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

<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_003.html#V8" title="GLIB_003:attr.8">nonnegative-weighted</a> <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</a>;<br/><b>let </b><font color="Maroon" title="c2">src</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>set </b><font color="Maroon" title="c3">DCS</font> =  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font>;<br/>
<b>set </b><font color="Maroon" title="c4">D0</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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>means </b>for <font color="Olive" title="b1">G2</font> being  <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> $1</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> $1</span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  holds <br/> ( <font color="Olive" title="b1">G2</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font> &amp; ( for <font color="Olive" title="b2">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> $1</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  holds <br/><font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Olive" title="b2">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> $1</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">v</font> ) );<br/>
<b>reconsider </b><font color="Maroon" title="c5">EL</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="partfun1.html#T56" title="PARTFUN1:th.56">PARTFUN1:56</a></i>;<br/>
<i><font color="Green" title="E26">A1</font></i>: <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0 = 
 <a href="glib_004.html#K4" title="GLIB_004:func.4">DIJK:Init</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font>
<b>by </b><i><a class="ref" href="glib_004.html#D7" target="_self" title="GLIB_004:def.7">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c2">src</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> 0</span>)</span>

;<br/>
<a NAME="E3:38"/><b>then </b><i><font color="Green" title="E27">A2</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> 0
 
<b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>;<br/>
<a NAME="E4:38"/><b>then </b><i><font color="Green" title="E28">A3</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</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"><font color="Maroon" title="c2">src</font></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#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<i><font color="Green" title="E29">A4</font></i>:  <a href="glib_003.html#K6" title="GLIB_003:func.6">the_ELabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c5">EL</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E2:38"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
<br/>.= 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">D0W</font> be   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> ;<br/><a NAME="E1:38_3"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/><a NAME="E2:38_3"/><b>then </b><i><font color="Green" title="E30">A5</font></i>: 
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c6">D0W</font> <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"><font color="Maroon" title="c2">src</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c6">D0W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="glib_004.html#E5:38"><i><font color="Green" title="E29">A4</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/><a NAME="E3:38_3"/><b>then </b><i><font color="Green" title="E31">A6</font></i>: 
(  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c6">D0W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c6">D0W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 <b>by </b><i><a class="ref" href="card_1.html#T78" title="CARD_1:th.78">CARD_1:78</a>, <a class="ref" href="card_1.html#T79" title="CARD_1:th.79">CARD_1:79</a></i>;<br/><a NAME="E4:38_3"/><i><font color="Green" title="E32">A7</font></i>: 
<font color="Maroon" title="c6">D0W</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">D0W</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_3"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="card_1.html#T78" title="CARD_1:th.78">CARD_1:78</a>, <a class="ref" href="card_1.html#T79" title="CARD_1:th.79">CARD_1:79</a></i>;<br/><a NAME="E5:38_3"/>
<font color="Maroon" title="c6">D0W</font> is <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_3"><i><font color="Green" title="E31">A6</font></i></a>, <a class="ref" href="glib_000.html#D21" title="GLIB_000:def.21">GLIB_000:def 21</a></i>;<br/><a NAME="E6:38_3"/><b>then </b>
<font color="Maroon" title="c6">D0W</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="glib_002.html#T7" title="GLIB_002:th.7">GLIB_002:7</a></i>;<br/><a NAME="E7:38_3"/><b>then </b><i><font color="Green" title="E33">A8</font></i>: 
<font color="Maroon" title="c6">D0W</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_3"><i><font color="Green" title="E32">A7</font></i></a>, <a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c6">D0W</font>;<br/><a NAME="E1:38_3_1"/><i><font color="Green" title="E34">A9</font></i>: 
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_3"><i><font color="Green" title="E30">A5</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>set </b><font color="Maroon" title="c8">W2</font> = <font color="Maroon" title="c6">D0W</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c7">x</font>;<br/><b>take </b><font color="Maroon" title="c9">W2</font> = <font color="Maroon" title="c6">D0W</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c7">x</font>;<br/><b>thus </b><a NAME="E2:38_3_1"/>
<font color="Maroon" title="c9">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_3_1"><i><font color="Green" title="E34">A9</font></i></a>, <a class="ref" href="glib_001.html#T14" title="GLIB_001:th.14">GLIB_001:14</a></i>;<br/><b>let </b><font color="Maroon" title="c10">W1</font> be   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><a NAME="E3:38_3_1"/>
<font color="Maroon" title="c10">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">x</font>
 ;<br/><a NAME="E4:38_3_1"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="ref" href="glib_003.html#T36" title="GLIB_003:th.36">GLIB_003:36</a></i>;<br/><b>hence </b><a NAME="E5:38_3_1"/>
<font color="Maroon" title="c9">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="ref" href="glib_003.html#T28" title="GLIB_003:th.28">GLIB_003:28</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:38_3"/>
<font color="Maroon" title="c6">D0W</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E7:38_3"><i><font color="Green" title="E33">A8</font></i></a>, <a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></i>;<br/><b>let </b><font color="Maroon" title="c7">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><a NAME="E10:38_3"/><i><font color="Green" title="E34">A10</font></i>: 
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><a NAME="E11:38_3"/><b>then </b><i><font color="Green" title="E35">A11</font></i>: 
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E12:38_3"/><i><font color="Green" title="E36">A12</font></i>: 
<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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">src</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_3_2"><b>now </b></a><div class="add"><b>set </b><font color="Maroon" title="c8">W1</font> = <font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c7">v</font>;<br/><a NAME="E1:38_3_2"/><i><font color="Green" title="E37">A13</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c7">v</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E11:38_3"><i><font color="Green" title="E35">A11</font></i></a>, <a class="ref" href="glib_001.html#T14" title="GLIB_001:th.14">GLIB_001:14</a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">W</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:38_3_2"/><i><font color="Green" title="E38">A14</font></i>: 
( <font color="Maroon" title="c9">W</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">v</font> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">W</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )
 <b>by </b><i><a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></i>;<br/><a NAME="E4:38_3_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c7">v</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="glib_003.html#T28" title="GLIB_003:th.28">GLIB_003:28</a></i>;<br/><a NAME="E5:38_3_2"/><b>then </b>
<font color="Maroon" title="c9">W</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_3_2"><i><font color="Green" title="E37">A13</font></i></a>, <a class="txt" href="glib_004.html#E3:38_3_2"><i><font color="Green" title="E38">A14</font></i></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E6:38_3_2"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_3_2"><i><font color="Green" title="E38">A14</font></i></a>, <a class="ref" href="glib_003.html#T36" title="GLIB_003:th.36">GLIB_003:36</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E14:38_3"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c7">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38"><i><font color="Green" title="E28">A3</font></i></a>, <a class="txt" href="glib_004.html#E10:38_3"><i><font color="Green" title="E34">A10</font></i></a>, <a class="txt" href="glib_004.html#E12:38_3"><i><font color="Green" title="E36">A12</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:38"/><b>then </b><i><font color="Green" title="E30">A15</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">n</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>set </b><font color="Maroon" title="c7">Dn</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>;<br/><b>set </b><font color="Maroon" title="c8">Dn1</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon" title="c9">BE</font> =  <a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c10">e</font> =  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c11">source</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c12">target</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c13">DnE</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1;<br/><b>set </b><font color="Maroon" title="c14">pc</font> = <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c15">ec</font> = <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>;<br/><b>consider </b><font color="Maroon" title="c16">DnW</font> being   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> ;<br/><b>assume </b><a NAME="E2:38_4"/><i><font color="Green" title="E31">A16</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">n</font>]
 ;<br/><b>let </b><font color="Maroon" title="c17">Dn1W</font> be   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> ;<br/><a NAME="E3:38_4"/><i><font color="Green" title="E32">A17</font></i>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_004.html#K3" title="GLIB_004:func.3">DIJK:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#D7" target="_self" title="GLIB_004:def.7">Def7</a></i>;<br/><a NAME="E4:38_4"/><b>then </b><i><font color="Green" title="E33">A18</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp;  <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  )
 <b>by </b><i><a class="ref" href="glib_004.html#T14" target="_self" title="GLIB_004:th.14">Th14</a></i>;<br/><a NAME="E5:38_4"/><i><font color="Green" title="E34">A19</font></i>: 
( <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font> &amp;  <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> )
 <b>by </b><i><a class="ref" href="glib_004.html#T17" target="_self" title="GLIB_004:th.17">Th17</a></i>;<br/><a NAME="E6:38_4"/><i><font color="Green" title="E35">A20</font></i>: 
