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

<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><br/>  for <font color="Olive" title="b2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/>  for <font color="Olive" title="b3">G2</font> being   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds <br/> ( <font color="Olive" title="b3">G2</font> <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Olive" title="b1">s</font> &amp; (  for <font color="Olive" title="b4">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="b4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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="Olive" title="b1">s</font>,<font color="Olive" title="b4">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b4">v</font> ) )</span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">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>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">v</font> ) )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">DCS</font> =  <a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">D0</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span> 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>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> $1</span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> $1</span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> $1</span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> $1</span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">v</font> ) );<br/>
<a NAME="E1:47"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_004.html#K8" title="GLIB_004:func.8">DIJK:Init</a> <font color="Maroon" title="c2">src</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D11" target="_self" title="GLIB_004:def.11">Def11</a></span>;<br/>
<a NAME="E2:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E3:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A3</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font>] implies  for <font color="Olive" title="b1">Dn1W</font> being   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds <br/> ( <font color="Olive" title="b1">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="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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">v</font> ) ) )</span><br/><span class="kw">set </span><font color="Maroon" title="c6">Dn</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font>;<br/><span class="kw">set </span><font color="Maroon" title="c7">Dn1</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c8">BE</font> =  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c9">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c10">source</font> = <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c11">target</font> = <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">DnE</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c13">pc</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">ec</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> <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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">DnW</font> =  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> ;<br/><a NAME="E1:47_1"/><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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#K7" title="GLIB_004:func.7">DIJK:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D11" target="_self" title="GLIB_004:def.11">Def11</a></span>;<br/><span class="kw">assume </span><a NAME="E2:47_1"/><span class="lab"><font color="Green" title="E37">A5</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Dn1W</font> being   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds <br/> ( <font color="Olive" title="b1">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="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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">v</font> ) )</span><br/><a NAME="E3:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A6</font></span>: 
 the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font>
 ;<br/><a NAME="E4:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A7</font></span>: 
 the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c16">Dn1W</font> be   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )</span><br/><a NAME="E5:47_1"/><span class="lab"><font color="Green" title="E40">A8</font></span>: 
( <font color="Maroon" title="c2">src</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="glib_004.html#T18" target="_self" title="GLIB_004:th.18">Th18</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:47_1"/><span class="lab"><font color="Green" title="E41">A9</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#T22" target="_self" title="GLIB_004:th.22">Th22</a></span>;<br/><a NAME="E7:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A10</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="glib_000.html#K17" title="GLIB_000:func.17">.size()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E8:47_1"/><span class="lab"><font color="Green" title="E43">A11</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#T22" target="_self" title="GLIB_004:th.22">Th22</a></span>;<br/><a NAME="E9:47_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A12</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E10:47_1"/><span class="lab"><font color="Green" title="E45">A13</font></span>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="txt" href="#E8:47_1"><span class="lab"><font color="Green" title="E43">A11</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E11:47_1"/><span class="lab"><font color="Green" title="E46">A14</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="txt" href="#E6:47_1"><span class="lab"><font color="Green" title="E41">A9</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:47_1_1_1"/>
(  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="47_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_1"/>
 <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )</span><br/><div class="add"><a NAME="E2:47_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="glib_004.html#D8" target="_self" title="GLIB_004:def.8">Def8</a></span>;<br/><span class="kw">hence </span><a NAME="E3:47_1_1_1_1"/>
( <font color="Maroon" title="c16">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2"/><span class="lab"><font color="Green" title="E47">A15</font></span>: 
 <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c17">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>);<br/><a NAME="E2:47_1_1_1_2"/><span class="lab"><font color="Green" title="E48">A16</font></span>: 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c16">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#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">Dn1W</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></span>;<br/><a NAME="E3:47_1_1_1_2"/><span class="lab"><font color="Green" title="E49">A17</font></span>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="glib_000.html#R4" title="GLIB_000:pred.4">DSJoins</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2"><span class="lab"><font color="Green" title="E47">A15</font></span></a>, <a class="ref" href="glib_004.html#D7" target="_self" title="GLIB_004:def.7">Def7</a></span>;<br/><a NAME="E4:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A18</font></span>: 
<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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></span>;<br/><a NAME="E5:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A19</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E6:47_1_1_1_2"/><span class="lab"><font color="Green" title="E52">A20</font></span>: 
 not <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1_1_1_2"><span class="lab"><font color="Green" title="E50">A18</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E7:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A21</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T41" title="CARD_2:th.41">CARD_2:41</a></span>;<br/><a NAME="E8:47_1_1_1_2"/><span class="lab"><font color="Green" title="E54">A22</font></span>: 
<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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1_1_2"><span class="lab"><font color="Green" title="E49">A17</font></span></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></span>;<br/><a NAME="E9:47_1_1_1_2"/><span class="lab"><font color="Green" title="E55">A23</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">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"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<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="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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p0">(<span class="default"><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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p5">(<span class="default"><span class="p0">(<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="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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2"><span class="lab"><font color="Green" title="E47">A15</font></span></a>, <a class="ref" href="glib_004.html#D8" target="_self" title="GLIB_004:def.8">Def8</a></span>;<br/><a NAME="E10:47_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E11:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A24</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glib_004.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><a NAME="E12:47_1_1_1_2"/><span class="lab"><font color="Green" title="E57">A25</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#T22" target="_self" title="GLIB_004:th.22">Th22</a></span>;<br/><a NAME="E13:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A26</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c16">Dn1W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1_1_1_2"><span class="lab"><font color="Green" title="E56">A24</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E14:47_1_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2"><span class="lab"><font color="Green" title="E55">A23</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E15:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A27</font></span>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1_1_1_2"><span class="lab"><font color="Green" title="E56">A24</font></span></a>, <a class="txt" href="#E12:47_1_1_1_2"><span class="lab"><font color="Green" title="E57">A25</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><div><span class="lab"><font color="Green" title="E60">A28</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">thus </span><a NAME="E1:47_1_1_1_2_1"/>
(  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c16">Dn1W</font> &amp;  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">Dn1W</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="txt" href="#E10:47_1"><span class="lab"><font color="Green" title="E45">A13</font></span></a>, <a class="txt" href="#E13:47_1_1_1_2"><span class="lab"><font color="Green" title="E58">A26</font></span></a>, <a class="txt" href="#E15:47_1_1_1_2"><span class="lab"><font color="Green" title="E59">A27</font></span></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds <br/>( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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="c16">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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="c16">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">e</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c18">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  implies ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c16">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>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c16">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> ) )</span><br/><span class="kw">assume </span><a NAME="E2:47_1_1_1_2_1"/><span class="lab"><font color="Green" title="E61">A29</font></span>: 
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c16">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>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c16">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> )</span><br/><a NAME="E3:47_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A30</font></span>: 
<span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D32" title="GLIB_000:def.32">GLIB_000:def 32</a></span>;<br/><a NAME="E4:47_1_1_1_2_1"/>
