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

<b>let </b><font color="Maroon" title="c1">R</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b3">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> holds <br/> <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Olive" title="b2">s</font></span>)</span>,<font color="Olive" title="b2">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">s</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> holds <br/> <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> implies  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )</span><br/>







<b>set </b><font color="Maroon" title="c5">mf</font> =  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font>;<br/>
<b>set </b><font color="Maroon" title="c6">nf</font> = <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font>;<br/>
<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E14">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> &amp; <font color="Maroon" title="c1">R</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><br/>

<a NAME="E2:19"/><b>then </b><i><font color="Green" title="E15">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2
 
<b>by </b><i><a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></i>;<br/>
<a NAME="E3:19"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 1
 
;<br/>
<a NAME="E4:19"/><b>then </b><i><font color="Green" title="E17">A4</font></i>: 
( <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 &amp; <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 &amp; <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E5:19"/><i><font color="Green" title="E18">A5</font></i>: 
 <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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="txt" href="#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E6:19"/><b>then </b>
 <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"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></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/>
<a NAME="E7:19"/><b>then </b><i><font color="Green" title="E19">A6</font></i>: 
(  <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"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font> &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/>
<a NAME="E8:19"/><i><font color="Green" title="E20">A7</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2
 
<b>by </b><i><a class="txt" href="#E4:19"><i><font color="Green" title="E17">A4</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E9:19"/><i><font color="Green" title="E21">X</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> implies <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font> )</span><br/><b>assume </b><a NAME="E1:19_1"/>
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font></span><br/><a NAME="E2:19_1"/><b>then </b><i><font color="Green" title="E22">A8</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">m</font> &amp; <font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 )
 <b>by </b><i><a class="txt" href="#E9:19"><i><font color="Green" title="E21">X</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1"/>
( <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 or <font color="Maroon" title="c7">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_1"/><i><font color="Green" title="E23">A9</font></i>: 
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font> = 
<font color="Maroon" title="c3">s</font>
<b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c4">n</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
<b>by </b><i><a class="txt" href="#E5:19"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E7:19"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="#E8:19"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="#E1:19_1_1_1_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="finseq_1.html#T37" title="FINSEQ_1:th.37">FINSEQ_1:37</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_2"/>
<font color="Maroon" title="c7">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font></span><br/><div class="add"><a NAME="E2:19_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2
 <b>by </b><i><a class="txt" href="#E2:19_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E3:19_1_1_1_2"/><b>then </b><i><font color="Green" title="E23">A10</font></i>: 
<font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 <b>by </b><i><a class="txt" href="#E3:19"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:19_1_1_1_2"/><i><font color="Green" title="E24">A11</font></i>: 
<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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 <b>by </b><i><a class="txt" href="#E2:19"><i><font color="Green" title="E15">A2</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_2_1_1"/>
( <font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 or <font color="Maroon" title="c7">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:19_1_1_1_2_1_1_1"/><i><font color="Green" title="E25">A12</font></i>: 
<font color="Maroon" title="c7">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font></span><br/><div class="add"><a NAME="E2:19_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E26">A13</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font> = 
<font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font>
<b>by </b><i><a class="txt" href="#E1:19"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E3:19"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="#E2:19_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="#E4:19_1_1_1_2"><i><font color="Green" title="E24">A11</font></i></a>, <a class="txt" href="#E1:19_1_1_1_2_1_1_1"><i><font color="Green" title="E25">A12</font></i></a>, <a class="ref" href="rfinseq.html#D3" target="_self" title="RFINSEQ:def.3">Def3</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c4">n</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
<b>by </b><i><a class="txt" href="#E5:19"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E7:19"><i><font color="Green" title="E19">A6</font></i></a>, <a class="txt" href="#E2:19_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="#E1:19_1_1_1_2_1_1_1"><i><font color="Green" title="E25">A12</font></i></a>, <a class="txt" href="#E2:19_1_1_1_2_1_1_1"><i><font color="Green" title="E26">A13</font></i></a>, <a class="ref" href="finseq_1.html#T37" title="FINSEQ_1:th.37">FINSEQ_1:37</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:19_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c7">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font></span><br/><div class="add"><a NAME="E2:19_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1
 <b>by </b><i><a class="txt" href="#E3:19_1_1_1_2"><i><font color="Green" title="E23">A10</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E3:19_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:19_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E25">A14</font></i>: 
( <font color="Maroon" title="c7">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c7">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 &amp; <font color="Maroon" title="c7">m</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 1 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> )
 <b>by </b><i><a class="txt" href="#E2:19_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:19_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E26">A15</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="#E4:19"><i><font color="Green" title="E17">A4</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E6:19_1_1_1_2_1_1_2"/><i><font color="Green" title="E27">A16</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
<b>by </b><i><a class="txt" href="#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E4:19_1_1_1_2_1_1_2"><i><font color="Green" title="E25">A14</font></i></a>, <a class="txt" href="#E5:19_1_1_1_2_1_1_2"><i><font color="Green" title="E26">A15</font></i></a>, <a class="ref" href="rfinseq.html#T19" target="_self" title="RFINSEQ:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
<b>by </b><i><a class="txt" href="#E5:19"><i><font color="Green" title="E18">A5</font></i></a>, <a class="txt" href="#E4:19_1_1_1_2_1_1_2"><i><font color="Green" title="E25">A14</font></i></a>, <a class="txt" href="#E6:19_1_1_1_2_1_1_2"><i><font color="Green" title="E27">A16</font></i></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:19_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:19_1"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:19"/>
 <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</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="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">r</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c3">s</font></span>)</span>,<font color="Maroon" title="c3">s</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E2:19"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E7:19"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