( <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp;  <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="glib_004.html#T17" target="_self" title="GLIB_004:th.17">Th17</a></i>;<br/><a NAME="E7:38_4"/><i><font color="Green" title="E36">A21</font></i>: 
<font color="Maroon" title="c2">src</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38"><i><font color="Green" title="E28">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E8:38_4"/><i><font color="Green" title="E37">A22</font></i>: 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><a NAME="E9:38_4"/><i><font color="Green" title="E38">A23</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> 0</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 <b>by </b><i><a class="ref" href="glib_004.html#T16" target="_self" title="GLIB_004:th.16">Th16</a></i>;<br/><a NAME="E10:38_4"/><b>then </b><i><font color="Green" title="E39">A24</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E7:38_4"><i><font color="Green" title="E36">A21</font></i></a>, <a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><a NAME="E11:38_4"/><i><font color="Green" title="E40">A25</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T21" target="_self" title="GLIB_004:th.21">Th21</a></i>;<br/><a NAME="E12:38_4"/><b>then </b><i><font color="Green" title="E41">A26</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="glib_000.html#T93" title="GLIB_000:th.93">GLIB_000:93</a></i>;<br/><a NAME="E13:38_4"/><b>then </b><i><font color="Green" title="E42">A27</font></i>: 
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c16">DnW</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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp;  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  )
 <b>by </b><i><a class="txt" href="glib_004.html#E10:38_4"><i><font color="Green" title="E39">A24</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><a NAME="E14:38_4"/><i><font color="Green" title="E43">A28</font></i>: 
(  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">DnW</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">DnW</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a>  )
 <b>by </b><i><a class="txt" href="glib_004.html#E10:38_4"><i><font color="Green" title="E39">A24</font></i></a>, <a class="txt" href="glib_004.html#E12:38_4"><i><font color="Green" title="E41">A26</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><a NAME="E15:38_4"/><i><font color="Green" title="E44">A29</font></i>: 
<font color="Maroon" title="c16">DnW</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a></i>;<br/><a NAME="E16:38_4"/><b>then </b><i><font color="Green" title="E45">A30</font></i>: 
<font color="Maroon" title="c16">DnW</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>
 <b>by </b><i><a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></i>;<br/><a NAME="E17:38_4"/><b>then </b><i><font color="Green" title="E46">A31</font></i>: 
( <font color="Maroon" title="c16">DnW</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> &amp; <font color="Maroon" title="c16">DnW</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">DnW</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_4_1_1"/>
(  <a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_1"><b>suppose </b></a><a NAME="E1:38_4_1_1_1"/>
 <a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:38_4_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4"><i><font color="Green" title="E32">A17</font></i></a>, <a class="ref" href="glib_004.html#D5" target="_self" title="GLIB_004:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E3:38_4_1_1_1"/>
( <font color="Maroon" title="c17">Dn1W</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font> &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  holds <br/><font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Olive" title="b1">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2"><b>suppose </b></a><a NAME="E1:38_4_1_1_2"/><i><font color="Green" title="E47">A32</font></i>: 
 <a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <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/><div class="add"><a NAME="E2:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E48">A33</font></i>: 
(  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="glib_003.html#K13" title="GLIB_003:func.13">.labelVertex</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4"><i><font color="Green" title="E32">A17</font></i></a>, <a class="ref" href="glib_004.html#D5" target="_self" title="GLIB_004:def.5">Def5</a></i>;<br/><a NAME="E3:38_4_1_1_2"/>
<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1
 <b>by </b><i><a class="ref" href="glib_003.html#T41" title="GLIB_003:th.41">GLIB_003:41</a></i>;<br/><a NAME="E4:38_4_1_1_2"/><b>then </b>
(  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp;  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> )
 <b>by </b><i><a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><a NAME="E5:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E49">A34</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E6:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E50">A35</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  <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"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="ref" href="glib_003.html#T49" title="GLIB_003:th.49">GLIB_003:49</a>, <a class="ref" href="glib_003.html#T59" title="GLIB_003:th.59">GLIB_003:59</a></i>;<br/><a NAME="E7:38_4_1_1_2"/><i><font color="Green" title="E51">A36</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#T43" title="GLIB_003:th.43">GLIB_003:43</a></i>;<br/><a NAME="E8:38_4_1_1_2"/><i><font color="Green" title="E52">A37</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  <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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="glib_004.html#E6:38_4_1_1_2"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="glib_003.html#T43" title="GLIB_003:th.43">GLIB_003:43</a>, <a class="ref" href="glib_003.html#T52" title="GLIB_003:th.52">GLIB_003:52</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:38_4_1_1_2_1"/><i><font color="Green" title="E53">A38</font></i>: 
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_4_1_1_2_1_1_1"/>
( <font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  or <font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="glib_004.html#E6:38_4_1_1_2"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="glib_004.html#E7:38_4_1_1_2"><i><font color="Green" title="E51">A36</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_1"><i><font color="Green" title="E53">A38</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:38_4_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E10:38_4"><i><font color="Green" title="E39">A24</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:38_4_1_1_2_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:38_4_1_1_2_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><b>hence </b><a NAME="E4:38_4_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:38_4_1_1_2_1"/>
<font color="Maroon" title="c18">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font>
 ;<br/></div><b>end;</b></div><a NAME="E10:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E53">A39</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E6:38_4_1_1_2"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><a NAME="E11:38_4_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="glib_004.html#T21" target="_self" title="GLIB_004:th.21">Th21</a></i>;<br/><a NAME="E12:38_4_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K22" title="GLIB_000:func.22">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E6:38_4"><i><font color="Green" title="E35">A20</font></i></a>, <a class="ref" href="glib_000.html#T93" title="GLIB_000:th.93">GLIB_000:93</a></i>;<br/><a NAME="E13:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E54">A40</font></i>: 
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c17">Dn1W</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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</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="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E8:38_4_1_1_2"><i><font color="Green" title="E52">A37</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2"><i><font color="Green" title="E53">A39</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><a NAME="E14:38_4_1_1_2"/><i><font color="Green" title="E55">A41</font></i>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="glib_000.html#R4" title="GLIB_000:pred.4">DSJoins</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2"><i><font color="Green" title="E47">A32</font></i></a>, <a class="ref" href="glib_004.html#D4" target="_self" title="GLIB_004:def.4">Def4</a></i>;<br/><a NAME="E15:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E56">A42</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D18" title="GLIB_000:def.18">GLIB_000:def 18</a></i>;<br/><a NAME="E16:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E57">A43</font></i>: 
not <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E17:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E58">A44</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="card_2.html#T54" title="CARD_2:th.54">CARD_2:54</a></i>;<br/><a NAME="E18:38_4_1_1_2"/><i><font color="Green" title="E59">A45</font></i>: 
not  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E11:38_4"><i><font color="Green" title="E40">A25</font></i></a>, <a class="txt" href="glib_004.html#E16:38_4_1_1_2"><i><font color="Green" title="E57">A43</font></i></a>, <a class="ref" href="glib_000.html#T34" title="GLIB_000:th.34">GLIB_000:34</a></i>;<br/><a NAME="E19:38_4_1_1_2"/><b>then </b>
<font color="Maroon" title="c17">Dn1W</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">DnW</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="glib_004.html#E14:38_4"><i><font color="Green" title="E43">A28</font></i></a>, <a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="card_2.html#T54" title="CARD_2:th.54">CARD_2:54</a></i>;<br/><a NAME="E20:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E60">A46</font></i>: 
<font color="Maroon" title="c17">Dn1W</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">Dn1W</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="txt" href="glib_004.html#E14:38_4"><i><font color="Green" title="E43">A28</font></i></a>, <a class="txt" href="glib_004.html#E16:38_4"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="txt" href="glib_004.html#E17:38_4_1_1_2"><i><font color="Green" title="E58">A44</font></i></a>, <a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></i>;<br/><a NAME="E21:38_4_1_1_2"/><i><font color="Green" title="E61">A47</font></i>: 
( <font color="Maroon" title="c16">DnW</font> is    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font> &amp; <font color="Maroon" title="c17">Dn1W</font> is    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="txt" href="glib_004.html#E6:38_4"><i><font color="Green" title="E35">A20</font></i></a>, <a class="ref" href="glib_000.html#T94" title="GLIB_000:th.94">GLIB_000:94</a></i>;<br/><div><i><font color="Green" title="E62">A48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_2"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:38_4_1_1_2_2"/>
(  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c16">DnW</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Vertices_of</a> <font color="Maroon" title="c17">Dn1W</font> &amp;  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font> )
 <b>by </b><i><a class="txt" href="glib_004.html#E13:38_4"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/><b>let </b><font color="Maroon" title="c18">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E2:38_4_1_1_2_2"/><i><font color="Green" title="E63">A49</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font>