( <font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">Dn1W</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:47_1"><span class="lab"><font color="Green" title="E45">A13</font></span></a>, <a class="txt" href="#E15:47_1_1_1_2"><span class="lab"><font color="Green" title="E59">A27</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A29</font></span></a>, <a class="ref" href="glib_000.html#D32" title="GLIB_000:def.32">GLIB_000:def 32</a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_1_1_1_2_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c16">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>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </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="c16">Dn1W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">e</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1_1_2_1"><span class="lab"><font color="Green" title="E62">A30</font></span></a>, <a class="ref" href="glib_000.html#D32" title="GLIB_000:def.32">GLIB_000:def 32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">DnW9</font> =  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  as   <a href="glib_003.html#V1" title="GLIB_003:attr.1">[Weighted]</a>   <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c16">Dn1W</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D32" title="GLIB_000:def.32">GLIB_000:def 32</a></span>;<br/><a NAME="E18:47_1_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E19:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A31</font></span>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:47_1_1_1_2"><span class="lab"><font color="Green" title="E59">A27</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E20:47_1_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2"><span class="lab"><font color="Green" title="E47">A15</font></span></a></span>;<br/><a NAME="E21:47_1_1_1_2"/><span class="kw">then </span>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><a NAME="E22:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A32</font></span>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:47_1_1_1_2"><span class="lab"><font color="Green" title="E61">A31</font></span></a>, <a class="ref" href="glib_000.html#T73" title="GLIB_000:th.73">GLIB_000:73</a></span>;<br/><a NAME="E23:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A33</font></span>: 
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T16" title="GLIB_000:th.16">GLIB_000:16</a></span>;<br/><a NAME="E24:47_1_1_1_2"/><span class="lab"><font color="Green" title="E64">A34</font></span>: 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW9</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#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></span>;<br/><div><span class="lab"><font color="Green" title="E65">A35</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c19">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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">DnW9</font></span>)</span> implies <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">DnW9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">y</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="c16">Dn1W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c19">y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:47_1_1_1_2_2"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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">DnW9</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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">DnW9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">y</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="c16">Dn1W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c19">y</font></span><br/><a NAME="E2:47_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A36</font></span>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/><span class="kw">hence </span><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">DnW9</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:47_1_1_1_2"><span class="lab"><font color="Green" title="E64">A34</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
<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="c16">Dn1W</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c19">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:47_1_1_1_2"><span class="lab"><font color="Green" title="E60">A28</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2"><span class="lab"><font color="Green" title="E48">A16</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2_2"><span class="lab"><font color="Green" title="E66">A36</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E26:47_1_1_1_2"/>
 <a href="relset_1.html#K1" title="RELSET_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="c16">Dn1W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/><a NAME="E27:47_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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="c16">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#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:47_1_1_1_2"><span class="lab"><font color="Green" title="E60">A28</font></span></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>;<br/><a NAME="E28:47_1_1_1_2"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_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">DnW9</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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="c16">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#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/><a NAME="E29:47_1_1_1_2"/><span class="kw">then </span>
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c18">DnW9</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="c16">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#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:47_1_1_1_2"><span class="lab"><font color="Green" title="E65">A35</font></span></a>, <a class="ref" href="funct_1.html#T46" title="FUNCT_1:th.46">FUNCT_1:46</a></span>;<br/><a NAME="E30:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A37</font></span>: 
 the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  is   <a href="glib_003.html#NM8" title="GLIB_003:NM.8">WSubgraph</a> of <font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></span>;<br/><a NAME="E31:47_1_1_1_2"/><span class="lab"><font color="Green" title="E67">A38</font></span>: 
 the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:47_1_1_1_2"><span class="lab"><font color="Green" title="E60">A28</font></span></a>, <a class="ref" href="glib_000.html#D32" title="GLIB_000:def.32">GLIB_000:def 32</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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="c16">Dn1W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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></span><br/><div><span class="lab"><font color="Green" title="E68">A39</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> implies  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="c16">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> )</span><br/><span class="kw">assume </span><a NAME="E1:47_1_1_1_2_3_1"/>
( <font color="Maroon" title="c21">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c22">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c23">u9</font> = <font color="Maroon" title="c21">u</font>, <font color="Maroon" title="c24">v9</font> = <font color="Maroon" title="c22">v</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47_1"><span class="lab"><font color="Green" title="E43">A11</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c25">W1</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> <span class="kw"> such that </span><br/><a NAME="E4:47_1_1_1_2_3_1"/><span class="lab"><font color="Green" title="E69">A40</font></span>: 
<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">u9</font>,<font color="Maroon" title="c24">v9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1"><span class="lab"><font color="Green" title="E39">A7</font></span></a>, <a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></span>;<br/><span class="kw">reconsider </span><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="c16">Dn1W</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:47_1_1_1_2"><span class="lab"><font color="Green" title="E67">A38</font></span></a>, <a class="ref" href="glib_001.html#T167" title="GLIB_001:th.167">GLIB_001:167</a></span>;<br/><a NAME="E6:47_1_1_1_2_3_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1_1_1_2_3_1"><span class="lab"><font color="Green" title="E69">A40</font></span></a>, <a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></span>;<br/><span class="kw">hence </span><a NAME="E7:47_1_1_1_2_3_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="c16">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_3_2"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_3_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:47_1_1_1_2_3_2_1"/>
( ( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> ) or ( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:47_1_1_1_2"><span class="lab"><font color="Green" title="E58">A26</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_3_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_3_2_1_1"/>
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> &amp; <font color="Maroon" title="c20">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:47_1_1_1_2_3_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="c16">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_3"><span class="lab"><font color="Green" title="E68">A39</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_3_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_3_2_1_2"/><span class="lab"><font color="Green" title="E69">A41</font></span>: 
( <font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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></span><br/><div class="add"><a NAME="E2:47_1_1_1_2_3_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A42</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">consider </span><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="c16">Dn1W</font><span class="kw"> such that </span><br/><a NAME="E4:47_1_1_1_2_3_2_1_2"/><span class="lab"><font color="Green" title="E71">A43</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47_1_1_1_2"><span class="lab"><font color="Green" title="E54">A22</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_3"><span class="lab"><font color="Green" title="E68">A39</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_3_2_1_2"><span class="lab"><font color="Green" title="E69">A41</font></span></a></span>;<br/><a NAME="E5:47_1_1_1_2_3_2_1_2"/>
<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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:47_1_1_1_2"><span class="lab"><font color="Green" title="E63">A33</font></span></a>, <a class="txt" href="#E4:47_1_1_1_2_3_2_1_2"><span class="lab"><font color="Green" title="E71">A43</font></span></a>, <a class="ref" href="glib_001.html#T66" title="GLIB_001:th.66">GLIB_001:66</a></span>;<br/><span class="kw">hence </span><a NAME="E6:47_1_1_1_2_3_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="c16">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_1_1_2_3_2_1_2"><span class="lab"><font color="Green" title="E70">A42</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_3_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_3_2_1_3"/><span class="lab"><font color="Green" title="E69">A44</font></span>: 
( <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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><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="c16">Dn1W</font><span class="kw"> such that </span><br/><a NAME="E3:47_1_1_1_2_3_2_1_3"/><span class="lab"><font color="Green" title="E70">A45</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47_1_1_1_2"><span class="lab"><font color="Green" title="E54">A22</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_3"><span class="lab"><font color="Green" title="E68">A39</font></span></a></span>;<br/><a NAME="E4:47_1_1_1_2_3_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:47_1_1_1_2"><span class="lab"><font color="Green" title="E63">A33</font></span></a>, <a class="txt" href="#E3:47_1_1_1_2_3_2_1_3"><span class="lab"><font color="Green" title="E70">A45</font></span></a>, <a class="ref" href="glib_001.html#T66" title="GLIB_001:th.66">GLIB_001:66</a></span>;<br/><a NAME="E5:47_1_1_1_2_3_2_1_3"/><span class="kw">then </span>
<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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_3_2_1_3"><span class="lab"><font color="Green" title="E69">A44</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E6:47_1_1_1_2_3_2_1_3"/><span class="kw">then </span>
