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

<b>let </b><font color="Maroon" title="c1">f</font> be  <a href="sprect_1.html#V1" title="SPRECT_1:attr.1">rectangular</a> <a href="goboard5.html#NM1" title="GOBOARD5:NM.1">special_circular_sequence</a>;<br/>

<a NAME="E1:38"/><i><font color="Green" title="E24">A1</font></i>: 
 <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></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"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <span class="p3">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="sprect_1.html#D1" title="SPRECT_1:def.1">SPRECT_1:def 1</a></i>;<br/>
<b>set </b><font color="Maroon" title="c2">C</font> =  <a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font>;<br/>
<b>set </b><font color="Maroon" title="c3">g</font> =  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c4">D</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="compts_1.html#V6" title="COMPTS_1:attr.6">compact</a> non <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a> non <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><b> such that </b><br/><a NAME="E3:38"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <font color="Maroon" title="c4">D</font>
 <b>by </b><i><a class="ref" href="sprect_1.html#D2" title="SPRECT_1:def.2">SPRECT_1:def 2</a></i>;<br/>
<a NAME="E4:38"/><i><font color="Green" title="E26">A3</font></i>: 
5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="sprect_1.html#T90" title="SPRECT_1:th.90">SPRECT_1:90</a></i>;<br/>
<i><font color="Green" title="E27">A4</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> = 
<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#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></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> <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"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="txt" href="sprect_3.html#E1:38"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></i>
<br/>.= 
3 <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"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <span class="p4">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></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#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>
<br/>.= 
3 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
<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="E6:38"/><b>then </b><i><font color="Green" title="E28">A5</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sprect_3.html#E4:38"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/>
<a NAME="E7:38"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="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="c1">f</font> holds <br/><font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Olive" title="b1">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:38_2"/>
<font color="Maroon" title="c5">i</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="c1">f</font>
 ;<br/>

<a NAME="E2:38_2"/><b>then </b><i><font color="Green" title="E29">A6</font></i>: 
( 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">i</font> &amp; <font color="Maroon" title="c5">i</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="c1">f</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<i><font color="Green" title="E30">A7</font></i>: <font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1 = 
 <a href="pscomp_1.html#K28" title="PSCOMP_1:func.28">W-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T91" title="SPRECT_1:th.91">SPRECT_1:91</a></i>
<br/>.= 
 <a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <font color="Maroon" title="c4">D</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T83" title="SPRECT_1:th.83">SPRECT_1:83</a></i>
<br/>.= 
 <a href="pscomp_1.html#K20" title="PSCOMP_1:func.20">NW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T70" title="SPRECT_1:th.70">SPRECT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1
<b>by </b><i><a class="ref" href="sprect_1.html#T37" title="SPRECT_1:th.37">SPRECT_1:37</a></i>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_2_2"/>
( <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 )
 </span><b>by </b><i><a class="txt" href="sprect_3.html#E4:38"><i><font color="Green" title="E26">A3</font></i></a>, <a class="txt" href="sprect_3.html#E2:38_2"><i><font color="Green" title="E29">A6</font></i></a>, <a class="ref" href="nat_1.html#T30" title="NAT_1:th.30">NAT_1:30</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_2_1"><b>suppose </b></a><a NAME="E1:38_2_2_1"/>
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:38_2_2_1"/>
<font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font>
 <b>by </b><i><a class="txt" href="sprect_3.html#E3:38_2"><i><font color="Green" title="E30">A7</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_2_2"><b>suppose </b></a><a NAME="E1:38_2_2_2"/><i><font color="Green" title="E31">A8</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font> = 
 <a href="pscomp_1.html#K31" title="PSCOMP_1:func.31">E-max</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T92" title="SPRECT_1:th.92">SPRECT_1:92</a></i>
<br/>.= 
 <a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <font color="Maroon" title="c4">D</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T87" title="SPRECT_1:th.87">SPRECT_1:87</a></i>
<br/>.= 
 <a href="pscomp_1.html#K21" title="PSCOMP_1:func.21">NE-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T71" title="SPRECT_1:th.71">SPRECT_1:71</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E1:38_2_2_2"><i><font color="Green" title="E31">A8</font></i></a>, <a class="ref" href="sprect_1.html#T38" title="SPRECT_1:th.38">SPRECT_1:38</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_2_3"><b>suppose </b></a><a NAME="E1:38_2_2_3"/><i><font color="Green" title="E31">A9</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font> = 
 <a href="pscomp_1.html#K32" title="PSCOMP_1:func.32">E-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T93" title="SPRECT_1:th.93">SPRECT_1:93</a></i>
<br/>.= 
 <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <font color="Maroon" title="c4">D</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T86" title="SPRECT_1:th.86">SPRECT_1:86</a></i>
<br/>.= 
 <a href="pscomp_1.html#K22" title="PSCOMP_1:func.22">SE-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T73" title="SPRECT_1:th.73">SPRECT_1:73</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E1:38_2_2_3"><i><font color="Green" title="E31">A9</font></i></a>, <a class="ref" href="sprect_1.html#T39" title="SPRECT_1:th.39">SPRECT_1:39</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_2_4"><b>suppose </b></a><a NAME="E1:38_2_2_4"/><i><font color="Green" title="E31">A10</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font> = 
 <a href="pscomp_1.html#K27" title="PSCOMP_1:func.27">W-min</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="ref" href="sprect_1.html#T94" title="SPRECT_1:th.94">SPRECT_1:94</a></i>
<br/>.= 
 <a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <font color="Maroon" title="c4">D</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T82" title="SPRECT_1:th.82">SPRECT_1:82</a></i>
<br/>.= 
 <a href="pscomp_1.html#K19" title="PSCOMP_1:func.19">SW-corner</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
<b>by </b><i><a class="txt" href="sprect_3.html#E3:38"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="sprect_1.html#T72" title="SPRECT_1:th.72">SPRECT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E1:38_2_2_4"><i><font color="Green" title="E31">A10</font></i></a>, <a class="ref" href="sprect_1.html#T40" title="SPRECT_1:th.40">SPRECT_1:40</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_2_2_5"><b>suppose </b></a><a NAME="E1:38_2_2_5"/><i><font color="Green" title="E31">A11</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ;<br/><div class="add"><b>hence </b><font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font> = 
<font color="Maroon" title="c1">f</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1
<b>by </b><i><a class="txt" href="sprect_3.html#E4:38"><i><font color="Green" title="E26">A3</font></i></a>, <a class="ref" href="finseq_6.html#D1" title="FINSEQ_6:def.1">FINSEQ_6:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p2">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="txt" href="sprect_3.html#E5:38"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="sprect_3.html#E3:38_2"><i><font color="Green" title="E30">A7</font></i></a>, <a class="txt" href="sprect_3.html#E1:38_2_2_5"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="finseq_6.html#D1" title="FINSEQ_6:def.1">FINSEQ_6:def 1</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E8:38"/>
<font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sprect_1.html#K1" title="SPRECT_1:func.1">SpStSeq</a> <span class="p1">(<span class="default"><a href="topreal1.html#K5" title="TOPREAL1:func.5">L~</a> <font color="Maroon" title="c1">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="sprect_3.html#E6:38"><i><font color="Green" title="E28">A5</font></i></a>, <a class="ref" href="finseq_5.html#T13" title="FINSEQ_5:th.13">FINSEQ_5:13</a></i>;<br/>


</div>