 ;<br/><a NAME="E3:38_4_1_1_2_2"/><b>then </b><i><font color="Green" title="E64">A50</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E13:38_4"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E4:38_4_1_1_2_2"/><i><font color="Green" title="E65">A51</font></i>: 
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> )
 <b>by </b><i><a class="txt" href="glib_004.html#E21:38_4_1_1_2"><i><font color="Green" title="E61">A47</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4_1_1_2_2"><i><font color="Green" title="E63">A49</font></i></a>, <a class="ref" href="glib_000.html#D34" title="GLIB_000:def.34">GLIB_000:def 34</a></i>;<br/><a NAME="E5:38_4_1_1_2_2"/>
(  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> &amp;  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_4"><i><font color="Green" title="E33">A18</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><b>hence </b><a NAME="E6:38_4_1_1_2_2"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> )
 <b>by </b><i><a class="txt" href="glib_004.html#E21:38_4_1_1_2"><i><font color="Green" title="E61">A47</font></i></a>, <a class="txt" href="glib_004.html#E3:38_4_1_1_2_2"><i><font color="Green" title="E64">A50</font></i></a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_2"><i><font color="Green" title="E65">A51</font></i></a>, <a class="ref" href="glib_000.html#D34" title="GLIB_000:def.34">GLIB_000:def 34</a></i>;<br/></div><b>end;</b></div><a NAME="E23:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E63">A52</font></i>: 
<font color="Maroon" title="c16">DnW</font> is    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D34" title="GLIB_000:def.34">GLIB_000:def 34</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">DnW'</font> = <font color="Maroon" title="c16">DnW</font> as  <a href="glib_003.html#V1" title="GLIB_003:attr.1">[Weighted]</a>  <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c17">Dn1W</font> <b>by </b><i><a class="txt" href="glib_004.html#E22:38_4_1_1_2"><i><font color="Green" title="E62">A48</font></i></a>, <a class="ref" href="glib_000.html#D34" title="GLIB_000:def.34">GLIB_000:def 34</a></i>;<br/><a NAME="E25:38_4_1_1_2"/><i><font color="Green" title="E64">A53</font></i>: 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></i>;<br/><a NAME="E26:38_4_1_1_2"/><i><font color="Green" title="E65">A54</font></i>: 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></i>;<br/><a NAME="E27:38_4_1_1_2"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/><a NAME="E28:38_4_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E22:38_4_1_1_2"><i><font color="Green" title="E62">A48</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/><a NAME="E29:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E66">A55</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:38_4_1_1_2_3"/>
<font color="Maroon" title="c19">y</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"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW'</font></span>)</span>
 ;<br/><a NAME="E2:38_4_1_1_2_3"/><b>then </b><i><font color="Green" title="E67">A56</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font>
 <b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c19">y</font>
<b>by </b><i><a class="txt" href="glib_004.html#E25:38_4_1_1_2"><i><font color="Green" title="E64">A53</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c19">y</font>
<b>by </b><i><a class="txt" href="glib_004.html#E26:38_4_1_1_2"><i><font color="Green" title="E65">A54</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4_1_1_2_3"><i><font color="Green" title="E67">A56</font></i></a>, <a class="txt" href="glib_004.html#E22:38_4_1_1_2"><i><font color="Green" title="E62">A48</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>
;<br/><br/></div><b>end;</b></div><a NAME="E31:38_4_1_1_2"/><b>then </b>
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E29:38_4_1_1_2"><i><font color="Green" title="E66">A55</font></i></a>, <a class="ref" href="funct_1.html#T68" title="FUNCT_1:th.68">FUNCT_1:68</a></i>;<br/><a NAME="E32:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E67">A57</font></i>: 
<font color="Maroon" title="c16">DnW</font> is   <a href="glib_003.html#NM8" title="GLIB_003:NM.8">WSubgraph</a> of <font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></i>;<br/><a NAME="E33:38_4_1_1_2"/><i><font color="Green" title="E68">A58</font></i>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E14:38_4_1_1_2"><i><font color="Green" title="E55">A41</font></i></a>, <a class="ref" href="glib_000.html#D18" title="GLIB_000:def.18">GLIB_000:def 18</a></i>;<br/><a NAME="E34:38_4_1_1_2"/>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E35:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E69">A59</font></i>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E36:38_4_1_1_2"/>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></i>;<br/><a NAME="E37:38_4_1_1_2"/><b>then </b>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_4"><i><font color="Green" title="E33">A18</font></i></a>, <a class="ref" href="glib_000.html#T91" title="GLIB_000:th.91">GLIB_000:91</a></i>;<br/><a NAME="E38:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E70">A60</font></i>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E35:38_4_1_1_2"><i><font color="Green" title="E69">A59</font></i></a>, <a class="txt" href="glib_004.html#E21:38_4_1_1_2"><i><font color="Green" title="E61">A47</font></i></a>, <a class="ref" href="glib_000.html#T76" title="GLIB_000:th.76">GLIB_000:76</a></i>;<br/><a NAME="E39:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E71">A61</font></i>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="ref" href="glib_000.html#T19" title="GLIB_000:th.19">GLIB_000:19</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">u</font>, <font color="Maroon" title="c20">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c17">Dn1W</font>;<br/><div><i><font color="Green" title="E72">A62</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c21">u</font>, <font color="Maroon" title="c22">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:38_4_1_1_2_4_1"/>
( <font color="Maroon" title="c21">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  )
 ;<br/><b>then reconsider </b><font color="Maroon" title="c23">u'</font> = <font color="Maroon" title="c21">u</font>, <font color="Maroon" title="c24">v'</font> = <font color="Maroon" title="c22">v</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c16">DnW</font> <b>by </b><i><a class="txt" href="glib_004.html#E12:38_4"><i><font color="Green" title="E41">A26</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4"><i><font color="Green" title="E39">A24</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><b>consider </b><font color="Maroon" title="c25">W1</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c16">DnW</font><b> such that </b><br/><a NAME="E4:38_4_1_1_2_4_1"/><i><font color="Green" title="E73">A63</font></i>: 
<font color="Maroon" title="c25">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c23">u'</font>,<font color="Maroon" title="c24">v'</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E17:38_4"><i><font color="Green" title="E46">A31</font></i></a>, <a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c26">W2</font> = <font color="Maroon" title="c25">W1</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font> <b>by </b><i><a class="txt" href="glib_004.html#E23:38_4_1_1_2"><i><font color="Green" title="E63">A52</font></i></a>, <a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></i>;<br/><a NAME="E6:38_4_1_1_2_4_1"/>
<font color="Maroon" title="c26">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c21">u</font>,<font color="Maroon" title="c22">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_4_1_1_2_4_1"><i><font color="Green" title="E73">A63</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><b>hence </b><a NAME="E7:38_4_1_1_2_4_1"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c21">u</font>,<font color="Maroon" title="c22">v</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_4_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_4_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_4_1_1_2_4_2_1"/>
( ( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  ) or ( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or ( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  ) or ( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 </span><b>by </b><i><a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_4_2_1_1"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_4_2_1_1"/>
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:38_4_1_1_2_4_2_1_1"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<font color="Maroon" title="c20">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_4"><i><font color="Green" title="E72">A62</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_4_2_1_2"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_4_2_1_2"/><i><font color="Green" title="E73">A64</font></i>: 
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c21">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font><b> such that </b><br/><a NAME="E3:38_4_1_1_2_4_2_1_2"/><i><font color="Green" title="E74">A65</font></i>: 
<font color="Maroon" title="c21">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E33:38_4_1_1_2"><i><font color="Green" title="E68">A58</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_4"><i><font color="Green" title="E72">A62</font></i></a></i>;<br/><a NAME="E4:38_4_1_1_2_4_2_1_2"/><i><font color="Green" title="E75">A66</font></i>: 
<font color="Maroon" title="c21">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4_1_1_2_4_2_1_2"><i><font color="Green" title="E74">A65</font></i></a>, <a class="txt" href="glib_004.html#E39:38_4_1_1_2"><i><font color="Green" title="E71">A61</font></i></a>, <a class="ref" href="glib_001.html#T67" title="GLIB_001:th.67">GLIB_001:67</a></i>;<br/><a NAME="E5:38_4_1_1_2_4_2_1_2"/>
<font color="Maroon" title="c20">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_4_2_1_2"><i><font color="Green" title="E73">A64</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="E6:38_4_1_1_2_4_2_1_2"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<font color="Maroon" title="c20">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_4_1_1_2_4_2_1_2"><i><font color="Green" title="E75">A66</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_4_2_1_3"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_4_2_1_3"/><i><font color="Green" title="E73">A67</font></i>: 
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c21">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font><b> such that </b><br/><a NAME="E3:38_4_1_1_2_4_2_1_3"/><i><font color="Green" title="E74">A68</font></i>: 
<font color="Maroon" title="c21">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c20">v</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E33:38_4_1_1_2"><i><font color="Green" title="E68">A58</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_4"><i><font color="Green" title="E72">A62</font></i></a></i>;<br/><a NAME="E4:38_4_1_1_2_4_2_1_3"/>
<font color="Maroon" title="c21">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c20">v</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4_1_1_2_4_2_1_3"><i><font color="Green" title="E74">A68</font></i></a>, <a class="txt" href="glib_004.html#E39:38_4_1_1_2"><i><font color="Green" title="E71">A61</font></i></a>, <a class="ref" href="glib_001.html#T67" title="GLIB_001:th.67">GLIB_001:67</a></i>;<br/><a NAME="E5:38_4_1_1_2_4_2_1_3"/><b>then </b>
<font color="Maroon" title="c21">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c20">v</font>,<font color="Maroon" title="c19">u</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_4_2_1_3"><i><font color="Green" title="E73">A67</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E6:38_4_1_1_2_4_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c21">W</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a>  <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<font color="Maroon" title="c20">v</font>