<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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T23" title="GLIB_001:th.23">GLIB_001:23</a></span>;<br/><span class="kw">hence </span><a NAME="E7:47_1_1_1_2_3_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="c16">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_3_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_3_2_1_4"/><span class="lab"><font color="Green" title="E69">A46</font></span>: 
( <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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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></span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c21">W</font> = <font color="Maroon" title="c16">Dn1W</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c19">u</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/><a NAME="E2:47_1_1_1_2_3_2_1_4"/>
( <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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_3_2_1_4"><span class="lab"><font color="Green" title="E69">A46</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:47_1_1_1_2_3_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T13" title="GLIB_001:th.13">GLIB_001:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:47_1_1_1_2_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="c16">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E33:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A47</font></span>: 
<font color="Maroon" title="c16">Dn1W</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#D1" title="GLIB_002:def.1">GLIB_002:def 1</a></span>;<br/><a NAME="E34:47_1_1_1_2"/><span class="lab"><font color="Green" title="E69">A48</font></span>: 
 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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:47_1"><span class="lab"><font color="Green" title="E41">A9</font></span></a>, <a class="txt" href="#E6:47_1_1_1_2"><span class="lab"><font color="Green" title="E52">A20</font></span></a>, <a class="ref" href="glib_000.html#T31" title="GLIB_000:th.31">GLIB_000:31</a></span>;<br/><a NAME="E35:47_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">Dn1W</font> <a href="glib_000.html#K17" title="GLIB_000:func.17">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"> the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="glib_000.html#K17" title="GLIB_000:func.17">.size()</a></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1"><span class="lab"><font color="Green" title="E42">A10</font></span></a>, <a class="txt" href="#E15:47_1_1_1_2"><span class="lab"><font color="Green" title="E59">A27</font></span></a>, <a class="ref" href="card_2.html#T41" title="CARD_2:th.41">CARD_2:41</a></span>;<br/><a NAME="E36:47_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">Dn1W</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">Dn1W</font> <a href="glib_000.html#K17" title="GLIB_000:func.17">.size()</a></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1"><span class="lab"><font color="Green" title="E46">A14</font></span></a>, <a class="txt" href="#E4:47_1"><span class="lab"><font color="Green" title="E39">A7</font></span></a>, <a class="txt" href="#E13:47_1_1_1_2"><span class="lab"><font color="Green" title="E58">A26</font></span></a>, <a class="txt" href="#E7:47_1_1_1_2"><span class="lab"><font color="Green" title="E53">A21</font></span></a>, <a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></span>;<br/><a NAME="E37:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A49</font></span>: 
<font color="Maroon" title="c16">Dn1W</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:47_1_1_1_2"><span class="lab"><font color="Green" title="E68">A47</font></span></a>, <a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_4"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c19">WT</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> <span class="kw"> such that </span><br/><a NAME="E2:47_1_1_1_2_4"/><span class="lab"><font color="Green" title="E71">A50</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:47_1_1_1_2_4"/><span class="lab"><font color="Green" title="E72">A51</font></span>: 
 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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="txt" href="#E3:47_1"><span class="lab"><font color="Green" title="E38">A6</font></span></a>, <a class="txt" href="#E8:47_1_1_1_2"><span class="lab"><font color="Green" title="E54">A22</font></span></a>, <a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c20">WT9</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="c16">Dn1W</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:47_1_1_1_2"><span class="lab"><font color="Green" title="E67">A38</font></span></a>, <a class="ref" href="glib_001.html#T175" title="GLIB_001:th.175">GLIB_001:175</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c21">W2</font> = <font color="Maroon" title="c20">WT9</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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E5:47_1_1_1_2_4"/><span class="lab"><font color="Green" title="E73">A52</font></span>: 
<font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_1_1_2_4"><span class="lab"><font color="Green" title="E71">A50</font></span></a>, <a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">W2</font> = <font color="Maroon" title="c20">WT9</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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c16">Dn1W</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:47_1_1_1_2"><span class="lab"><font color="Green" title="E62">A32</font></span></a>, <a class="ref" href="glib_001.html#T123" title="GLIB_001:th.123">GLIB_001:123</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_4_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:47_1_1_1_2_4_1"/>
<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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E2:47_1_1_1_2_4_1"/>
<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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:47_1_1_1_2"><span class="lab"><font color="Green" title="E58">A26</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c16">Dn1W</font> &amp;  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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">WT9</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; ( <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  or  not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>  ) &amp; (  for <font color="Olive" title="b1">n</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>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">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">WT9</font> holds <br/><font color="Maroon" title="c20">WT9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> ) )</span><br/><span class="kw">thus </span><a NAME="E3:47_1_1_1_2_4_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c16">Dn1W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:47_1_1_1_2"><span class="lab"><font color="Green" title="E63">A33</font></span></a>, <a class="txt" href="#E5:47_1_1_1_2_4"><span class="lab"><font color="Green" title="E73">A52</font></span></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">WT9</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  &amp; ( <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  or  not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>  ) &amp; (  for <font color="Olive" title="b1">n</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>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">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">WT9</font> holds <br/><font color="Maroon" title="c20">WT9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> ) )</span><br/><a NAME="E4:47_1_1_1_2_4_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a>  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  &amp; <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">WT9</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="txt" href="#E6:47_1"><span class="lab"><font color="Green" title="E41">A9</font></span></a>, <a class="txt" href="#E34:47_1_1_1_2"><span class="lab"><font color="Green" title="E69">A48</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a>, <a class="ref" href="glib_001.html#T110" title="GLIB_001:th.110">GLIB_001:110</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_1_1_1_2_4_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">WT9</font> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  or  not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>  ) &amp; (  for <font color="Olive" title="b1">n</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>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">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">WT9</font> holds <br/><font color="Maroon" title="c20">WT9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> ) )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_4_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:47_1_1_1_2_4_1_1"/><span class="lab"><font color="Green" title="E74">A53</font></span>: 
 not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_4_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:47_1_1_1_2_4_1_1_1"/>
<font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:47_1_1_1_2_4_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V8" title="GLIB_001:attr.8">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_4_1_1"><span class="lab"><font color="Green" title="E74">A53</font></span></a>, <a class="ref" href="glib_001.html#D31" title="GLIB_001:def.31">GLIB_001:def 31</a></span>;<br/><span class="kw">hence </span><a NAME="E3:47_1_1_1_2_4_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:47_1_1_1_2"><span class="lab"><font color="Green" title="E70">A49</font></span></a>, <a class="ref" href="glib_002.html#D2" title="GLIB_002:def.2">GLIB_002:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:47_1_1_1_2_4_1_1"/>
 not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:47_1_1_1_2_4_1"/>
( <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a>  or  not <font color="Maroon" title="c20">WT9</font> is  <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</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>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">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">WT9</font> holds <br/><font color="Maroon" title="c20">WT9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><br/><span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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">WT9</font> implies <font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E8:47_1_1_1_2_4_1"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c23">n</font>
 <span class="kw">and </span><br/><a NAME="E9:47_1_1_1_2_4_1"/><span class="lab"><font color="Green" title="E74">A54</font></span>: 
<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">WT9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span><br/><a NAME="E10:47_1_1_1_2_4_1"/>
<font color="Maroon" title="c20">WT9</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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T98" title="GLIB_001:th.98">GLIB_001:98</a></span>;<br/><a NAME="E11:47_1_1_1_2_4_1"/><span class="kw">then </span>
 not <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">WT9</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1"><span class="lab"><font color="Green" title="E44">A12</font></span></a>, <a class="txt" href="#E4:47_1_1_1_2"><span class="lab"><font color="Green" title="E50">A18</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E12:47_1_1_1_2_4_1"/>
<font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2_4_1"><span class="lab"><font color="Green" title="E74">A54</font></span></a>, <a class="ref" href="glib_001.html#T87" title="GLIB_001:th.87">GLIB_001:87</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">reconsider </span><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="c16">Dn1W</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T150" title="GLIB_001:th.150">GLIB_001:150</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c24">W2</font> = <font color="Maroon" title="c23">W2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> &amp; <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E9:47_1_1_1_2_4"/>
