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

<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">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>let </b><font color="Maroon" title="c3">f</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">R</font> =  <a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font>;<br/>
<b>set </b><font color="Maroon" title="c5">M</font> =  <a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font>;<br/>
<b>set </b><font color="Maroon" title="c6">ff</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p4">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font>;<br/>
<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E56">A1</font></i>: 
 <a href="graphsp.html#K7" title="GRAPHSP:func.7">OuterVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<b>set </b><font color="Maroon" title="c7">Fi1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p4">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font>;<br/>
<i><font color="Green" title="E57">A2</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"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> = 
 <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"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>
<b>by </b><i><a class="ref" href="graphsp.html#T38" target="_self" title="GRAPHSP:th.38">Th38</a></i>
<br/>.= 
 <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="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p0">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="graphsp.html#T34" target="_self" title="GRAPHSP:th.34">Th34</a></i>
;<br/>
<b>consider </b><font color="Maroon" title="c8">j</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> <b> such that </b><br/><a NAME="E4:68"/><i><font color="Green" title="E58">A3</font></i>: 
( <font color="Maroon" title="c8">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graphsp.html#K7" title="GRAPHSP:func.7">OuterVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">j</font> &amp; <font color="Maroon" title="c8">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p0">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c8">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 )
 <b>by </b><i><a class="txt" href="graphsp.html#E1:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="graphsp.html#T35" target="_self" title="GRAPHSP:th.35">Th35</a></i>;<br/>
<a NAME="E5:68"/><i><font color="Green" title="E59">A4</font></i>: 
 <a href="graphsp.html#K7" title="GRAPHSP:func.7">OuterVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="graphsp.html#T28" target="_self" title="GRAPHSP:th.28">Th28</a></i>;<br/>
<a NAME="E6:68"/><i><font color="Green" title="E60">A5</font></i>: 
 <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:68_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c10">k</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> <b> such that </b><br/><a NAME="E3:68_2"/><i><font color="Green" title="E61">A6</font></i>: 
( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font> &amp; <font color="Maroon" title="c10">k</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font> &amp; <font color="Maroon" title="c10">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 )
 ;<br/>
<a NAME="E4:68_2"/><i><font color="Green" title="E62">A7</font></i>: 
<font color="Maroon" title="c10">k</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="graphsp.html#E3:68_2"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="graphsp.html#T38" target="_self" title="GRAPHSP:th.38">Th38</a></i>;<br/>
<a NAME="E5:68_2"/><i><font color="Green" title="E63">A8</font></i>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">3 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="graphsp.html#E52"><i><font color="Green" title="E46">Lm7</font></i></a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p1">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font>
<b>by </b><i><a class="ref" href="graphsp.html#T23" target="_self" title="GRAPHSP:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p0">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font>
<b>by </b><i><a class="txt" href="graphsp.html#E2:68"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="graphsp.html#E3:68_2"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="graphsp.html#T37" target="_self" title="GRAPHSP:th.37">Th37</a></i>
;<br/>
<a NAME="E7:68_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
 
<b>by </b><i><a class="txt" href="graphsp.html#E3:68_2"><i><font color="Green" title="E61">A6</font></i></a>, <a class="txt" href="graphsp.html#E4:68_2"><i><font color="Green" title="E62">A7</font></i></a>, <a class="txt" href="graphsp.html#E5:68_2"><i><font color="Green" title="E63">A8</font></i></a>, <a class="ref" href="graphsp.html#T33" target="_self" title="GRAPHSP:th.33">Th33</a></i>;<br/>
<b>hence </b><a NAME="E8:68_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="graphsp.html#E3:68_2"><i><font color="Green" title="E61">A6</font></i></a>, <a class="txt" href="graphsp.html#E4:68_2"><i><font color="Green" title="E62">A7</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:68_3"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c10">k</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> <b> such that </b><br/><a NAME="E3:68_3"/><i><font color="Green" title="E61">A9</font></i>: 
( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font> &amp; <font color="Maroon" title="c10">k</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font> &amp; <font color="Maroon" title="c10">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 )
 ;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p1">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font>
<b>by </b><i><a class="ref" href="graphsp.html#T23" target="_self" title="GRAPHSP:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p0">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c10">k</font>
<b>by </b><i><a class="txt" href="graphsp.html#E2:68"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="graphsp.html#E3:68_3"><i><font color="Green" title="E61">A9</font></i></a>, <a class="ref" href="graphsp.html#T37" target="_self" title="GRAPHSP:th.37">Th37</a></i>
;<br/><b>hence </b><a NAME="E5:68_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p0">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c9">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1
 <b>by </b><i><a class="txt" href="graphsp.html#E3:68_3"><i><font color="Green" title="E61">A9</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E8:68"/><b>then </b>
 <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="txt" href="graphsp.html#E4:68"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="graphsp.html#E5:68"><i><font color="Green" title="E59">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:68"/>
 <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a>  <a href="graphsp.html#K13" title="GRAPHSP:func.13">UnusedVx</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="graphsp.html#K5" title="GRAPHSP:func.5">repeat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="graphsp.html#K19" title="GRAPHSP:func.19">Relax</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="graphsp.html#K3" title="GRAPHSP:func.3">*</a> <span class="p5">(<span class="default"><a href="graphsp.html#K16" title="GRAPHSP:func.16">findmin</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="graphsp.html#K6" title="GRAPHSP:func.6">.</a> <font color="Maroon" title="c3">f</font></span>)</span>,<font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="txt" href="graphsp.html#E6:68"><i><font color="Green" title="E60">A5</font></i></a>, <a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a></i>;<br/>


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