 <b>by </b><i><a class="ref" href="glib_001.html#T24" title="GLIB_001:th.24">GLIB_001:24</a></i>;<br/><b>hence </b><a NAME="E7:38_4_1_1_2_4_2_1_3"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<font color="Maroon" title="c20">v</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_4_2_1_4"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_4_2_1_4"/>
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><div class="add"><a NAME="E2:38_4_1_1_2_4_2_1_4"/><b>then </b><i><font color="Green" title="E73">A69</font></i>: 
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>take </b><font color="Maroon" title="c21">W</font> = <font color="Maroon" title="c17">Dn1W</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c19">u</font>;<br/><b>thus </b><a NAME="E3:38_4_1_1_2_4_2_1_4"/>
<font color="Maroon" title="c21">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<font color="Maroon" title="c20">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_4_2_1_4"><i><font color="Green" title="E73">A69</font></i></a>, <a class="ref" href="glib_001.html#T14" title="GLIB_001:th.14">GLIB_001:14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:38_4_1_1_2_4"/>
 ex <font color="Olive" title="b1">W</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c17">Dn1W</font> st <font color="Olive" title="b1">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c19">u</font>,<font color="Maroon" title="c20">v</font>
 ;<br/></div><b>end;</b></div><a NAME="E41:38_4_1_1_2"/><b>then </b>
<font color="Maroon" title="c17">Dn1W</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></i>;<br/><a NAME="E42:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E72">A70</font></i>: 
<font color="Maroon" title="c17">Dn1W</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E20:38_4_1_1_2"><i><font color="Green" title="E60">A46</font></i></a>, <a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_5"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon" title="c19">WT</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c16">DnW</font><b> such that </b><br/><a NAME="E2:38_4_1_1_2_5"/><i><font color="Green" title="E73">A71</font></i>: 
( <font color="Maroon" title="c19">WT</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">W1</font> being  <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c19">WT</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  ) )
 <b>by </b><i><a class="txt" href="glib_004.html#E13:38_4"><i><font color="Green" title="E42">A27</font></i></a>, <a class="txt" href="glib_004.html#E33:38_4_1_1_2"><i><font color="Green" title="E68">A58</font></i></a>, <a class="txt" href="glib_004.html#E15:38_4"><i><font color="Green" title="E44">A29</font></i></a>, <a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c20">WT'</font> = <font color="Maroon" title="c19">WT</font> as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c17">Dn1W</font> <b>by </b><i><a class="txt" href="glib_004.html#E23:38_4_1_1_2"><i><font color="Green" title="E63">A52</font></i></a>, <a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></i>;<br/><b>set </b><font color="Maroon" title="c21">W2</font> = <font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E4:38_4_1_1_2_5"/><i><font color="Green" title="E74">A72</font></i>: 
<font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_5"><i><font color="Green" title="E73">A71</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c22">W2</font> = <font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> as   <a href="glib_001.html#NM6" title="GLIB_001:NM.6">DWalk</a> of <font color="Maroon" title="c17">Dn1W</font> <b>by </b><i><a class="txt" href="glib_004.html#E38:38_4_1_1_2"><i><font color="Green" title="E70">A60</font></i></a>, <a class="ref" href="glib_001.html#T124" title="GLIB_001:th.124">GLIB_001:124</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_5_1"><b>now </b></a><div class="add"><a NAME="E1:38_4_1_1_2_5_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E2:38_4_1_1_2_5_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> is   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><b>thus </b><a NAME="E3:38_4_1_1_2_5_1"/>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c17">Dn1W</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E39:38_4_1_1_2"><i><font color="Green" title="E71">A61</font></i></a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_5"><i><font color="Green" title="E74">A72</font></i></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>;<br/><a NAME="E4:38_4_1_1_2_5_1"/><i><font color="Green" title="E75">A73</font></i>: 
not  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c16">DnW</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E18:38_4_1_1_2"><i><font color="Green" title="E59">A45</font></i></a>, <a class="txt" href="glib_004.html#E12:38_4"><i><font color="Green" title="E41">A26</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4"><i><font color="Green" title="E39">A24</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><a NAME="E5:38_4_1_1_2_5_1"/>
<font color="Maroon" title="c19">WT</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#T111" title="GLIB_001:th.111">GLIB_001:111</a></i>;<br/><b>hence </b><a NAME="E6:38_4_1_1_2_5_1"/>
not  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_4_1_1_2_5_1"><i><font color="Green" title="E75">A73</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_5_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:38_4_1_1_2_5_1_1"/><i><font color="Green" title="E76">A74</font></i>: 
not <font color="Maroon" title="c20">WT'</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_5_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:38_4_1_1_2_5_1_1_1"/>
<font color="Maroon" title="c20">WT'</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 ;<br/><a NAME="E2:38_4_1_1_2_5_1_1_1"/><b>then </b><i><font color="Green" title="E77">A75</font></i>: 
<font color="Maroon" title="c20">WT'</font> is <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_5_1_1"><i><font color="Green" title="E76">A74</font></i></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></i>;<br/><a NAME="E3:38_4_1_1_2_5_1_1_1"/>
<font color="Maroon" title="c17">Dn1W</font> is <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E42:38_4_1_1_2"><i><font color="Green" title="E72">A70</font></i></a>, <a class="ref" href="glib_002.html#D3" title="GLIB_002:def.3">GLIB_002:def 3</a></i>;<br/><b>hence </b><a NAME="E4:38_4_1_1_2_5_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_5_1_1_1"><i><font color="Green" title="E77">A75</font></i></a>, <a class="ref" href="glib_002.html#D2" title="GLIB_002:def.2">GLIB_002:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:38_4_1_1_2_5_1_1"/>
not <font color="Maroon" title="c20">WT'</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:38_4_1_1_2_5_1"/>
( <font color="Maroon" title="c20">WT'</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> or  not <font color="Maroon" title="c20">WT'</font> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> )
 ;<br/><a NAME="E9:38_4_1_1_2_5_1"/>
<font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">WT</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#T99" title="GLIB_001:th.99">GLIB_001:99</a></i>;<br/><a NAME="E10:38_4_1_1_2_5_1"/><b>then </b><i><font color="Green" title="E76">A76</font></i>: 
not <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E15:38_4_1_1_2"><i><font color="Green" title="E56">A42</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a>, <a class="txt" href="glib_004.html#E13:38_4"><i><font color="Green" title="E42">A27</font></i></a></i>;<br/><b>let </b><font color="Maroon" title="c23">n</font> be  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <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="E11:38_4_1_1_2_5_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c23">n</font> &amp; <font color="Maroon" title="c23">n</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="c20">WT'</font> )
 ;<br/><b>hence </b><a NAME="E12:38_4_1_1_2_5_1"/>
<font color="Maroon" title="c20">WT'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E10:38_4_1_1_2_5_1"><i><font color="Green" title="E76">A76</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/></div><b>end;</b></div><b>then reconsider </b><font color="Maroon" title="c23">W2</font> = <font color="Maroon" title="c22">W2</font> as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c17">Dn1W</font> <b>by </b><i><a class="ref" href="glib_001.html#T151" title="GLIB_001:th.151">GLIB_001:151</a></i>;<br/><b>take </b><font color="Maroon" title="c24">W2</font> = <font color="Maroon" title="c23">W2</font>;<br/><b>thus </b><a NAME="E8:38_4_1_1_2_5"/>
<font color="Maroon" title="c24">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E39:38_4_1_1_2"><i><font color="Green" title="E71">A61</font></i></a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_5"><i><font color="Green" title="E74">A72</font></i></a>, <a class="ref" href="glib_001.html#T67" title="GLIB_001:th.67">GLIB_001:67</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c25">W2G</font> = <font color="Maroon" title="c24">W2</font> as   <a href="glib_001.html#NM6" title="GLIB_001:NM.6">DWalk</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_5_2"><b>now </b></a><div class="add"><a NAME="E1:38_4_1_1_2_5_2"/><i><font color="Green" title="E75">A77</font></i>: 
<font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:38_4_1_1_2_5"><i><font color="Green" title="E74">A72</font></i></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>;<br/><a NAME="E2:38_4_1_1_2_5_2"/><i><font color="Green" title="E76">A78</font></i>: 
(  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E38:38_4_1_1_2"><i><font color="Green" title="E70">A60</font></i></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></i>;<br/><b>hence </b><a NAME="E3:38_4_1_1_2_5_2"/>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c20">WT'</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_5_2"><i><font color="Green" title="E75">A77</font></i></a>, <a class="ref" href="glib_000.html#T64" title="GLIB_000:th.64">GLIB_000:64</a></i>;<br/><a NAME="E4:38_4_1_1_2_5_2"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></i>;<br/><b>hence </b><a NAME="E5:38_4_1_1_2_5_2"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></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#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c17">Dn1W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4_1_1_2_5_2"><i><font color="Green" title="E76">A78</font></i></a>, <a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/><a NAME="E6:38_4_1_1_2_5_2"/><i><font color="Green" title="E77">A79</font></i>: 
<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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a>, <a class="txt" href="glib_004.html#E33:38_4_1_1_2"><i><font color="Green" title="E68">A58</font></i></a>, <a class="txt" href="glib_004.html#E8:38_4"><i><font color="Green" title="E37">A22</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c26">WTG</font> = <font color="Maroon" title="c19">WT</font> as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></i>;<br/><a NAME="E8:38_4_1_1_2_5_2"/><i><font color="Green" title="E78">A80</font></i>: 
<font color="Maroon" title="c26">WTG</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_5"><i><font color="Green" title="E73">A71</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><b>then consider </b><font color="Maroon" title="c27">WX</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E10:38_4_1_1_2_5_2"/><i><font color="Green" title="E79">A81</font></i>: 