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:47_1_1_1_2"><span class="lab"><font color="Green" title="E63">A33</font></span></a>, <a class="txt" href="#E5:47_1_1_1_2_4"><span class="lab"><font color="Green" title="E73">A52</font></span></a>, <a class="ref" href="glib_001.html#T66" title="GLIB_001:th.66">GLIB_001:66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_4_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:47_1_1_1_2_4_2"/>
( <font color="Maroon" title="c20">WT9</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> &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="c16">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:47_1_1_1_2"><span class="lab"><font color="Green" title="E62">A32</font></span></a>, <a class="txt" href="#E5:47_1_1_1_2_4"><span class="lab"><font color="Green" title="E73">A52</font></span></a>, <a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>;<br/><span class="kw">hence </span><a NAME="E2:47_1_1_1_2_4_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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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">WT9</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a></span>)</span> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:47_1_1_1_2"><span class="lab"><font color="Green" title="E61">A31</font></span></a>, <a class="ref" href="glib_000.html#T61" title="GLIB_000:th.61">GLIB_000:61</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c16">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Maroon" title="c20">WT9</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"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> )</span><br/><span class="kw">reconsider </span><font color="Maroon" title="c25">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T175" title="GLIB_001:th.175">GLIB_001:175</a></span>;<br/><a NAME="E4:47_1_1_1_2_4_2"/><span class="lab"><font color="Green" title="E74">A55</font></span>: 
<font color="Maroon" title="c25">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_1_1_2_4"><span class="lab"><font color="Green" title="E71">A50</font></span></a>, <a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></span>;<br/><a NAME="E5:47_1_1_1_2_4_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="c16">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c16">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#D10" title="GLIB_003:def.10">GLIB_003:def 10</a></span>;<br/><span class="kw">hence </span><a NAME="E6:47_1_1_1_2_4_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="c1">G</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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c16">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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:47_1_1_1_2"><span class="lab"><font color="Green" title="E61">A31</font></span></a>, <a class="ref" href="funct_1.html#T49" title="FUNCT_1:th.49">FUNCT_1:49</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c20">WT9</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"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><br/><a NAME="E7:47_1_1_1_2_4_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="txt" href="#E8:47_1_1_1_2"><span class="lab"><font color="Green" title="E54">A22</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">WX</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E9:47_1_1_1_2_4_2"/><span class="lab"><font color="Green" title="E75">A56</font></span>: 
<font color="Maroon" title="c26">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E10:47_1_1_1_2_4_2"/><span class="lab"><font color="Green" title="E76">A57</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">WX</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E74">A55</font></span></a>, <a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></span>;<br/><a NAME="E11:47_1_1_1_2_4_2"/>
<font color="Maroon" title="c26">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E75">A56</font></span></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></span>;<br/><a NAME="E12:47_1_1_1_2_4_2"/><span class="kw">then </span>
<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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1_1_2_4"><span class="lab"><font color="Green" title="E72">A51</font></span></a>, <a class="txt" href="#E10:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E76">A57</font></span></a></span>;<br/><a NAME="E13:47_1_1_1_2_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A58</font></span>: 
<font color="Maroon" title="c20">WT9</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:47_1_1_1_2"><span class="lab"><font color="Green" title="E66">A37</font></span></a>, <a class="ref" href="glib_003.html#T27" title="GLIB_003:th.27">GLIB_003:27</a></span>;<br/><a NAME="E14:47_1_1_1_2_4_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c25">WTG</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E74">A55</font></span></a>, <a class="txt" href="#E9:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E75">A56</font></span></a>, <a class="txt" href="#E10:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E76">A57</font></span></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></span>;<br/><a NAME="E15:47_1_1_1_2_4_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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">WT9</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T27" title="GLIB_003:th.27">GLIB_003:27</a></span>;<br/><span class="kw">hence </span><a NAME="E16:47_1_1_1_2_4_2"/>
<font color="Maroon" title="c20">WT9</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"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:47_1_1_1_2_4_2"><span class="lab"><font color="Green" title="E77">A58</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E11:47_1_1_1_2_4"/>
<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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T25" title="GLIB_003:th.25">GLIB_003:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><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="c16">Dn1W</font><span class="kw"> such that </span><br/><a NAME="E40:47_1_1_1_2"/><span class="lab"><font color="Green" title="E71">A59</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E41:47_1_1_1_2"/><span class="lab"><font color="Green" title="E72">A60</font></span>: 
<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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T175" title="GLIB_001:th.175">GLIB_001:175</a></span>;<br/><a NAME="E43:47_1_1_1_2"/><span class="lab"><font color="Green" title="E73">A61</font></span>: 
<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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:47_1_1_1_2"><span class="lab"><font color="Green" title="E71">A59</font></span></a>, <a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></span>;<br/><a NAME="E44:47_1_1_1_2"/><span class="lab"><font color="Green" title="E74">A62</font></span>: 
<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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:47_1_1_1_2"><span class="lab"><font color="Green" title="E72">A60</font></span></a>, <a class="ref" href="glib_003.html#T27" title="GLIB_003:th.27">GLIB_003:27</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_5"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c21">WB</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E2:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E75">A63</font></span>: 
<font color="Maroon" title="c21">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E76">A64</font></span>: 
<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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">WB</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:47_1_1_1_2"><span class="lab"><font color="Green" title="E73">A61</font></span></a>, <a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></span>;<br/><span class="kw">thus </span><a NAME="E4:47_1_1_1_2_5"/>
<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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:47_1_1_1_2"><span class="lab"><font color="Green" title="E73">A61</font></span></a>, <a class="txt" href="#E44:47_1_1_1_2"><span class="lab"><font color="Green" title="E74">A62</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E75">A63</font></span></a>, <a class="txt" href="#E3:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E76">A64</font></span></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><br/><a NAME="E5:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E77">A65</font></span>: 
<font color="Maroon" title="c21">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E75">A63</font></span></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">target9</font> = <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T18" title="GLIB_001:th.18">GLIB_001:18</a></span>;<br/><a NAME="E7:47_1_1_1_2_5"/>
( <font color="Maroon" title="c21">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="c21">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E77">A65</font></span></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><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> <span class="kw"> such that </span><br/><a NAME="E9:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E78">A66</font></span>: 
<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="c21">WB</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2
 <span class="kw">and </span><br/><a NAME="E10:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E79">A67</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c21">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="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">WB</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2"><span class="lab"><font color="Green" title="E51">A19</font></span></a>, <a class="ref" href="glib_001.html#T127" title="GLIB_001:th.127">GLIB_001:127</a>, <a class="ref" href="glib_001.html#T133" title="GLIB_001:th.133">GLIB_001:133</a></span>;<br/><a NAME="E11:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E80">A68</font></span>: 
<font color="Maroon" title="c23">lenWB2h</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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="c21">WB</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E78">A66</font></span></a>, <a class="ref" href="xreal_1.html#T15" title="XREAL_1:th.15">XREAL_1:15</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c24">sa</font> = <font color="Maroon" title="c21">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">lenWB2h</font>;<br/><span class="kw">set </span><font color="Maroon" title="c25">ea</font> = <font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c26">WA</font> = <font color="Maroon" title="c21">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (1,<font color="Maroon" title="c23">lenWB2h</font>);<br/><a NAME="E12:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E81">A69</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c23">lenWB2h</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a></span>;<br/><span class="lab"><font color="Green" title="E82">A70</font></span>: <font color="Maroon" title="c21">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c21">WB</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D6" title="GLIB_001:def.6">GLIB_001:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c2">src</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E77">A65</font></span></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>
;<br/><a NAME="E14:47_1_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c21">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="c21">WB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c23">lenWB2h</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E81">A69</font></span></a>, <a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c27">sa</font> = <font color="Maroon" title="c21">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T18" title="GLIB_001:th.18">GLIB_001:18</a></span>;<br/><a NAME="E16:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E83">A71</font></span>: 
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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="c21">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#K2" title="NAT_1:func.2">+</a> 2</span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="ref" href="glib_001.html#T122" title="GLIB_001:th.122">GLIB_001:122</a></span>;<br/><a NAME="E17:47_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A72</font></span>: 
