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<span class="kw">let </span><font color="Maroon" title="c1">G1</font> be   <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a>   <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-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="Red">::  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_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds  <font color="Olive" title="b2">G2</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><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_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> $1</span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> $1</span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds  <font color="Olive" title="b1">G2</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">G0</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">v</font> =  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</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">G1</font></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/><span class="kw">assume </span><a NAME="E1:65_1"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/><span class="kw">set </span><font color="Maroon" title="c5">Gn</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font>;<br/><span class="kw">set </span><font color="Maroon" title="c6">Gn1</font> = <span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c7">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c8">v1</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c9">v2</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>;<br/><a NAME="E2:65_1"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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#K14" title="GLIB_004:func.14">PRIM:Step</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D17" target="_self" title="GLIB_004:def.17">Def17</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">Gn1s</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">Gn1s</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><br/><a NAME="E1:65_1_1"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">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">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#T30" target="_self" title="GLIB_004:th.30">Th30</a></span>;<br/><a NAME="E2:65_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A4</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c10">Gn1s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><a NAME="E3:65_1_1"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c10">Gn1s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_1_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_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="E1:65_1_1_1_1"/>
(  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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>  &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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  ) or (  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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>  &amp; not <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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_1"/>
 <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">Gn1s</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><br/><div class="add"><a NAME="E2:65_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="glib_004.html#D15" target="_self" title="GLIB_004:def.15">Def15</a></span>;<br/><span class="kw">hence </span><a NAME="E3:65_1_1_1_1_1"/>
<font color="Maroon" title="c10">Gn1s</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="txt" href="#E1:65_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="65_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_2"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
(  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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>  &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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">Gn1s</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><br/><div class="add"><a NAME="E2:65_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A7</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</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"><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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="#E2:65_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="glib_004.html#D15" target="_self" title="GLIB_004:def.15">Def15</a></span>;<br/><a NAME="E3:65_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E4:65_1_1_1_1_2"/><span class="lab"><font color="Green" title="E52">A9</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A6</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">v1</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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">G1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></span>;<br/><a NAME="E6:65_1_1_1_1_2"/><span class="lab"><font color="Green" title="E53">A10</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c11">v1</font>,<font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="ref" href="glib_000.html#D15" title="GLIB_000:def.15">GLIB_000:def 15</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">Gns</font> being    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> ;<br/><a NAME="E8:65_1_1_1_1_2"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<font color="Maroon" title="c12">Gns</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="txt" href="#E1:65_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a></span>;<br/><a NAME="E9:65_1_1_1_1_2"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#T30" target="_self" title="GLIB_004:th.30">Th30</a></span>;<br/><a NAME="E10:65_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A13</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c12">Gns</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><a NAME="E11:65_1_1_1_1_2"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c11">v1</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="#E2:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E12:65_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A15</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c12">Gns</font> <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="c10">Gn1s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E10:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E13:65_1_1_1_1_2"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c12">Gns</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="#E9:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">Gns</font> = <font color="Maroon" title="c12">Gns</font> as    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E3:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="txt" href="#E12:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="ref" href="glib_000.html#T47" title="GLIB_000:th.47">GLIB_000:47</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c14">src</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c13">Gns</font>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c15">src9</font> = <font color="Maroon" title="c14">src</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T45" title="GLIB_000:th.45">GLIB_000:45</a></span>;<br/><a NAME="E17:65_1_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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="E18:65_1_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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="c10">Gn1s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E3:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A8</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="E19:65_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A16</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c11">v1</font>,<font color="Maroon" title="c10">Gn1s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="glib_000.html#T76" title="GLIB_000:th.76">GLIB_000:76</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c10">Gn1s</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1_1_2_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="E1:65_1_1_1_1_2_1_1_1"/>
( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">v1</font> or <font color="Maroon" title="c16">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">v1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1_1_2_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E60">A17</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">v1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c17">v29</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="c13">Gns</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="txt" href="#E9:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c18">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c13">Gns</font><span class="kw"> such that </span><br/><a NAME="E4:65_1_1_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E61">A18</font></span>: 