( <font color="Maroon" title="c27">WX</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">WX</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )
 <b>by </b><i><a class="txt" href="glib_004.html#E6:38_4_1_1_2_5_2"><i><font color="Green" title="E77">A79</font></i></a>, <a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></i>;<br/><a NAME="E11:38_4_1_1_2_5_2"/>
( <font color="Maroon" title="c27">WX</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">WY</font> being  <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">WY</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> holds <br/><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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">WY</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  ) )
 <b>by </b><i><a class="txt" href="glib_004.html#E10:38_4_1_1_2_5_2"><i><font color="Green" title="E79">A81</font></i></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></i>;<br/><a NAME="E12:38_4_1_1_2_5_2"/><b>then </b>
<font color="Maroon" title="c19">WT</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_5"><i><font color="Green" title="E73">A71</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_5_2"><i><font color="Green" title="E79">A81</font></i></a></i>;<br/><a NAME="E13:38_4_1_1_2_5_2"/><b>then </b><i><font color="Green" title="E80">A82</font></i>: 
<font color="Maroon" title="c20">WT'</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E32:38_4_1_1_2"><i><font color="Green" title="E67">A57</font></i></a>, <a class="ref" href="glib_003.html#T34" title="GLIB_003:th.34">GLIB_003:34</a></i>;<br/><a NAME="E14:38_4_1_1_2_5_2"/>
<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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c26">WTG</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E8:38_4_1_1_2_5_2"><i><font color="Green" title="E78">A80</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_5_2"><i><font color="Green" title="E79">A81</font></i></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></i>;<br/><a NAME="E15:38_4_1_1_2_5_2"/><b>then </b>
<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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c20">WT'</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="ref" href="glib_003.html#T34" title="GLIB_003:th.34">GLIB_003:34</a></i>;<br/><b>hence </b><a NAME="E16:38_4_1_1_2_5_2"/>
<font color="Maroon" title="c20">WT'</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</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"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E13:38_4_1_1_2_5_2"><i><font color="Green" title="E80">A82</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E11:38_4_1_1_2_5"/>
<font color="Maroon" title="c24">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#T32" title="GLIB_003:th.32">GLIB_003:32</a></i>;<br/></div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c19">W2</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c17">Dn1W</font><b> such that </b><br/><a NAME="E45:38_4_1_1_2"/><i><font color="Green" title="E73">A83</font></i>: 
( <font color="Maroon" title="c19">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c19">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> )
 ;<br/><b>reconsider </b><font color="Maroon" title="c20">W2G</font> = <font color="Maroon" title="c19">W2</font> as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></i>;<br/><a NAME="E47:38_4_1_1_2"/><i><font color="Green" title="E74">A84</font></i>: 
<font color="Maroon" title="c20">W2G</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E45:38_4_1_1_2"><i><font color="Green" title="E73">A83</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><a NAME="E48:38_4_1_1_2"/><i><font color="Green" title="E75">A85</font></i>: 
<font color="Maroon" title="c20">W2G</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E45:38_4_1_1_2"><i><font color="Green" title="E73">A83</font></i></a>, <a class="ref" href="glib_003.html#T34" title="GLIB_003:th.34">GLIB_003:34</a></i>;<br/><a NAME="E49:38_4_1_1_2"/><i><font color="Green" title="E76">A86</font></i>: 
<font color="Maroon" title="c2">src</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E7:38_4"><i><font color="Green" title="E36">A21</font></i></a>, <a class="txt" href="glib_004.html#E9:38_4"><i><font color="Green" title="E38">A23</font></i></a>, <a class="txt" href="glib_004.html#E15:38_4_1_1_2"><i><font color="Green" title="E56">A42</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><b>set </b><font color="Maroon" title="c21">mc</font> = <font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_6"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon" title="c22">WB</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E2:38_4_1_1_2_6"/><i><font color="Green" title="E77">A87</font></i>: 
( <font color="Maroon" title="c22">WB</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">WB</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )
 <b>by </b><i><a class="txt" href="glib_004.html#E47:38_4_1_1_2"><i><font color="Green" title="E74">A84</font></i></a>, <a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></i>;<br/><a NAME="E3:38_4_1_1_2_6"/><i><font color="Green" title="E78">A88</font></i>: 
( <font color="Maroon" title="c22">WB</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">WA</font> being  <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">WA</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> holds <br/><font color="Maroon" title="c22">WB</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">WA</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  ) )
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_6"><i><font color="Green" title="E77">A87</font></i></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></i>;<br/><b>thus </b><a NAME="E4:38_4_1_1_2_6"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <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"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_6"><i><font color="Green" title="E77">A87</font></i></a>, <a class="txt" href="glib_004.html#E47:38_4_1_1_2"><i><font color="Green" title="E74">A84</font></i></a>, <a class="txt" href="glib_004.html#E48:38_4_1_1_2"><i><font color="Green" title="E75">A85</font></i></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></i>;<br/><a NAME="E5:38_4_1_1_2_6"/>
( <font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font> &amp; <font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4_1_1_2_6"><i><font color="Green" title="E78">A88</font></i></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>;<br/><a NAME="E6:38_4_1_1_2_6"/><b>then </b>
not <font color="Maroon" title="c22">WB</font> is <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E49:38_4_1_1_2"><i><font color="Green" title="E76">A86</font></i></a>, <a class="ref" href="glib_001.html#T128" title="GLIB_001:th.128">GLIB_001:128</a></i>;<br/><b>then consider </b><font color="Maroon" title="c23">lenWB2h</font> being  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <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="E8:38_4_1_1_2_6"/><i><font color="Green" title="E79">A89</font></i>: 
( <font color="Maroon" title="c23">lenWB2h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c22">WB</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">WB</font> )
 <b>by </b><i><a class="ref" href="glib_001.html#T134" title="GLIB_001:th.134">GLIB_001:134</a></i>;<br/><b>set </b><font color="Maroon" title="c24">WA</font> = <font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font>;<br/><b>set </b><font color="Maroon" title="c25">sa</font> = <font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">lenWB2h</font>;<br/><b>set </b><font color="Maroon" title="c26">ea</font> = <font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/><a NAME="E9:38_4_1_1_2_6"/><i><font color="Green" title="E80">A90</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c23">lenWB2h</font> &amp; not 1 is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> )
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a>, <a class="ref" href="jordan12.html#T3" title="JORDAN12:th.3">JORDAN12:3</a></i>;<br/><a NAME="E10:38_4_1_1_2_6"/><i><font color="Green" title="E81">A91</font></i>: 
<font color="Maroon" title="c23">lenWB2h</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c22">WB</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0
 <b>by </b><i><a class="txt" href="glib_004.html#E8:38_4_1_1_2_6"><i><font color="Green" title="E79">A89</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><i><font color="Green" title="E82">A92</font></i>: <font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<b>by </b><i><a class="ref" href="glib_001.html#D6" title="GLIB_001:def.6">GLIB_001:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c2">src</font>
<b>by </b><i><a class="txt" href="glib_004.html#E3:38_4_1_1_2_6"><i><font color="Green" title="E78">A88</font></i></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>
;<br/><a NAME="E12:38_4_1_1_2_6"/><b>then </b>
<font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">lenWB2h</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E9:38_4_1_1_2_6"><i><font color="Green" title="E80">A90</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_6"><i><font color="Green" title="E81">A91</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c27">sa</font> = <font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">lenWB2h</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c28">target'</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4_1_1_2_6"><i><font color="Green" title="E78">A88</font></i></a>, <a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></i>;<br/><a NAME="E15:38_4_1_1_2_6"/><i><font color="Green" title="E83">A93</font></i>: 
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c27">sa</font>,<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E10:38_4_1_1_2_6"><i><font color="Green" title="E81">A91</font></i></a>, <a class="ref" href="glib_001.html#T123" title="GLIB_001:th.123">GLIB_001:123</a></i>;<br/><a NAME="E16:38_4_1_1_2_6"/><b>then </b>
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c27">sa</font>,<font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E8:38_4_1_1_2_6"><i><font color="Green" title="E79">A89</font></i></a>, <a class="ref" href="glib_001.html#D7" title="GLIB_001:def.7">GLIB_001:def 7</a></i>;<br/><a NAME="E17:38_4_1_1_2_6"/><b>then </b><i><font color="Green" title="E84">A94</font></i>: 
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c27">sa</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E3:38_4_1_1_2_6"><i><font color="Green" title="E78">A88</font></i></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></i>;<br/><a NAME="E18:38_4_1_1_2_6"/><b>then </b>
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c27">sa</font>,<font color="Maroon" title="c28">target'</font>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="glib_000.html#T19" title="GLIB_000:th.19">GLIB_000:19</a></i>;<br/><a NAME="E19:38_4_1_1_2_6"/><b>then </b>
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">sa</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a> 
 <b>by </b><i><a class="ref" href="glib_000.html#T65" title="GLIB_000:th.65">GLIB_000:65</a></i>;<br/><a NAME="E20:38_4_1_1_2_6"/><b>then </b><i><font color="Green" title="E85">A95</font></i>: 
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E9:38_4_1_1_2_6"><i><font color="Green" title="E80">A90</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_6"><i><font color="Green" title="E81">A91</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/><a NAME="E21:38_4_1_1_2_6"/><b>then </b><i><font color="Green" title="E86">A96</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <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="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_6"><i><font color="Green" title="E77">A87</font></i></a>, <a class="txt" href="glib_004.html#E8:38_4_1_1_2_6"><i><font color="Green" title="E79">A89</font></i></a>, <a class="ref" href="glib_003.html#T32" title="GLIB_003:th.32">GLIB_003:32</a></i>;<br/><a NAME="E22:38_4_1_1_2_6"/><i><font color="Green" title="E87">A97</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">sa</font> )
