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

<b>let </b><font color="Maroon" title="c1">a</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> ;<br/><b>let </b><font color="Maroon" title="c2">fs1</font>, <font color="Maroon" title="c3">fs2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>





<b>set </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>;<br/>
<a NAME="E1:49"/><i><font color="Green" title="E36">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">fs2</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">fs2</font></span>)</span> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/>
<div><i><font color="Green" title="E37">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_1"/><i><font color="Green" title="E38">A3</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font>
 ;<br/><b>set </b><font color="Maroon" title="c5">f1</font> =  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<font color="Maroon" title="c1">a</font>;<br/><b>set </b><font color="Maroon" title="c6">f2</font> = <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>;<br/><b>set </b><font color="Maroon" title="c7">f3</font> = <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>;<br/><a NAME="E2:49_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E3:49_1"/><b>then </b><i><font color="Green" title="E39">A4</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_1_1_1"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 or <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1_1"><b>suppose </b></a><a NAME="E1:49_1_1_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ;<br/><div class="add"><a NAME="E2:49_1_1_1_1"/><b>then </b><i><font color="Green" title="E40">A5</font></i>: 
( not <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">fs1</font> &amp; not <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>hence </b> <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<font color="Maroon" title="c1">a</font> = 
<font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
<b>by </b><i><a class="ref" href="wsierp_1.html#D1" target="_self" title="WSIERP_1:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
<b>by </b><i><a class="txt" href="wsierp_1.html#E2:49_1_1_1_1"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="wsierp_1.html#D1" target="_self" title="WSIERP_1:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1_2"><b>suppose </b></a><a NAME="E1:49_1_1_1_2"/>
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ;<br/><div class="add"><a NAME="E2:49_1_1_1_2"/><b>then </b><i><font color="Green" title="E40">A6</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> &amp; <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">fs1</font> )
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="wsierp_1.html#E3:49_1"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">g1</font>, <font color="Maroon" title="c9">g2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E4:49_1_1_1_2"/><i><font color="Green" title="E41">A7</font></i>: 
( <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c9">g2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font> )
 <b>by </b><i><a class="txt" href="wsierp_1.html#E38"><i><font color="Green" title="E31">Lm15</font></i></a></i>;<br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
<b>by </b><i><a class="txt" href="wsierp_1.html#E4:49_1_1_1_2"><i><font color="Green" title="E41">A7</font></i></a>, <a class="ref" href="finseq_2.html#T19" title="FINSEQ_2:th.19">FINSEQ_2:19</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font>