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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="c21">WB</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> ,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E78">A66</font></span></a>, <a class="ref" href="glib_001.html#D7" title="GLIB_001:def.7">GLIB_001:def 7</a></span>;<br/><a NAME="E18:47_1_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E77">A65</font></span></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>;<br/><a NAME="E19:47_1_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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="c22">target9</font>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T16" title="GLIB_000:th.16">GLIB_000:16</a></span>;<br/><a NAME="E20:47_1_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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#K28" title="GLIB_000:func.28">.edgesInOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T62" title="GLIB_000:th.62">GLIB_000:62</a></span>;<br/><a NAME="E21:47_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A73</font></span>: 
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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="c21">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#K28" title="GLIB_000:func.28">.edgesInOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E81">A69</font></span></a>, <a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><a NAME="E22:47_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A74</font></span>: 
<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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c21">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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E76">A64</font></span></a>, <a class="txt" href="#E10:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E79">A67</font></span></a>, <a class="ref" href="glib_003.html#T25" title="GLIB_003:th.25">GLIB_003:25</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">WA</font> = <font color="Maroon" title="c21">WB</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (1,<font color="Maroon" title="c23">lenWB2h</font>) as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font> ;<br/><a NAME="E24:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E87">A75</font></span>: 
<font color="Maroon" title="c28">WA</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E81">A69</font></span></a>, <a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="txt" href="#E13:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E82">A70</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><a NAME="E25:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E88">A76</font></span>: 
<font color="Maroon" title="c28">WA</font> <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E81">A69</font></span></a>, <a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><a NAME="E26:47_1_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A77</font></span>: 
<font color="Maroon" title="c28">WA</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E75">A63</font></span></a>, <a class="txt" href="#E24:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E87">A75</font></span></a>, <a class="ref" href="glib_004.html#T12" target="_self" title="GLIB_004:th.12">Th12</a></span>;<br/><a NAME="E27:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E90">A78</font></span>: 
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E77">A65</font></span></a>, <a class="txt" href="#E17:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E84">A72</font></span></a>, <a class="ref" href="glib_001.html#D23" title="GLIB_001:def.23">GLIB_001:def 23</a></span>;<br/><a NAME="E28:47_1_1_1_2_5"/><span class="lab"><font color="Green" title="E91">A79</font></span>: 
<font color="Maroon" title="c28">WA</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="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>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E75">A63</font></span></a>, <a class="txt" href="#E24:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E87">A75</font></span></a>, <a class="txt" href="#E25:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E88">A76</font></span></a>, <a class="ref" href="glib_004.html#T12" target="_self" title="GLIB_004:th.12">Th12</a>, <a class="ref" href="glib_004.html#T14" target="_self" title="GLIB_004:th.14">Th14</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_5_2"><span class="kw">now </span></a><div class="add"><span class="kw">defpred </span><font color="Maroon">S<sub>2</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span>(  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> <font color="Maroon" title="c28">WA</font> &amp;  not <font color="Maroon" title="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> );<br/><a NAME="E1:47_1_1_1_2_5_2"/><span class="lab"><font color="Green" title="E92">A80</font></span>: 
<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"><font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">sa</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E83">A71</font></span></a>, <a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><span class="kw">assume </span><a NAME="E2:47_1_1_1_2_5_2"/><span class="lab"><font color="Green" title="E93">A81</font></span>: 
<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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div><span class="lab"><font color="Green" title="E94">A82</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_5_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E95">A83</font></span>: 
 not <font color="Maroon" title="c27">sa</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><font color="Maroon" title="c27">sa</font> = 
<font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E81">A69</font></span></a>, <a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>
<br/>.= 
<font color="Maroon" title="c28">WA</font> <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> <font color="Maroon" title="c28">WA</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D7" title="GLIB_001:def.7">GLIB_001:def 7</a></span>
;<br/><a NAME="E3:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A84</font></span>: 
 ex <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E95">A83</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c29">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E5:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E97">A85</font></span>: 
( <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="nat_1.html#NM1" title="NAT_1:NM.1">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> ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="#E3:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E96">A84</font></span></a>);<br/></span><span class="kw">reconsider </span><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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><a NAME="E7:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E98">A86</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a></span>;<br/><font color="Maroon" title="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 = 
<font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D6" title="GLIB_001:def.6">GLIB_001:def 6</a></span>
<br/>.= 
<font color="Maroon" title="c2">src</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E81">A69</font></span></a>, <a class="txt" href="#E11:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E80">A68</font></span></a>, <a class="txt" href="#E13:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E82">A70</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>
;<br/><a NAME="E9:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c30">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1"><span class="lab"><font color="Green" title="E40">A8</font></span></a>, <a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a></span>;<br/><a NAME="E10:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c30">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E98">A86</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E11:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c30">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/><a NAME="E12:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c31">k2a</font> = <font color="Maroon" title="c30">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T5" title="INT_1:th.5">INT_1:5</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c32">sk</font> = <font color="Maroon" title="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c31">k2a</font>;<br/><span class="kw">set </span><font color="Maroon" title="c33">ek</font> = <font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c34">tk</font> = <font color="Maroon" title="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c30">k</font>;<br/><a NAME="E14:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E99">A87</font></span>: 
<font color="Maroon" title="c31">k2a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&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="c28">WA</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="ref" href="xreal_1.html#T15" title="XREAL_1:th.15">XREAL_1:15</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c35">WKA</font> = <font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (1,<font color="Maroon" title="c30">k</font>);<br/><span class="kw">set </span><font color="Maroon" title="c36">WKB</font> = <font color="Maroon" title="c28">WA</font> <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> <font color="Maroon" title="c28">WA</font></span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c37">WK1</font> = <font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (1,<font color="Maroon" title="c31">k2a</font>);<br/><span class="kw">reconsider </span><font color="Maroon" title="c38">WK1</font> = <font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (1,<font color="Maroon" title="c31">k2a</font>), <font color="Maroon" title="c39">WKA</font> = <font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (1,<font color="Maroon" title="c30">k</font>), <font color="Maroon" title="c40">WKB</font> = <font color="Maroon" title="c28">WA</font> <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> <font color="Maroon" title="c28">WA</font></span>)</span>) as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font> ;<br/><a NAME="E16:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E100">A88</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c30">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A89</font></span>: <font color="Maroon" title="c39">WKA</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c40">WKB</font> = 
<font color="Maroon" title="c28">WA</font> <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> <font color="Maroon" title="c28">WA</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>
<br/>.= 
<font color="Maroon" title="c28">WA</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T39" title="GLIB_001:th.39">GLIB_001:39</a></span>
;<br/><a NAME="E18:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E102">A90</font></span>: 
<font color="Maroon" title="c31">k2a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c30">k</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T15" title="XREAL_1:th.15">XREAL_1:15</a></span>;<br/><a NAME="E19:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A91</font></span>: 
<font color="Maroon" title="c28">WA</font> <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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="txt" href="#E14:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E99">A87</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c41">sk</font> = <font color="Maroon" title="c28">WA</font> <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> ;<br/><a NAME="E21:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E104">A92</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c31">k2a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a></span>;<br/><a NAME="E22:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A93</font></span>: 
<font color="Maroon" title="c38">WK1</font> <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="c41">sk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E99">A87</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><a NAME="E23:47_1_1_1_2_5_2_1"/>