 <b>by </b><i><a class="txt" href="glib_004.html#E11:38_4_1_1_2_6"><i><font color="Green" title="E82">A92</font></i></a>, <a class="txt" href="glib_004.html#E9:38_4_1_1_2_6"><i><font color="Green" title="E80">A90</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_6"><i><font color="Green" title="E81">A91</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/><a NAME="E23:38_4_1_1_2_6"/><b>then </b><i><font color="Green" title="E88">A98</font></i>: 
<font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c27">sa</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_6"><i><font color="Green" title="E77">A87</font></i></a>, <a class="ref" href="glib_004.html#T10" target="_self" title="GLIB_004:th.10">Th10</a></i>;<br/><a NAME="E24:38_4_1_1_2_6"/><b>then </b><i><font color="Green" title="E89">A99</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c27">sa</font>
 <b>by </b><i><a class="ref" href="glib_004.html#T12" target="_self" title="GLIB_004:th.12">Th12</a></i>;<br/><a NAME="E25:38_4_1_1_2_6"/><i><font color="Green" title="E90">A100</font></i>: 
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c27">sa</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="txt" href="glib_004.html#E17:38_4_1_1_2_6"><i><font color="Green" title="E84">A94</font></i></a>, <a class="ref" href="glib_000.html#T91" title="GLIB_000:th.91">GLIB_000:91</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_6_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:38_4_1_1_2_6_2"/><i><font color="Green" title="E91">A101</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <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"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <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>means </b>( not $1 is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; $1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> &amp; not <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  );<br/><div><i><font color="Green" title="E92">A102</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_6_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:38_4_1_1_2_6_2_1"/><i><font color="Green" title="E93">A103</font></i>: 
not <font color="Maroon" title="c27">sa</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><font color="Maroon" title="c27">sa</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E9:38_4_1_1_2_6"><i><font color="Green" title="E80">A90</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_6"><i><font color="Green" title="E81">A91</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="glib_001.html#D7" title="GLIB_001:def.7">GLIB_001:def 7</a></i>
;<br/><a NAME="E3:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E94">A104</font></i>: 
 ex <font color="Olive" title="b1">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>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>]
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_6_2_1"><i><font color="Green" title="E93">A103</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c29">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="E5:38_4_1_1_2_6_2_1"/><i><font color="Green" title="E95">A105</font></i>: 
( <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c29">k</font>] &amp; ( for <font color="Olive" title="b1">m</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="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">m</font>] holds <br/><font color="Maroon" title="c29">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> ) )
 <b>from </b><i><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="glib_004.html#E3:38_4_1_1_2_6_2_1"><i><font color="Green" title="E94">A104</font></i></a>);<br/></i><b>reconsider </b><font color="Maroon" title="c30">k</font> = <font color="Maroon" title="c29">k</font> as  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <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>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<b>by </b><i><a class="ref" href="glib_001.html#D6" title="GLIB_001:def.6">GLIB_001:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c2">src</font>
<b>by </b><i><a class="txt" href="glib_004.html#E11:38_4_1_1_2_6"><i><font color="Green" title="E82">A92</font></i></a>, <a class="txt" href="glib_004.html#E9:38_4_1_1_2_6"><i><font color="Green" title="E80">A90</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4_1_1_2_6"><i><font color="Green" title="E81">A91</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>
;<br/><a NAME="E8:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E96">A106</font></i>: 
<font color="Maroon" title="c30">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>by </b><i><a class="txt" href="glib_004.html#E7:38_4"><i><font color="Green" title="E36">A21</font></i></a>, <a class="txt" href="glib_004.html#E9:38_4"><i><font color="Green" title="E38">A23</font></i></a>, <a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a></i>;<br/><a NAME="E9:38_4_1_1_2_6_2_1"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">k</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a></i>;<br/><a NAME="E10:38_4_1_1_2_6_2_1"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c30">k</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E8:38_4_1_1_2_6_2_1"><i><font color="Green" title="E96">A106</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E11:38_4_1_1_2_6_2_1"/><b>then </b>
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c30">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E12:38_4_1_1_2_6_2_1"/><b>then </b>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">k</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>then reconsider </b><font color="Maroon" title="c31">k2a</font> = <font color="Maroon" title="c30">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> as  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <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>by </b><i><a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a></i>;<br/><b>set </b><font color="Maroon" title="c32">sk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c31">k2a</font>;<br/><b>set </b><font color="Maroon" title="c33">ek</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon" title="c34">tk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c30">k</font>;<br/><a NAME="E14:38_4_1_1_2_6_2_1"/><i><font color="Green" title="E97">A107</font></i>: 
( not 1 is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c31">k2a</font> &amp; <font color="Maroon" title="c31">k2a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0 )
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a>, <a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a>, <a class="ref" href="jordan12.html#T3" title="JORDAN12:th.3">JORDAN12:3</a></i>;<br/><a NAME="E15:38_4_1_1_2_6_2_1"/>
<font color="Maroon" title="c31">k2a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c30">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 0
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E16:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E98">A108</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c31">k2a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a>, <a class="txt" href="glib_004.html#E14:38_4_1_1_2_6_2_1"><i><font color="Green" title="E97">A107</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c35">sk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c31">k2a</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c36">tk</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c30">k</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a>, <a class="ref" href="glib_001.html#T8" title="GLIB_001:th.8">GLIB_001:8</a></i>;<br/><b>set </b><font color="Maroon" title="c37">WK1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font>;<br/><b>set </b><font color="Maroon" title="c38">WK2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c31">k2a</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c39">WKA</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font>;<br/><b>set </b><font color="Maroon" title="c40">WKB</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c30">k</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span>;<br/><a NAME="E19:38_4_1_1_2_6_2_1"/>
<font color="Maroon" title="c36">tk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>
 ;<br/><a NAME="E20:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E99">A109</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c35">sk</font>,<font color="Maroon" title="c36">tk</font>,<font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E14:38_4_1_1_2_6_2_1"><i><font color="Green" title="E97">A107</font></i></a>, <a class="ref" href="glib_001.html#T123" title="GLIB_001:th.123">GLIB_001:123</a></i>;<br/><a NAME="E21:38_4_1_1_2_6_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c35">sk</font>,<font color="Maroon" title="c36">tk</font>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="glib_000.html#T91" title="GLIB_000:th.91">GLIB_000:91</a></i>;<br/><a NAME="E22:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E100">A110</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">sk</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">tk</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></i>;<br/><a NAME="E23:38_4_1_1_2_6_2_1"/><i><font color="Green" title="E101">A111</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">sk</font> )
 <b>by </b><i><a class="txt" href="glib_004.html#E14:38_4_1_1_2_6_2_1"><i><font color="Green" title="E97">A107</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/><a NAME="E24:38_4_1_1_2_6_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1,<font color="Maroon" title="c35">sk</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E23:38_4_1_1_2_6"><i><font color="Green" title="E88">A98</font></i></a>, <a class="ref" href="glib_004.html#T10" target="_self" title="GLIB_004:th.10">Th10</a></i>;<br/><a NAME="E25:38_4_1_1_2_6_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<font color="Maroon" title="c35">sk</font>
 <b>by </b><i><a class="ref" href="glib_001.html#D6" title="GLIB_001:def.6">GLIB_001:def 6</a></i>;<br/><a NAME="E26:38_4_1_1_2_6_2_1"/><b>then </b>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c35">sk</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="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E22:38_4_1_1_2_6"><i><font color="Green" title="E87">A97</font></i></a>, <a class="ref" href="glib_004.html#T12" target="_self" title="GLIB_004:th.12">Th12</a></i>;<br/><a NAME="E27:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E102">A112</font></i>: 
<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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c35">sk</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="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a>, <a class="txt" href="glib_004.html#E16:38_4_1_1_2_6_2_1"><i><font color="Green" title="E98">A108</font></i></a></i>;<br/><a NAME="E28:38_4_1_1_2_6_2_1"/>
<font color="Maroon" title="c36">tk</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E22:38_4_1_1_2_6_2_1"><i><font color="Green" title="E100">A110</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><a NAME="E29:38_4_1_1_2_6_2_1"/><b>then </b>