;<br/><b>then consider </b><font color="Maroon" title="c10">t</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E7:49_1_1_1_2"/><i><font color="Green" title="E42">A8</font></i>: 
<font color="Maroon" title="c2">fs1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="wsierp_1.html#E4:49_1_1_1_2"><i><font color="Green" title="E41">A7</font></i></a>, <a class="ref" href="finseq_1.html#T64" title="FINSEQ_1:th.64">FINSEQ_1:64</a></i>;<br/><a NAME="E8:49_1_1_1_2"/><i><font color="Green" title="E43">A9</font></i>: 
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:49_1_1_1_2"><i><font color="Green" title="E40">A6</font></i></a>, <a class="txt" href="wsierp_1.html#E4:49_1_1_1_2"><i><font color="Green" title="E41">A7</font></i></a>, <a class="txt" href="wsierp_1.html#E7:49_1_1_1_2"><i><font color="Green" title="E42">A8</font></i></a>, <a class="txt" href="wsierp_1.html#E40"><i><font color="Green" title="E33">Lm16</font></i></a></i>;<br/><a NAME="E9:49_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">a</font></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E4:49_1_1_1_2"><i><font color="Green" title="E41">A7</font></i></a>, <a class="txt" href="wsierp_1.html#E7:49_1_1_1_2"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:49_1_1_1_2"/><b>then </b><i><font color="Green" title="E44">A10</font></i>: 
<font color="Maroon" title="c9">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T46" title="FINSEQ_1:th.46">FINSEQ_1:46</a></i>;<br/><b>thus </b> <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<font color="Maroon" title="c1">a</font> = 
<font color="Maroon" title="c8">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c9">g2</font>
<b>by </b><i><a class="txt" href="wsierp_1.html#E2:49_1_1_1_2"><i><font color="Green" title="E40">A6</font></i></a>, <a class="txt" href="wsierp_1.html#E4:49_1_1_1_2"><i><font color="Green" title="E41">A7</font></i></a>, <a class="txt" href="wsierp_1.html#E40"><i><font color="Green" title="E33">Lm16</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
<b>by </b><i><a class="txt" href="wsierp_1.html#E8:49_1_1_1_2"><i><font color="Green" title="E43">A9</font></i></a>, <a class="txt" href="wsierp_1.html#E10:49_1_1_1_2"><i><font color="Green" title="E44">A10</font></i></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:49_1"/>
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_2"/><i><font color="Green" title="E38">A11</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ;<br/><b>set </b><font color="Maroon" title="c5">f1</font> =  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c6">f2</font> = <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_2_1_1"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">fs2</font> or <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">fs2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_2_1_1_1"><b>suppose </b></a><a NAME="E1:49_2_1_1_1"/><i><font color="Green" title="E39">A12</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">fs2</font>
 ;<br/><div class="add"><a NAME="E2:49_2_1_1_1"/><b>then </b><i><font color="Green" title="E40">A13</font></i>: 
not <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">fs2</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:49_2_1_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="wsierp_1.html#E1:49_2_1_1_1"><i><font color="Green" title="E39">A12</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E4:49_2_1_1_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>hence </b> <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> = 
<font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
<b>by </b><i><a class="ref" href="wsierp_1.html#D1" target="_self" title="WSIERP_1:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span>
<b>by </b><i><a class="txt" href="wsierp_1.html#E2:49_2_1_1_1"><i><font color="Green" title="E40">A13</font></i></a>, <a class="ref" href="wsierp_1.html#D1" target="_self" title="WSIERP_1:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_2_1_1_2"><b>suppose </b></a><a NAME="E1:49_2_1_1_2"/><i><font color="Green" title="E39">A14</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">fs2</font>
 ;<br/><div class="add"><a NAME="E2:49_2_1_1_2"/><b>then </b><i><font color="Green" title="E40">A15</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">fs2</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49_2"><i><font color="Green" title="E38">A11</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:49_2_1_1_2"/><i><font color="Green" title="E41">A16</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="wsierp_1.html#E1:49_2_1_1_2"><i><font color="Green" title="E39">A14</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E4:49_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49_2"><i><font color="Green" title="E38">A11</font></i></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></i>;<br/><a NAME="E5:49_2_1_1_2"/><b>then </b><i><font color="Green" title="E42">A17</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E3:49_2_1_1_2"><i><font color="Green" title="E41">A16</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">g1</font>, <font color="Maroon" title="c8">g2</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E7:49_2_1_1_2"/><i><font color="Green" title="E43">A18</font></i>: 
( <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">g1</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="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> )
 <b>by </b><i><a class="txt" href="wsierp_1.html#E38"><i><font color="Green" title="E31">Lm15</font></i></a></i>;<br/><a NAME="E8:49_2_1_1_2"/><i><font color="Green" title="E44">A19</font></i>: 
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E5:49_2_1_1_2"><i><font color="Green" title="E42">A17</font></i></a>, <a class="txt" href="wsierp_1.html#E7:49_2_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="wsierp_1.html#E40"><i><font color="Green" title="E33">Lm16</font></i></a></i>;<br/><a NAME="E9:49_2_1_1_2"/><i><font color="Green" title="E45">A20</font></i>: 
<font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E7:49_2_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>;<br/><a NAME="E10:49_2_1_1_2"/>
<font color="Maroon" title="c1">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="wsierp_1.html#E1:49_2"><i><font color="Green" title="E38">A11</font></i></a>, <a class="ref" href="xreal_1.html#T50" title="XREAL_1:th.50">XREAL_1:50</a></i>;<br/><a NAME="E11:49_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E7"><i><font color="Green" title="E4">Lm1</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">t</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E13:49_2_1_1_2"/><i><font color="Green" title="E46">A21</font></i>: 
<font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c9">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g1</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E7:49_2_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="wsierp_1.html#E9:49_2_1_1_2"><i><font color="Green" title="E45">A20</font></i></a>, <a class="ref" href="finseq_1.html#T64" title="FINSEQ_1:th.64">FINSEQ_1:64</a></i>;<br/><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>
<br/>.= 
<font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font>
<b>by </b><i><a class="txt" href="wsierp_1.html#E7:49_2_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="wsierp_1.html#E13:49_2_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>
;<br/><a NAME="E15:49_2_1_1_2"/><b>then </b><i><font color="Green" title="E47">A22</font></i>: 
<font color="Maroon" title="c3">fs2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T46" title="FINSEQ_1:th.46">FINSEQ_1:46</a></i>;<br/><a NAME="E16:49_2_1_1_2"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">t</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E7:49_2_1_1_2"><i><font color="Green" title="E43">A18</font></i></a>, <a class="txt" href="wsierp_1.html#E13:49_2_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>;<br/><a NAME="E17:49_2_1_1_2"/><b>then </b>
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c8">g2</font>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:49_2_1_1_2"><i><font color="Green" title="E40">A15</font></i></a>, <a class="txt" href="wsierp_1.html#E15:49_2_1_1_2"><i><font color="Green" title="E47">A22</font></i></a>, <a class="txt" href="wsierp_1.html#E40"><i><font color="Green" title="E33">Lm16</font></i></a></i>;<br/><b>hence </b><a NAME="E18:49_2_1_1_2"/>
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="wsierp_1.html#E8:49_2_1_1_2"><i><font color="Green" title="E44">A19</font></i></a>, <a class="txt" href="wsierp_1.html#E13:49_2_1_1_2"><i><font color="Green" title="E46">A21</font></i></a>, <a class="ref" href="finseq_1.html#T45" title="FINSEQ_1:th.45">FINSEQ_1:45</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:49_2"/>
 <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:49"/>
( ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font> implies  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c2">fs1</font>,<font color="Maroon" title="c1">a</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font> ) &amp; ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies  <a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">fs2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">fs1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">fs1</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><a href="finseq_3.html#K2" title="FINSEQ_3:func.2">Del</a> <font color="Maroon" title="c3">fs2</font>,<font color="Maroon" title="c1">a</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="wsierp_1.html#E2:49"><i><font color="Green" title="E37">A2</font></i></a></i>;<br/>


</div>