<font color="Maroon" title="c38">WK1</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="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E104">A92</font></span></a>, <a class="txt" href="#E14:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E99">A87</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><a NAME="E24:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c38">WK1</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1,<font color="Maroon" title="c41">sk</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E89">A77</font></span></a>, <a class="txt" href="#E22:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E105">A93</font></span></a>, <a class="ref" href="glib_004.html#T12" target="_self" title="GLIB_004:th.12">Th12</a></span>;<br/><a NAME="E25:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c38">WK1</font> <a href="glib_004.html#R2" title="GLIB_004:pred.2">is_mincost_DPath_from</a> <font color="Maroon" title="c28">WA</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> ,<font color="Maroon" title="c41">sk</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D6" title="GLIB_001:def.6">GLIB_001:def 6</a></span>;<br/><a NAME="E26:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<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="c41">sk</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">WK1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E87">A75</font></span></a>, <a class="ref" href="glib_004.html#T14" target="_self" title="GLIB_004:th.14">Th14</a></span>;<br/><a NAME="E27:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A94</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c41">sk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c38">WK1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="txt" href="#E14:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E99">A87</font></span></a>, <a class="txt" href="#E18:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E102">A90</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c42">tk</font> = <font color="Maroon" title="c28">WA</font> <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="ref" href="glib_001.html#T7" title="GLIB_001:th.7">GLIB_001:7</a></span>;<br/><a NAME="E29:47_1_1_1_2_5_2_1"/><span class="lab"><font color="Green" title="E107">A95</font></span>: 
<font color="Maroon" title="c42">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> <font color="Maroon" title="c1">G</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E30:47_1_1_1_2_5_2_1"/>
<font color="Maroon" title="c42">tk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 ;<br/><a NAME="E31:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A96</font></span>: 
<font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="glib_000.html#R2" title="GLIB_000:pred.2">DJoins</a> <font color="Maroon" title="c41">sk</font>,<font color="Maroon" title="c42">tk</font>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E99">A87</font></span></a>, <a class="ref" href="glib_001.html#T122" title="GLIB_001:th.122">GLIB_001:122</a></span>;<br/><a NAME="E32:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A97</font></span>: 
<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"><font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c41">sk</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><font color="Maroon" title="c40">WKB</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  = 
<font color="Maroon" title="c28">WA</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c30">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a></span>
<br/>.= 
<font color="Maroon" title="c39">WKA</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E97">A85</font></span></a>, <a class="txt" href="#E16:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E100">A88</font></span></a>, <a class="ref" href="glib_001.html#T37" title="GLIB_001:th.37">GLIB_001:37</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>
;<br/><a NAME="E34:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A98</font></span>: 
<font color="Maroon" title="c28">WA</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"><font color="Maroon" title="c39">WKA</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c40">WKB</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E101">A89</font></span></a>, <a class="ref" href="glib_003.html#T24" title="GLIB_003:th.24">GLIB_003:24</a></span>;<br/><a NAME="E35:47_1_1_1_2_5_2_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c40">WKB</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T29" title="GLIB_003:th.29">GLIB_003:29</a></span>;<br/><a NAME="E36:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">A99</font></span>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c39">WKA</font> <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> <font color="Maroon" title="c28">WA</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E110">A98</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><a NAME="E37:47_1_1_1_2_5_2_1"/>
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E83">A71</font></span></a>, <a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><a NAME="E38:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A100</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</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#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="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T31" title="GLIB_003:th.31">GLIB_003:31</a></span>;<br/><a NAME="E39:47_1_1_1_2_5_2_1"/>
( <font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</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#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"><font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c42">tk</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E108">A96</font></span></a>, <a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><a NAME="E40:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="glib_000.html#R4" title="GLIB_000:pred.4">DSJoins</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E103">A91</font></span></a>, <a class="txt" href="#E32:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E109">A97</font></span></a>, <a class="txt" href="#E29:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E107">A95</font></span></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></span>;<br/><a NAME="E41:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A101</font></span>: 
<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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c38">WK1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2"><span class="lab"><font color="Green" title="E47">A15</font></span></a>, <a class="txt" href="#E32:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E109">A97</font></span></a>, <a class="txt" href="#E27:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E106">A94</font></span></a>, <a class="ref" href="glib_004.html#D7" target="_self" title="GLIB_004:def.7">Def7</a></span>;<br/><a NAME="E42:47_1_1_1_2_5_2_1"/>
( <font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</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"><font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c41">sk</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E108">A96</font></span></a>, <a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><a NAME="E43:47_1_1_1_2_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E114">A102</font></span>: 
<font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">sk</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T61" title="GLIB_000:th.61">GLIB_000:61</a></span>;<br/><a NAME="E44:47_1_1_1_2_5_2_1"/>
<font color="Maroon" title="c31">k2a</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c30">k</font>
 ;<br/><a NAME="E45:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c38">WK1</font> <a href="glib_001.html#K10" title="GLIB_001:func.10">.addEdge</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">WA</font> <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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c39">WKA</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E99">A87</font></span></a>, <a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a>, <a class="ref" href="glib_001.html#T41" title="GLIB_001:th.41">GLIB_001:41</a>, <a class="ref" href="jordan12.html#T2" title="JORDAN12:th.2">JORDAN12:2</a></span>;<br/><a NAME="E46:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c39">WKA</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E105">A93</font></span></a>, <a class="txt" href="#E41:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E113">A101</font></span></a>, <a class="txt" href="#E43:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E114">A102</font></span></a>, <a class="ref" href="glib_003.html#T25" title="GLIB_003:th.25">GLIB_003:25</a></span>;<br/><a NAME="E47:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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="c28">WA</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E111">A99</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E48:47_1_1_1_2_5_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">WA</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:47_1_1_1_2_5_2_1"><span class="lab"><font color="Green" title="E112">A100</font></span></a>, <a class="ref" href="xreal_1.html#T7" title="XREAL_1:th.7">XREAL_1:7</a></span>;<br/><span class="kw">hence </span><a NAME="E49:47_1_1_1_2_5_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E76">A64</font></span></a>, <a class="txt" href="#E10:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E79">A67</font></span></a>, <a class="txt" href="#E21:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E85">A73</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2_5_2"><span class="lab"><font color="Green" title="E93">A81</font></span></a>, <a class="ref" href="glib_003.html#T25" title="GLIB_003:th.25">GLIB_003:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:47_1_1_1_2_5_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A103</font></span>: 
<font color="Maroon" title="c28">WA</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"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c27">sa</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a>, <a class="txt" href="#E28:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E91">A79</font></span></a></span>;<br/><a NAME="E5:47_1_1_1_2_5_2"/>
( <font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</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#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"><font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E90">A78</font></span></a>, <a class="ref" href="glib_000.html#D14" title="GLIB_000:def.14">GLIB_000:def 14</a></span>;<br/><a NAME="E6:47_1_1_1_2_5_2"/><span class="kw">then </span>
<font color="Maroon" title="c21">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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="glib_000.html#R4" title="GLIB_000:pred.4">DSJoins</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<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> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>,<font color="Maroon" title="c1">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1_1_1_2"><span class="lab"><font color="Green" title="E50">A18</font></span></a>, <a class="txt" href="#E3:47_1_1_1_2_5_2"><span class="lab"><font color="Green" title="E94">A82</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_5_2"><span class="lab"><font color="Green" title="E92">A80</font></span></a>, <a class="ref" href="glib_000.html#D16" title="GLIB_000:def.16">GLIB_000:def 16</a></span>;<br/><span class="kw">hence </span><a NAME="E7:47_1_1_1_2_5_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2"><span class="lab"><font color="Green" title="E47">A15</font></span></a>, <a class="txt" href="#E22:47_1_1_1_2_5"><span class="lab"><font color="Green" title="E86">A74</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2_5_2"><span class="lab"><font color="Green" title="E93">A81</font></span></a>, <a class="txt" href="#E4:47_1_1_1_2_5_2"><span class="lab"><font color="Green" title="E95">A103</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_5_2"><span class="lab"><font color="Green" title="E92">A80</font></span></a>, <a class="ref" href="glib_004.html#D7" target="_self" title="GLIB_004:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E30:47_1_1_1_2_5"/>
<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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E46:47_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A104</font></span>: 
<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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_6"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c21">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c16">Dn1W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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="c21">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="c21">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>  ) )</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_6_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_6_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:47_1_1_1_2_6_1_1"/>