<font color="Maroon" title="c36">tk</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E30:38_4_1_1_2_6_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R4" title="GLIB_000:pred.4">DSJoins</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E22:38_4_1_1_2_6_2_1"><i><font color="Green" title="E100">A110</font></i></a>, <a class="txt" href="glib_004.html#E16:38_4_1_1_2_6_2_1"><i><font color="Green" title="E98">A108</font></i></a>, <a class="ref" href="glib_000.html#D18" title="GLIB_000:def.18">GLIB_000:def 18</a></i>;<br/><a NAME="E31:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E103">A113</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <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"><span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="txt" href="glib_004.html#E27:38_4_1_1_2_6_2_1"><i><font color="Green" title="E102">A112</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2"><i><font color="Green" title="E47">A32</font></i></a>, <a class="ref" href="glib_004.html#D4" target="_self" title="GLIB_004:def.4">Def4</a>, <a class="txt" href="glib_004.html#E22:38_4_1_1_2_6_2_1"><i><font color="Green" title="E100">A110</font></i></a></i>;<br/><a NAME="E32:38_4_1_1_2_6_2_1"/>
<font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">k</font>
 ;<br/><a NAME="E33:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E104">A114</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c31">k2a</font></span>)</span> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E14:38_4_1_1_2_6_2_1"><i><font color="Green" title="E97">A107</font></i></a>, <a class="ref" href="glib_001.html#T42" title="GLIB_001:th.42">GLIB_001:42</a></i>;<br/><a NAME="E34:38_4_1_1_2_6_2_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">sk</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">tk</font> )
 <b>by </b><i><a class="txt" href="glib_004.html#E20:38_4_1_1_2_6_2_1"><i><font color="Green" title="E99">A109</font></i></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></i>;<br/><a NAME="E35:38_4_1_1_2_6_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c35">sk</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a> 
 <b>by </b><i><a class="ref" href="glib_000.html#T64" title="GLIB_000:th.64">GLIB_000:64</a></i>;<br/><a NAME="E36:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E105">A115</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <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="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E23:38_4_1_1_2_6_2_1"><i><font color="Green" title="E101">A111</font></i></a>, <a class="txt" href="glib_004.html#E31:38_4_1_1_2_6_2_1"><i><font color="Green" title="E103">A113</font></i></a>, <a class="txt" href="glib_004.html#E33:38_4_1_1_2_6_2_1"><i><font color="Green" title="E104">A114</font></i></a>, <a class="ref" href="glib_003.html#T32" title="GLIB_003:th.32">GLIB_003:32</a></i>;<br/><a NAME="E37:38_4_1_1_2_6_2_1"/><i><font color="Green" title="E106">A116</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">k</font> &amp; <font color="Maroon" title="c30">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> )
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a>, <a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a></i>;<br/><b>then </b><i><font color="Green" title="E107">A117</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c30">k</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jordan12.html#T3" title="JORDAN12:th.3">JORDAN12:3</a>, <a class="ref" href="glib_001.html#T39" title="GLIB_001:th.39">GLIB_001:39</a></i>
<br/>.= 
<font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font>
<b>by </b><i><a class="ref" href="glib_001.html#T40" title="GLIB_001:th.40">GLIB_001:40</a></i>
;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c30">k</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c30">k</font>
<b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_6_2_1"><i><font color="Green" title="E95">A105</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E37:38_4_1_1_2_6_2_1"><i><font color="Green" title="E106">A116</font></i></a>, <a class="ref" href="jordan12.html#T3" title="JORDAN12:th.3">JORDAN12:3</a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>
;<br/><a NAME="E40:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E108">A118</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <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"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c30">k</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E38:38_4_1_1_2_6_2_1"><i><font color="Green" title="E107">A117</font></i></a>, <a class="ref" href="glib_003.html#T31" title="GLIB_003:th.31">GLIB_003:31</a></i>;<br/><a NAME="E41:38_4_1_1_2_6_2_1"/>
0 <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="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c30">k</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span></span>)</span></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="ref" href="glib_003.html#T36" title="GLIB_003:th.36">GLIB_003:36</a></i>;<br/><a NAME="E42:38_4_1_1_2_6_2_1"/><b>then </b>
0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c30">k</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E40:38_4_1_1_2_6_2_1"><i><font color="Green" title="E108">A118</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E43:38_4_1_1_2_6_2_1"/><b>then </b><i><font color="Green" title="E109">A119</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E36:38_4_1_1_2_6_2_1"><i><font color="Green" title="E105">A115</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E44:38_4_1_1_2_6_2_1"/>
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E15:38_4_1_1_2_6"><i><font color="Green" title="E83">A93</font></i></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></i>;<br/><a NAME="E45:38_4_1_1_2_6_2_1"/><b>then </b>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="glib_003.html#T38" title="GLIB_003:th.38">GLIB_003:38</a></i>;<br/><a NAME="E46:38_4_1_1_2_6_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0 <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="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E43:38_4_1_1_2_6_2_1"><i><font color="Green" title="E109">A119</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><b>hence </b><a NAME="E47:38_4_1_1_2_6_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_004.html#E20:38_4_1_1_2_6"><i><font color="Green" title="E85">A95</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4_1_1_2_6"><i><font color="Green" title="E77">A87</font></i></a>, <a class="txt" href="glib_004.html#E8:38_4_1_1_2_6"><i><font color="Green" title="E79">A89</font></i></a>, <a class="ref" href="glib_003.html#T32" title="GLIB_003:th.32">GLIB_003:32</a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_6_2"><i><font color="Green" title="E91">A101</font></i></a></i>;<br/></div><b>end;</b></div><a NAME="E3:38_4_1_1_2_6_2"/><b>then </b><i><font color="Green" title="E93">A120</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> 1,<font color="Maroon" title="c23">lenWB2h</font></span>)</span> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c27">sa</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E24:38_4_1_1_2_6"><i><font color="Green" title="E89">A99</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a></i>;<br/><a NAME="E4:38_4_1_1_2_6_2"/><i><font color="Green" title="E94">A121</font></i>: 
( <font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">sa</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_004.html#E25:38_4_1_1_2_6"><i><font color="Green" title="E90">A100</font></i></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></i>;<br/><a NAME="E5:38_4_1_1_2_6_2"/><b>then </b>
<font color="Maroon" title="c22">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c23">lenWB2h</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="glib_000.html#R4" title="GLIB_000:pred.4">DSJoins</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> </span>)</span>,<span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_6_2"><i><font color="Green" title="E92">A102</font></i></a>, <a class="txt" href="glib_004.html#E15:38_4_1_1_2"><i><font color="Green" title="E56">A42</font></i></a>, <a class="ref" href="glib_000.html#D18" title="GLIB_000:def.18">GLIB_000:def 18</a></i>;<br/><b>hence </b><a NAME="E6:38_4_1_1_2_6_2"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_004.html#E21:38_4_1_1_2_6"><i><font color="Green" title="E86">A96</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_6_2"><i><font color="Green" title="E91">A101</font></i></a>, <a class="txt" href="glib_004.html#E3:38_4_1_1_2_6_2"><i><font color="Green" title="E93">A120</font></i></a>, <a class="txt" href="glib_004.html#E5:38_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2"><i><font color="Green" title="E47">A32</font></i></a>, <a class="ref" href="glib_004.html#D4" target="_self" title="GLIB_004:def.4">Def4</a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_6_2"><i><font color="Green" title="E94">A121</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E27:38_4_1_1_2_6"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div><a NAME="E51:38_4_1_1_2"/><b>then </b><i><font color="Green" title="E77">A122</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c22">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c17">Dn1W</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_4_1_1_2_7_1_1"/>
( <font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  or <font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="glib_004.html#E13:38_4_1_1_2"><i><font color="Green" title="E54">A40</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_7_1_1_1"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_7_1_1_1"/>
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c23">x'</font> = <font color="Maroon" title="c22">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c16">DnW</font> <b>by </b><i><a class="txt" href="glib_004.html#E12:38_4"><i><font color="Green" title="E41">A26</font></i></a>, <a class="txt" href="glib_004.html#E10:38_4"><i><font color="Green" title="E39">A24</font></i></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></i>;<br/><a NAME="E3:38_4_1_1_2_7_1_1_1"/>
<font color="Maroon" title="c16">DnW</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c24">W2</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c16">DnW</font><b> such that </b><br/><a NAME="E5:38_4_1_1_2_7_1_1_1"/><i><font color="Green" title="E78">A123</font></i>: 
( <font color="Maroon" title="c24">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c23">x'</font> &amp; ( for <font color="Olive" title="b1">W1</font> being  <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c23">x'</font> holds <br/><font color="Maroon" title="c24">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  ) )
 <b>by </b><i><a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c25">W2'</font> = <font color="Maroon" title="c24">W2</font> as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c17">Dn1W</font> <b>by </b><i><a class="txt" href="glib_004.html#E23:38_4_1_1_2"><i><font color="Green" title="E63">A52</font></i></a>, <a class="ref" href="glib_001.html#T176" title="GLIB_001:th.176">GLIB_001:176</a></i>;<br/><b>take </b><font color="Maroon" title="c26">W2'</font> = <font color="Maroon" title="c25">W2'</font>;<br/><b>thus </b><a NAME="E7:38_4_1_1_2_7_1_1_1"/>
<font color="Maroon" title="c26">W2'</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">x</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_7_1_1_1"><i><font color="Green" title="E78">A123</font></i></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></i>;<br/><b>let </b><font color="Maroon" title="c27">W1</font> be   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><a NAME="E8:38_4_1_1_2_7_1_1_1"/>
<font color="Maroon" title="c27">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">x</font>
 ;<br/><a NAME="E9:38_4_1_1_2_7_1_1_1"/><b>then </b>