<font color="Maroon" title="c18">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c14">src</font>,<font color="Maroon" title="c17">v29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A11</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="c19">W</font> = <font color="Maroon" title="c18">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></span>;<br/><a NAME="E6:65_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c19">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c15">src9</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_1_1_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E61">A18</font></span></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></span>;<br/><a NAME="E7:65_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E59">A16</font></span></a>, <a class="txt" href="#E1:65_1_1_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E60">A17</font></span></a>, <a class="ref" href="glib_001.html#T67" title="GLIB_001:th.67">GLIB_001:67</a></span>;<br/><span class="kw">hence </span><a NAME="E8:65_1_1_1_1_2_1_1_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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="65_1_1_1_1_2_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">v1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font></span><br/><div class="add"><a NAME="E2:65_1_1_1_1_2_1_1_1_2"/><span class="kw">then </span>
not <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c11">v1</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="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">x9</font> = <font color="Maroon" title="c16">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c13">Gns</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E11:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="txt" href="#E10:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c18">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c13">Gns</font><span class="kw"> such that </span><br/><a NAME="E5:65_1_1_1_1_2_1_1_1_2"/><span class="lab"><font color="Green" title="E60">A19</font></span>: 
<font color="Maroon" title="c18">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c14">src</font>,<font color="Maroon" title="c17">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:65_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A11</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="c19">W9</font> = <font color="Maroon" title="c18">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></span>;<br/><a NAME="E7:65_1_1_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c19">W9</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65_1_1_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E60">A19</font></span></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></span>;<br/><span class="kw">hence </span><a NAME="E8:65_1_1_1_1_2_1_1_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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E2:65_1_1_1_1_2_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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E21:65_1_1_1_1_2"/>
<font color="Maroon" title="c10">Gn1s</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#T6" title="GLIB_002:th.6">GLIB_002:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="65_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E49">A20</font></span>: 
(  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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>  &amp; not <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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">Gn1s</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><br/><div class="add"><a NAME="E2:65_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A21</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</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"><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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="#E2:65_1"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="glib_004.html#D15" target="_self" title="GLIB_004:def.15">Def15</a></span>;<br/><a NAME="E3:65_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A22</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E4:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E52">A23</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span> <a href="glib_000.html#R3" title="GLIB_000:pred.3">SJoins</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</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">G1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E49">A20</font></span></a>, <a class="ref" href="glib_004.html#D13" target="_self" title="GLIB_004:def.13">Def13</a></span>;<br/><a NAME="E5:65_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A24</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></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">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D17" title="GLIB_000:def.17">GLIB_000:def 17</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">v2</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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">G1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></span>;<br/><a NAME="E7:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E54">A25</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E53">A24</font></span></a>, <a class="ref" href="glib_000.html#D15" title="GLIB_000:def.15">GLIB_000:def 15</a></span>;<br/><a NAME="E8:65_1_1_1_1_3"/>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1">(<span class="default"><a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="E9:65_1_1_1_1_3"/><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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="c10">Gn1s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E3:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E51">A22</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="E10:65_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A26</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c11">v2</font>,<font color="Maroon" title="c10">Gn1s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E54">A25</font></span></a>, <a class="ref" href="glib_000.html#T76" title="GLIB_000:th.76">GLIB_000:76</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">Gns</font> being    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> ;<br/><a NAME="E12:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E56">A27</font></span>: 
<font color="Maroon" title="c12">Gns</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="txt" href="#E1:65_1"><span class="lab"><font color="Green" title="E44">A1</font></span></a></span>;<br/><a NAME="E13:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E57">A28</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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">G1</font> <a href="glib_000.html#K21" title="GLIB_000:func.21">.edgesBetween</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#T30" target="_self" title="GLIB_004:th.30">Th30</a></span>;<br/><a NAME="E14:65_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A29</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c12">Gns</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><a NAME="E15:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E59">A30</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`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#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c11">v2</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="#E2:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E50">A21</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E16:65_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A31</font></span>: 
 <a href="glib_000.html#K24" title="GLIB_000:func.24">the_Vertices_of</a> <font color="Maroon" title="c12">Gns</font> <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="c10">Gn1s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E14:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E58">A29</font></span></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E17:65_1_1_1_1_3"/>