( <font color="Maroon" title="c21">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> or <font color="Maroon" title="c21">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:47_1_1_1_2"><span class="lab"><font color="Green" title="E58">A26</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_6_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_6_1_1_1"/>
<font color="Maroon" title="c21">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">W29</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c16">Dn1W</font> st <br/>( <font color="Olive" title="b1">W29</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="c21">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="c21">x</font> holds <br/><font color="Olive" title="b1">W29</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>  ) )</span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c22">x9</font> = <font color="Maroon" title="c21">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:47_1"><span class="lab"><font color="Green" title="E43">A11</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E3:47_1_1_1_2_6_1_1_1"/>
 the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="glib_004.html#R1" title="GLIB_004:pred.1">is_mincost_DTree_rooted_at</a> <font color="Maroon" title="c2">src</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">W2</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of  the   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> <span class="kw"> such that </span><br/><a NAME="E5:47_1_1_1_2_6_1_1_1"/><span class="lab"><font color="Green" title="E76">A105</font></span>: 
<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">x9</font>
 <span class="kw">and </span><br/><a NAME="E6:47_1_1_1_2_6_1_1_1"/><span class="lab"><font color="Green" title="E77">A106</font></span>: 
 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="c22">x9</font> holds <br/><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="Olive" title="b1">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">W29</font> = <font color="Maroon" title="c23">W2</font> as   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c16">Dn1W</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:47_1_1_1_2"><span class="lab"><font color="Green" title="E67">A38</font></span></a>, <a class="ref" href="glib_001.html#T175" title="GLIB_001:th.175">GLIB_001:175</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c25">W29</font> = <font color="Maroon" title="c24">W29</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c25">W29</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="c21">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="c21">x</font> holds <br/><font color="Maroon" title="c25">W29</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>  ) )</span><br/><span class="kw">thus </span><a NAME="E8:47_1_1_1_2_6_1_1_1"/>
<font color="Maroon" title="c25">W29</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="c21">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_1_1_1_2_6_1_1_1"><span class="lab"><font color="Green" title="E76">A105</font></span></a>, <a class="ref" href="glib_001.html#T19" title="GLIB_001:th.19">GLIB_001:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c21">x</font> holds <br/><font color="Maroon" title="c25">W29</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> </span><br/><span class="kw">let </span><font color="Maroon" title="c26">W1</font> be   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c26">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="c21">x</font> implies <font color="Maroon" title="c25">W29</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="c26">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )</span><br/><span class="kw">assume </span><a NAME="E9:47_1_1_1_2_6_1_1_1"/>
<font color="Maroon" title="c26">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="c21">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c25">W29</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="c26">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span><br/><a NAME="E10:47_1_1_1_2_6_1_1_1"/><span class="kw">then </span>
<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="c26">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:47_1_1_1_2_6_1_1_1"><span class="lab"><font color="Green" title="E77">A106</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E11:47_1_1_1_2_6_1_1_1"/>
<font color="Maroon" title="c25">W29</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="c26">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:47_1_1_1_2"><span class="lab"><font color="Green" title="E66">A37</font></span></a>, <a class="ref" href="glib_003.html#T27" title="GLIB_003:th.27">GLIB_003:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_6_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_6_1_1_2"/><span class="lab"><font color="Green" title="E76">A107</font></span>: 
<font color="Maroon" title="c21">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c16">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="c21">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="c21">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>  ) )</span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c22">W2</font> = <font color="Maroon" title="c19">W2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">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="c21">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="c21">x</font> holds <br/><font color="Maroon" title="c22">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>  ) )</span><br/><span class="kw">thus </span><a NAME="E2:47_1_1_1_2_6_1_1_2"/>
<font color="Maroon" title="c22">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="c21">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:47_1_1_1_2"><span class="lab"><font color="Green" title="E71">A59</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_6_1_1_2"><span class="lab"><font color="Green" title="E76">A107</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c21">x</font> holds <br/><font color="Maroon" title="c22">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> </span><br/><span class="kw">let </span><font color="Maroon" title="c23">W1</font> be   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c23">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="c21">x</font> implies <font color="Maroon" title="c22">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="c23">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )</span><br/><span class="kw">assume </span><a NAME="E3:47_1_1_1_2_6_1_1_2"/><span class="lab"><font color="Green" title="E77">A108</font></span>: 
<font color="Maroon" title="c23">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="c21">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c22">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="c23">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span><br/><a NAME="E4:47_1_1_1_2_6_1_1_2"/><span class="lab"><font color="Green" title="E78">A109</font></span>: 
<font color="Maroon" title="c21">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_6_1_1_2"><span class="lab"><font color="Green" title="E76">A107</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:47_1_1_1_2_6_1_1_2"/>
 ex <font color="Olive" title="b1">WX</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive" title="b1">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="c22">W2</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:47_1_1_1_2"><span class="lab"><font color="Green" title="E72">A60</font></span></a>, <a class="txt" href="#E43:47_1_1_1_2"><span class="lab"><font color="Green" title="E73">A61</font></span></a>, <a class="txt" href="#E46:47_1_1_1_2"><span class="lab"><font color="Green" title="E75">A104</font></span></a>, <a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></span>;<br/><span class="kw">hence </span><a NAME="E6:47_1_1_1_2_6_1_1_2"/>
<font color="Maroon" title="c22">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="c23">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_1_1_1_2_6_1_1_2"><span class="lab"><font color="Green" title="E78">A109</font></span></a>, <a class="txt" href="#E3:47_1_1_1_2_6_1_1_2"><span class="lab"><font color="Green" title="E77">A108</font></span></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E2:47_1_1_1_2_6"/>
 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="c16">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="c21">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="c21">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>  ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E48:47_1_1_1_2"/>
<font color="Maroon" title="c16">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:47_1_1_1_2"><span class="lab"><font color="Green" title="E70">A49</font></span></a>, <a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c21">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> implies <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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font> )</span><br/><span class="kw">assume </span><a NAME="E49:47_1_1_1_2"/><span class="lab"><font color="Green" title="E76">A110</font></span>: 
<font color="Maroon" title="c21">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1_2_7"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_7_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:47_1_1_1_2_7_1"/>
( <font color="Maroon" title="c21">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> or <font color="Maroon" title="c21">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1_1_1_2"><span class="lab"><font color="Green" title="E56">A24</font></span></a>, <a class="txt" href="#E49:47_1_1_1_2"><span class="lab"><font color="Green" title="E76">A110</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_7_1_1"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_7_1_1"/><span class="lab"><font color="Green" title="E77">A111</font></span>: 
<font color="Maroon" title="c21">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font></span><br/><div class="add"><a NAME="E2:47_1_1_1_2_7_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A112</font></span>: 
<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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_1"><span class="lab"><font color="Green" title="E37">A5</font></span></a></span>;<br/><a NAME="E3:47_1_1_1_2_7_1_1"/><span class="lab"><font color="Green" title="E79">A113</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2"><span class="lab"><font color="Green" title="E55">A23</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E4:47_1_1_1_2_7_1_1"/><span class="lab"><font color="Green" title="E80">A114</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/><a NAME="E5:47_1_1_1_2_7_1_1"/><span class="kw">then </span>
 not <font color="Maroon" title="c21">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:47_1_1_1_2"><span class="lab"><font color="Green" title="E52">A20</font></span></a>, <a class="txt" href="#E1:47_1_1_1_2_7_1_1"><span class="lab"><font color="Green" title="E77">A111</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:47_1_1_1_2_7_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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_1_1_1_2"><span class="lab"><font color="Green" title="E56">A24</font></span></a>, <a class="txt" href="#E49:47_1_1_1_2"><span class="lab"><font color="Green" title="E76">A110</font></span></a>, <a class="txt" href="#E2:47_1_1_1_2_7_1_1"><span class="lab"><font color="Green" title="E78">A112</font></span></a>, <a class="txt" href="#E3:47_1_1_1_2_7_1_1"><span class="lab"><font color="Green" title="E79">A113</font></span></a>, <a class="txt" href="#E4:47_1_1_1_2_7_1_1"><span class="lab"><font color="Green" title="E80">A114</font></span></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1_1_2_7_1_2"><span class="kw">suppose </span></a><a NAME="E1:47_1_1_1_2_7_1_2"/><span class="lab"><font color="Green" title="E77">A115</font></span>: 