<font color="Maroon" title="c24">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c27">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E5:38_4_1_1_2_7_1_1_1"><i><font color="Green" title="E78">A123</font></i></a></i>;<br/><b>hence </b><a NAME="E10:38_4_1_1_2_7_1_1_1"/>
<font color="Maroon" title="c26">W2'</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c27">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E32:38_4_1_1_2"><i><font color="Green" title="E67">A57</font></i></a>, <a class="ref" href="glib_003.html#T34" title="GLIB_003:th.34">GLIB_003:34</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_7_1_1_2"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_7_1_1_2"/><i><font color="Green" title="E78">A124</font></i>: 
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:38_4_1_1_2_7_1_1_2"/><b>then </b><i><font color="Green" title="E79">A125</font></i>: 
<font color="Maroon" title="c22">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>take </b><font color="Maroon" title="c23">W2</font> = <font color="Maroon" title="c19">W2</font>;<br/><b>thus </b><a NAME="E3:38_4_1_1_2_7_1_1_2"/>
<font color="Maroon" title="c23">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">x</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E45:38_4_1_1_2"><i><font color="Green" title="E73">A83</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_7_1_1_2"><i><font color="Green" title="E78">A124</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>let </b><font color="Maroon" title="c24">W1</font> be   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><a NAME="E4:38_4_1_1_2_7_1_1_2"/><i><font color="Green" title="E80">A126</font></i>: 
<font color="Maroon" title="c24">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">x</font>
 ;<br/><b>consider </b><font color="Maroon" title="c25">WX</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E6:38_4_1_1_2_7_1_1_2"/><i><font color="Green" title="E81">A127</font></i>: 
( <font color="Maroon" title="c25">WX</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c2">src</font>,<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c25">WX</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )
 <b>by </b><i><a class="txt" href="glib_004.html#E47:38_4_1_1_2"><i><font color="Green" title="E74">A84</font></i></a>, <a class="txt" href="glib_004.html#E45:38_4_1_1_2"><i><font color="Green" title="E73">A83</font></i></a>, <a class="txt" href="glib_004.html#E51:38_4_1_1_2"><i><font color="Green" title="E77">A122</font></i></a>, <a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></i>;<br/><b>thus </b><a NAME="E7:38_4_1_1_2_7_1_1_2"/>
<font color="Maroon" title="c23">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2_7_1_1_2"><i><font color="Green" title="E79">A125</font></i></a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_7_1_1_2"><i><font color="Green" title="E80">A126</font></i></a>, <a class="txt" href="glib_004.html#E6:38_4_1_1_2_7_1_1_2"><i><font color="Green" title="E81">A127</font></i></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E2:38_4_1_1_2_7"/>
 ex <font color="Olive" title="b1">W2</font> being  <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c17">Dn1W</font> st <br/>( <font color="Olive" title="b1">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">x</font> &amp; ( for <font color="Olive" title="b2">W1</font> being  <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">x</font> holds <br/><font color="Olive" title="b1">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  ) )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E53:38_4_1_1_2"/>
<font color="Maroon" title="c17">Dn1W</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E42:38_4_1_1_2"><i><font color="Green" title="E72">A70</font></i></a>, <a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></i>;<br/><b>let </b><font color="Maroon" title="c22">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>;<br/><b>assume </b><a NAME="E54:38_4_1_1_2"/><i><font color="Green" title="E78">A128</font></i>: 
<font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_4_1_1_2_8"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_8_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:38_4_1_1_2_8_1"/>
( <font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  or <font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="glib_004.html#E6:38_4_1_1_2"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="glib_004.html#E7:38_4_1_1_2"><i><font color="Green" title="E51">A36</font></i></a>, <a class="txt" href="glib_004.html#E54:38_4_1_1_2"><i><font color="Green" title="E78">A128</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_8_1_1"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_8_1_1"/><i><font color="Green" title="E79">A129</font></i>: 
<font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 ;<br/><div class="add"><a NAME="E2:38_4_1_1_2_8_1_1"/><b>then </b><i><font color="Green" title="E80">A130</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">v</font> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c22">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E7:38_4_1_1_2"><i><font color="Green" title="E51">A36</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4"><i><font color="Green" title="E31">A16</font></i></a></i>;<br/><a NAME="E3:38_4_1_1_2_8_1_1"/><i><font color="Green" title="E81">A131</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="glib_004.html#E5:38_4_1_1_2"><i><font color="Green" title="E49">A34</font></i></a>, <a class="ref" href="glib_003.html#T45" title="GLIB_003:th.45">GLIB_003:45</a></i>;<br/><a NAME="E4:38_4_1_1_2_8_1_1"/><i><font color="Green" title="E82">A132</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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E5:38_4_1_1_2_8_1_1"/><b>then </b>
not <font color="Maroon" title="c22">v</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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E16:38_4_1_1_2"><i><font color="Green" title="E57">A43</font></i></a>, <a class="txt" href="glib_004.html#E1:38_4_1_1_2_8_1_1"><i><font color="Green" title="E79">A129</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="E6:38_4_1_1_2_8_1_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c22">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E6:38_4_1_1_2"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="glib_004.html#E54:38_4_1_1_2"><i><font color="Green" title="E78">A128</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4_1_1_2_8_1_1"><i><font color="Green" title="E80">A130</font></i></a>, <a class="txt" href="glib_004.html#E3:38_4_1_1_2_8_1_1"><i><font color="Green" title="E81">A131</font></i></a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_8_1_1"><i><font color="Green" title="E82">A132</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_4_1_1_2_8_1_2"><b>suppose </b></a><a NAME="E1:38_4_1_1_2_8_1_2"/><i><font color="Green" title="E79">A133</font></i>: 
<font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:38_4_1_1_2_8_1_2"/><b>then </b><i><font color="Green" title="E80">A134</font></i>: 
<font color="Maroon" title="c22">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:38_4_1_1_2_8_1_2"/><i><font color="Green" title="E81">A135</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:38_4_1_1_2"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="glib_004.html#E5:38_4_1_1_2"><i><font color="Green" title="E49">A34</font></i></a>, <a class="ref" href="glib_003.html#T45" title="GLIB_003:th.45">GLIB_003:45</a></i>;<br/><a NAME="E4:38_4_1_1_2_8_1_2"/><i><font color="Green" title="E82">A136</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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></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"><span class="p3">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E5:38_4_1_1_2_8_1_2"/><b>then </b>
<font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="glib_003.html#K12" title="GLIB_003:func.12">.labelEdge</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span>,1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K14" title="FUNCOP_1:func.14">.--&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p0">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_8_1_2"><i><font color="Green" title="E79">A133</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E6:38_4_1_1_2_8_1_2"/><b>then </b>
<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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c22">v</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="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></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"><span class="p4">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p5">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p0">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p4">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p5">(<span class="default"><a href="glib_004.html#K2" title="GLIB_004:func.2">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:38_4_1_1_2_8_1_2"><i><font color="Green" title="E79">A133</font></i></a>, <a class="txt" href="glib_004.html#E3:38_4_1_1_2_8_1_2"><i><font color="Green" title="E81">A135</font></i></a>, <a class="txt" href="glib_004.html#E4:38_4_1_1_2_8_1_2"><i><font color="Green" title="E82">A136</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/><b>hence </b><a NAME="E7:38_4_1_1_2_8_1_2"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c22">v</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E51:38_4_1_1_2"><i><font color="Green" title="E77">A122</font></i></a>, <a class="txt" href="glib_004.html#E2:38_4_1_1_2_8_1_2"><i><font color="Green" title="E80">A134</font></i></a>, <a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E56:38_4_1_1_2"/>
<font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Maroon" title="c22">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c22">v</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E19:38_4"/>
( <font color="Maroon" title="c17">Dn1W</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font> &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  holds <br/><font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Olive" title="b1">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )
 ;<br/></div><b>end;</b></div>
<a NAME="E9:38"/><b>then </b><i><font color="Green" title="E31">A137</font></i>: 
for <font color="Olive" title="b1">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>   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="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
;<br/>
<a NAME="E10:38"/>
for <font color="Olive" title="b1">n</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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="glib_004.html#E7:38"><i><font color="Green" title="E30">A15</font></i></a>, <a class="txt" href="glib_004.html#E9:38"><i><font color="Green" title="E31">A137</font></i></a>);<br/></i>
<b>hence </b><a NAME="E11:38"/>
for <font color="Olive" title="b1">n</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> <br/> for <font color="Olive" title="b2">G2</font> being  <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_003.html#K11" title="GLIB_003:func.11">.labeledE()</a>  holds <br/> ( <font color="Olive" title="b2">G2</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font> &amp; ( for <font color="Olive" title="b3">v</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  holds <br/><font color="Maroon" title="c1">G</font> <a href="glib_004.html#K1" title="GLIB_004:func.1">.min_DPath_cost</a> <font color="Maroon" title="c2">src</font>,<font color="Olive" title="b3">v</font> <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"><span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:CompSeq</a> <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">.</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">v</font> ) )
 ;<br/>


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