 <a href="glib_000.html#K25" title="GLIB_000:func.25">the_Edges_of</a> <font color="Maroon" title="c12">Gns</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="#E13:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E57">A28</font></span></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">Gns</font> = <font color="Maroon" title="c12">Gns</font> as    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:65_1_1"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E3:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E51">A22</font></span></a>, <a class="txt" href="#E16:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E60">A31</font></span></a>, <a class="ref" href="glib_000.html#T47" title="GLIB_000:th.47">GLIB_000:47</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c14">src</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c13">Gns</font>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c15">src9</font> = <font color="Maroon" title="c14">src</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T45" title="GLIB_000:th.45">GLIB_000:45</a></span>;<br/><a NAME="E21:65_1_1_1_1_3"/><span class="lab"><font color="Green" title="E61">A32</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E49">A20</font></span></a>, <a class="txt" href="#E4:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E52">A23</font></span></a>, <a class="ref" href="glib_000.html#D17" title="GLIB_000:def.17">GLIB_000:def 17</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_1_1_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c16">x</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c10">Gn1s</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_1_1_1_1_3_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1_1_3_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="E1:65_1_1_1_1_3_1_1_1"/>
( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">v2</font> or <font color="Maroon" title="c16">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">v2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="65_1_1_1_1_3_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_3_1_1_1_1"/><span class="lab"><font color="Green" title="E62">A33</font></span>: 
<font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">v2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c17">v19</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="c13">Gns</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E61">A32</font></span></a>, <a class="txt" href="#E13:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E57">A28</font></span></a>, <a class="ref" href="glib_000.html#D39" title="GLIB_000:def.39">GLIB_000:def 39</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c18">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c13">Gns</font><span class="kw"> such that </span><br/><a NAME="E4:65_1_1_1_1_3_1_1_1_1"/><span class="lab"><font color="Green" title="E63">A34</font></span>: 
<font color="Maroon" title="c18">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c14">src</font>,<font color="Maroon" title="c17">v19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E56">A27</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="c19">W</font> = <font color="Maroon" title="c18">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></span>;<br/><a NAME="E6:65_1_1_1_1_3_1_1_1_1"/>
<font color="Maroon" title="c19">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c15">src9</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">G1</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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_1_1_1_1_3_1_1_1_1"><span class="lab"><font color="Green" title="E63">A34</font></span></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></span>;<br/><a NAME="E7:65_1_1_1_1_3_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">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#K12" title="GLIB_004:func.12">PRIM:NextBestEdges</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Maroon" title="c4">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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E55">A26</font></span></a>, <a class="txt" href="#E1:65_1_1_1_1_3_1_1_1_1"><span class="lab"><font color="Green" title="E62">A33</font></span></a>, <a class="ref" href="glib_001.html#T67" title="GLIB_001:th.67">GLIB_001:67</a></span>;<br/><span class="kw">hence </span><a NAME="E8:65_1_1_1_1_3_1_1_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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="65_1_1_1_1_3_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:65_1_1_1_1_3_1_1_1_2"/>
<font color="Maroon" title="c16">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">v2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font></span><br/><div class="add"><a NAME="E2:65_1_1_1_1_3_1_1_1_2"/><span class="kw">then </span>
not <font color="Maroon" title="c16">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c11">v2</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="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">x9</font> = <font color="Maroon" title="c16">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c13">Gns</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E15:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E59">A30</font></span></a>, <a class="txt" href="#E14:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E58">A29</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c18">W</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c13">Gns</font><span class="kw"> such that </span><br/><a NAME="E5:65_1_1_1_1_3_1_1_1_2"/><span class="lab"><font color="Green" title="E62">A35</font></span>: 
<font color="Maroon" title="c18">W</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c14">src</font>,<font color="Maroon" title="c17">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:65_1_1_1_1_3"><span class="lab"><font color="Green" title="E56">A27</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="c19">W9</font> = <font color="Maroon" title="c18">W</font> as    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c10">Gn1s</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T168" title="GLIB_001:th.168">GLIB_001:168</a></span>;<br/><a NAME="E7:65_1_1_1_1_3_1_1_1_2"/>
<font color="Maroon" title="c19">W9</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65_1_1_1_1_3_1_1_1_2"><span class="lab"><font color="Green" title="E62">A35</font></span></a>, <a class="ref" href="glib_001.html#T20" title="GLIB_001:th.20">GLIB_001:20</a></span>;<br/><span class="kw">hence </span><a NAME="E8:65_1_1_1_1_3_1_1_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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E2:65_1_1_1_1_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="c10">Gn1s</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="c15">src9</font>,<font color="Maroon" title="c16">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E23:65_1_1_1_1_3"/>
<font color="Maroon" title="c10">Gn1s</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#T6" title="GLIB_002:th.6">GLIB_002:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E5:65_1_1"/>
<font color="Maroon" title="c10">Gn1s</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:65_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E2:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A36</font></span>: 
for <font color="Olive" title="b1">n</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">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="65_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">G</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">G</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><br/><a NAME="E1:65_2"/><span class="lab"><font color="Green" title="E45">A37</font></span>: 
<span class="p1">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</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#K13" title="GLIB_004:func.13">PRIM:Init</a> <font color="Maroon" title="c1">G1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_004.html#D17" target="_self" title="GLIB_004:def.17">Def17</a></span>;<br/><a NAME="E2:65_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span></span>)</span></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="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">G9</font> = <font color="Maroon" title="c4">G</font> as    <a href="glib_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</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_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G1</font></span>)</span></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:65_2"><span class="lab"><font color="Green" title="E45">A37</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/><a NAME="E4:65_2"/>
<font color="Maroon" title="c5">G9</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 ;<br/><span class="kw">hence </span><a NAME="E5:65_2"/>
<font color="Maroon" title="c4">G</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E4:65"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A38</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
;<br/>
<a NAME="E5:65"/>
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="#E4:65"><span class="lab"><font color="Green" title="E45">A38</font></span></a>, <a class="txt" href="#E2:65"><span class="lab"><font color="Green" title="E44">A36</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E6:65"/>
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_000.html#M2" title="GLIB_000:mode.2">inducedSubgraph</a> of <font color="Maroon" title="c1">G1</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_004.html#K16" title="GLIB_004:func.16">PRIM:CompSeq</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="glib_004.html#K15" title="GLIB_004:func.15">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  holds  <font color="Olive" title="b2">G2</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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