;*&gt;</a> <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">u</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="E1:2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k1</font> &amp;  <a href="ami_3.html#K16">il.</a> <font color="Maroon">il1</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</a> <font color="Maroon">u</font> )
 ;<br/>

<a NAME="E2:2"/><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">I1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">I2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>;<br/>
<div><i><font color="Green">E36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="2_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="E1:2_1"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">I2</font>
 ;<br/><a NAME="E2:2_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <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"><font color="Maroon">I1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">I2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:2_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">I1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">I2</font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><i><font color="Green">E40</font></i>: <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"><span class="p3">(<span class="default"><font color="Maroon">ps</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> = 
<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"><font color="Maroon">ps</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">I1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">I2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scm_1.html#D1">SCM_1:def 1</a></i>
;<br/><a NAME="E5:2_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">I1</font> <a href="finseq_1.html#K8">^</a> <font color="Maroon">I2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">I2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T36">FINSEQ_1:36</a></i>
<br/>.= 
<font color="Maroon">I2</font> <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>

;<br/><b>hence </b><a NAME="E8:2_1"/>
<font color="Maroon">u</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"><span class="p3">(<span class="default"><font color="Maroon">ps</font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">I2</font> <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="ami_1.html#T54">AMI_1:54</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_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="E1:2_2"/>
<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"><a href="lang1.html#K2">&lt;*&gt;</a> <a href="numbers.html#K4">INT</a> </span>)</span>
 ;<br/><a NAME="E2:2_2"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><b>hence </b><a NAME="E3:2_2"/>
<font color="Maroon">u</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"><font color="Maroon">ds</font> <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"><a href="lang1.html#K2">&lt;*&gt;</a> <a href="numbers.html#K4">INT</a> </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>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:2"/>
<font color="Maroon">u</font> is    <a href="scm_1.html#M1">State-consisting</a> of <font color="Maroon">il1</font>,<font color="Maroon">ps</font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">I1</font></span>)</span>,<font color="Maroon">ds</font>,<font color="Maroon">I2</font>, <a href="lang1.html#K2">&lt;*&gt;</a> <a href="numbers.html#K4">INT</a> 
 <b>by </b><i>, , <a class="ref" href="scm_1.html#D1">SCM_1:def 1</a></i>;<br/>


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