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

<b>let </b><font color="Maroon" title="c1">GS</font> be   <a href="lexbfs.html#NM10" title="LEXBFS:NM.10">VLabelNumberingSeq</a>;<br/><b>let </b><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>



<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b> <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> $1</span>)</span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>;<br/>
<a NAME="E1:123"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<b>by </b><i><a class="ref" href="lexbfs.html#D24" target="_self" title="LEXBFS:def.24">Def24</a></i>;<br/>
<a NAME="E2:123"/><i><font color="Green" title="E55">A2</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="123_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:123_1"/><i><font color="Green" title="E56">A3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">k</font>]
 ;<br/>

<b>set </b><font color="Maroon" title="c4">CSK</font> = <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">k</font>;<br/>
<b>set </b><font color="Maroon" title="c5">VLK</font> =  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c6">CK1</font> = <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">VL1</font> =  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">GN</font> = <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> ;<br/>
<b>set </b><font color="Maroon" title="c9">w</font> = <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="123_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:123_1_1"/>
( <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a>  or <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="123_1_1_1"><b>suppose </b></a><a NAME="E1:123_1_1_1"/>
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> 
 ;<br/><div class="add"><a NAME="E2:123_1_1_1"/><b>then </b><i><font color="Green" title="E57">A4</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#D27" target="_self" title="LEXBFS:def.27">Def27</a></i>;<br/><b>set </b><font color="Maroon" title="c10">wf</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span>;<br/><a NAME="E3:123_1_1_1"/><i><font color="Green" title="E58">A5</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>by </b><i><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a>, <a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="123_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:123_1_1_1_1"/><i><font color="Green" title="E59">A6</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:123_1_1_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">k</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#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#T21" target="_self" title="LEXBFS:th.21">Th21</a></i>;<br/><b>hence </b><a NAME="E3:123_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:123_1_1_1_1"><i><font color="Green" title="E59">A6</font></i></a>, <a class="ref" href="lexbfs.html#T5" target="_self" title="LEXBFS:th.5">Th5</a></i>;<br/></div><b>end;</b></div><a NAME="E5:123_1_1_1"/><b>then </b><i><font color="Green" title="E59">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:123_1_1_1"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T56" title="ZFMISC_1:th.56">ZFMISC_1:56</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="123_1_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">x1</font>, <font color="Maroon" title="c12">x2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:123_1_1_1_2"/><i><font color="Green" title="E60">A8</font></i>: 
( <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> &amp; <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> )
 <b>and </b><br/><a NAME="E2:123_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x2</font>
 ;<br/><a NAME="E3:123_1_1_1_2"/>
( <font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c12">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:123_1_1_1"><i><font color="Green" title="E58">A5</font></i></a>, <a class="txt" href="lexbfs.html#E1:123_1_1_1_2"><i><font color="Green" title="E60">A8</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:123_1_1_1_2"/>
<font color="Maroon" title="c11">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x2</font>
 ;<br/></div><b>end;</b></div><a NAME="E7:123_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k</font></span>)</span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></i>;<br/><b>hence </b><a NAME="E8:123_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1]
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:123_1"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="lexbfs.html#E2:123_1_1_1"><i><font color="Green" title="E57">A4</font></i></a>, <a class="txt" href="lexbfs.html#E5:123_1_1_1"><i><font color="Green" title="E59">A7</font></i></a>, <a class="ref" href="knaster.html#T1" title="KNASTER:th.1">KNASTER:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="123_1_1_2"><b>suppose </b></a><a NAME="E1:123_1_1_2"/><i><font color="Green" title="E57">A9</font></i>: 
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> 
 ;<br/><div class="add"><a NAME="E2:123_1_1_2"/>
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E3:123_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1]
 <b>by </b><i><a class="ref" href="lexbfs.html#T17" target="_self" title="LEXBFS:th.17">Th17</a>, <a class="txt" href="lexbfs.html#E1:123_1"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="lexbfs.html#E1:123_1_1_2"><i><font color="Green" title="E57">A9</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E3:123"/>
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="lexbfs.html#E1:123"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="lexbfs.html#E2:123"><i><font color="Green" title="E55">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:123"/>
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c2">n</font></span>)</span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 ;<br/>


</div>