<font color="Maroon" title="c21">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font></span><br/><div class="add"><a NAME="E2:47_1_1_1_2_7_1_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</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#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> &amp;  <a href="relset_1.html#K1" title="RELSET_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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:47_1_1_1_2"><span class="lab"><font color="Green" title="E55">A23</font></span></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E3:47_1_1_1_2_7_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A116</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</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> <font color="Maroon" title="c1">G</font></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#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_7_1_2"><span class="lab"><font color="Green" title="E77">A115</font></span></a>, <a class="ref" href="funct_4.html#T13" title="FUNCT_4:th.13">FUNCT_4:13</a></span>;<br/><a NAME="E4:47_1_1_1_2_7_1_2"/>
<font color="Maroon" title="c21">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> <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"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_004.html#K6" title="GLIB_004:func.6">DIJK:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_1_1_1_2_7_1_2"><span class="lab"><font color="Green" title="E77">A115</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_1_1_1_2_7_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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:47_1_1_1_2"><span class="lab"><font color="Green" title="E75">A104</font></span></a>, <a class="txt" href="#E3:47_1_1_1_2_7_1_2"><span class="lab"><font color="Green" title="E78">A116</font></span></a>, <a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E51:47_1_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="c21">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c21">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E13:47_1"/>
( <font color="Maroon" title="c16">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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E5:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A117</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
;<br/>
<a NAME="E6:47"/><span class="lab"><font color="Green" title="E37">A118</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">D0W</font> be   <a href="glib_003.html#NM15" title="GLIB_003:NM.15">inducedWSubgraph</a> of <font color="Maroon" title="c1">G</font>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">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> &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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font> ) )</span><br/><a NAME="E1:47_2"/><span class="lab"><font color="Green" title="E38">A119</font></span>: 
 <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#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/><a NAME="E2:47_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A120</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c5">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E37">A118</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E3:47_2"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c5">D0W</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T30" title="CARD_1:th.30">CARD_1:30</a></span>;<br/><a NAME="E4:47_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A121</font></span>: 
<font color="Maroon" title="c5">D0W</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D19" title="GLIB_000:def.19">GLIB_000:def 19</a></span>;<br/><div><span class="lab"><font color="Green" title="E41">A122</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c5">D0W</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">W2</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c5">D0W</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="c6">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="c6">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>  ) )</span><br/><span class="kw">set </span><font color="Maroon" title="c7">W2</font> = <font color="Maroon" title="c5">D0W</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c6">x</font>;<br/><span class="kw">take </span><font color="Maroon" title="c8">W2</font> = <font color="Maroon" title="c5">D0W</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c6">x</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c8">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="c6">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="c6">x</font> holds <br/><font color="Maroon" title="c8">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>  ) )</span><br/><a NAME="E1:47_2_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_2"><span class="lab"><font color="Green" title="E39">A120</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E2:47_2_1"/>
<font color="Maroon" title="c8">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="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T13" title="GLIB_001:th.13">GLIB_001:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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="c6">x</font> holds <br/><font color="Maroon" title="c8">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> </span><br/><span class="kw">let </span><font color="Maroon" title="c9">W1</font> be   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">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="c6">x</font> implies <font color="Maroon" title="c8">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="c9">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a>  )</span><br/><span class="kw">assume </span><a NAME="E3:47_2_1"/>
<font color="Maroon" title="c9">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="c6">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">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="c9">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> </span><br/><a NAME="E4:47_2_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T29" title="GLIB_003:th.29">GLIB_003:29</a></span>;<br/><span class="kw">hence </span><a NAME="E5:47_2_1"/>
<font color="Maroon" title="c8">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="c9">W1</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T21" title="GLIB_003:th.21">GLIB_003:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E6:47_2"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c5">D0W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E37">A118</font></span></a>, <a class="txt" href="#E1:47_2"><span class="lab"><font color="Green" title="E38">A119</font></span></a>, <a class="ref" href="glib_000.html#D37" title="GLIB_000:def.37">GLIB_000:def 37</a></span>;<br/><a NAME="E7:47_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">D0W</font> <a href="glib_000.html#K15" title="GLIB_000:func.15">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">D0W</font> <a href="glib_000.html#K17" title="GLIB_000:func.17">.size()</a></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47_2"><span class="lab"><font color="Green" title="E39">A120</font></span></a>, <a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a>, <a class="ref" href="card_1.html#T30" title="CARD_1:th.30">CARD_1:30</a></span>;<br/><a NAME="E8:47_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">D0W</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_2"><span class="lab"><font color="Green" title="E40">A121</font></span></a>, <a class="ref" href="glib_002.html#T47" title="GLIB_002:th.47">GLIB_002:47</a></span>;<br/><span class="kw">hence </span><a NAME="E9:47_2"/>
<font color="Maroon" title="c5">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:47_2"><span class="lab"><font color="Green" title="E41">A122</font></span></a>, <a class="ref" href="glib_004.html#D1" target="_self" title="GLIB_004:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> implies <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="c6">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">v</font> )</span><br/><span class="kw">assume </span><a NAME="E10:47_2"/><span class="lab"><font color="Green" title="E42">A123</font></span>: 
<font color="Maroon" title="c6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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="c6">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">v</font></span><br/><a NAME="E11:47_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A124</font></span>: 
<font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">src</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><div><span class="lab"><font color="Green" title="E44">A125</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">set </span><font color="Maroon" title="c7">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="c6">v</font>;<br/><a NAME="E1:47_2_2"/><span class="lab"><font color="Green" title="E45">A126</font></span>: 
<font color="Maroon" title="c1">G</font> <a href="glib_001.html#K1" title="GLIB_001:func.1">.walkOf</a> <font color="Maroon" title="c6">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="c6">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:47_2"><span class="lab"><font color="Green" title="E43">A124</font></span></a>, <a class="ref" href="glib_001.html#T13" title="GLIB_001:th.13">GLIB_001:13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">W</font> being   <a href="glib_001.html#NM8" title="GLIB_001:NM.8">DPath</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><br/><a NAME="E3:47_2_2"/><span class="lab"><font color="Green" title="E46">A127</font></span>: 
<font color="Maroon" title="c8">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="c6">v</font>
 <span class="kw">and </span><br/><a NAME="E4:47_2_2"/><span class="lab"><font color="Green" title="E47">A128</font></span>: 
<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="c6">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">W</font> <a href="glib_003.html#K10" title="GLIB_003:func.10">.cost()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D3" target="_self" title="GLIB_004:def.3">Def3</a></span>;<br/><a NAME="E5:47_2_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="c6">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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_003.html#T21" title="GLIB_003:th.21">GLIB_003:21</a></span>;<br/><a NAME="E6:47_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47_2_2"><span class="lab"><font color="Green" title="E45">A126</font></span></a>, <a class="txt" href="#E3:47_2_2"><span class="lab"><font color="Green" title="E46">A127</font></span></a>, <a class="ref" href="glib_004.html#D2" target="_self" title="GLIB_004:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:47_2_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="c6">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47_2_2"><span class="lab"><font color="Green" title="E47">A128</font></span></a>, <a class="ref" href="glib_003.html#T29" title="GLIB_003:th.29">GLIB_003:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E13:47_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></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>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="funcop_1.html#T72" title="FUNCOP_1:th.72">FUNCOP_1:72</a></span>;<br/><span class="kw">hence </span><a NAME="E14:47_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="c6">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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c6">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E10:47_2"><span class="lab"><font color="Green" title="E42">A123</font></span></a>, <a class="txt" href="#E12:47_2"><span class="lab"><font color="Green" title="E44">A125</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E8:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A129</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
;<br/>
<a NAME="E9:47"/>
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E8:47"><span class="lab"><font color="Green" title="E38">A129</font></span></a>, <a class="txt" href="#E5:47"><span class="lab"><font color="Green" title="E36">A117</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E10:47"/>
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">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>, <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</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>  <a href="relset_1.html#K1" title="RELSET_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_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> 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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K10" title="GLIB_004:func.10">DIJK:CompSeq</a> <font color="Maroon" title="c2">src</font></span>)</span> <a href="glib_004.html#K9" title="GLIB_004:func.9">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="glib_004.html#K5" title="GLIB_004:func.5">`1</a></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">v</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
