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

<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="helly.html#NM1" title="HELLY:NM.1">_Tree</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c5">P1</font>, <font color="Maroon" title="c6">P4</font> be   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c1">T</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c5">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c6">P4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>
 <b>and </b><br/><a NAME="E3:49"/><i><font color="Green" title="E42">A3</font></i>: 
not <font color="Maroon" title="c5">P1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P4</font>
 <b>and </b><br/><a NAME="E4:49"/><i><font color="Green" title="E43">A4</font></i>: 
not <font color="Maroon" title="c6">P4</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">P1</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c7">P2</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>;<br/>
<b>set </b><font color="Maroon" title="c8">P3</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>;<br/>
<div><i><font color="Green" title="E44">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_1"/>
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 ;<br/><a NAME="E2:49_1"/><b>then </b>
<font color="Maroon" title="c5">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="helly.html#T35" target="_self" title="HELLY:th.35">Th35</a></i>;<br/><b>hence </b><a NAME="E3:49_1"/>
contradiction
 <b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="helly.html#E4:49"><i><font color="Green" title="E43">A4</font></i></a>, <a class="ref" href="helly.html#T15" target="_self" title="HELLY:th.15">Th15</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E45">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_2"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 ;<br/><a NAME="E2:49_2"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 <b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="helly.html#T31" target="_self" title="HELLY:th.31">Th31</a></i>;<br/><a NAME="E3:49_2"/><b>then </b>
<font color="Maroon" title="c6">P4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span>
 <b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="helly.html#T35" target="_self" title="HELLY:th.35">Th35</a></i>;<br/><b>hence </b><a NAME="E4:49_2"/>
contradiction
 <b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="helly.html#E3:49"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="helly.html#T15" target="_self" title="HELLY:th.15">Th15</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:49"/><i><font color="Green" title="E46">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="helly.html#T31" target="_self" title="HELLY:th.31">Th31</a></i>;<br/>
<a NAME="E8:49"/>
<font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>;<br/>
<a NAME="E9:49"/><b>then </b><i><font color="Green" title="E47">A8</font></i>: 
<font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">i</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">i'</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span> as  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="helly.html#E9:49"><i><font color="Green" title="E47">A8</font></i></a>, <a class="ref" href="helly.html#T21" target="_self" title="HELLY:th.21">Th21</a></i>;<br/>
<a NAME="E11:49"/><i><font color="Green" title="E48">A9</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E12:49"/><i><font color="Green" title="E49">A10</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font>
 
<b>by </b><i><a class="txt" href="helly.html#E3:49"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="helly.html#E9:49"><i><font color="Green" title="E47">A8</font></i></a>, <a class="ref" href="helly.html#T22" target="_self" title="HELLY:th.22">Th22</a></i>;<br/>
<a NAME="E13:49"/><b>then </b><i><font color="Green" title="E50">A11</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font>
 
<b>by </b><i><a class="txt" href="helly.html#E11:49"><i><font color="Green" title="E48">A9</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E14:49"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font>
 
<b>by </b><i><a class="txt" href="helly.html#E4:49"><i><font color="Green" title="E43">A4</font></i></a>, <a class="txt" href="helly.html#E9:49"><i><font color="Green" title="E47">A8</font></i></a>, <a class="ref" href="helly.html#T22" target="_self" title="HELLY:th.22">Th22</a></i>;<br/>
<a NAME="E15:49"/><b>then </b><i><font color="Green" title="E51">A12</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font>
 
<b>by </b><i><a class="txt" href="helly.html#E11:49"><i><font color="Green" title="E48">A9</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c5">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i'</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">x</font> = <font color="Maroon" title="c5">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i'</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">T</font> <b>by </b><i><a class="txt" href="helly.html#E11:49"><i><font color="Green" title="E48">A9</font></i></a>, <a class="txt" href="helly.html#E12:49"><i><font color="Green" title="E49">A10</font></i></a>, <a class="ref" href="glib_001.html#T8" title="GLIB_001:th.8">GLIB_001:8</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">P1b</font> = <font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c14">P4c</font> = <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span>;<br/>
<a NAME="E17:49"/><i><font color="Green" title="E52">A13</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i'</font>
 
<b>by </b><i><a class="txt" href="helly.html#E13:49"><i><font color="Green" title="E50">A11</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/>
<i><font color="Green" title="E53">A14</font></i>: <font color="Maroon" title="c5">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span> = 
<font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 

<br/>.= 
<font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
;<br/>
<a NAME="E19:49"/><b>then </b><i><font color="Green" title="E54">A15</font></i>: 
<font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="helly.html#E13:49"><i><font color="Green" title="E50">A11</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/>
<a NAME="E20:49"/><i><font color="Green" title="E55">A16</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="helly.html#E13:49"><i><font color="Green" title="E50">A11</font></i></a>, <a class="txt" href="helly.html#E18:49"><i><font color="Green" title="E53">A14</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/>
<a NAME="E21:49"/><i><font color="Green" title="E56">A17</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">P4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">i'</font>
 
<b>by </b><i><a class="ref" href="helly.html#T7" target="_self" title="HELLY:th.7">Th7</a></i>;<br/>
<a NAME="E22:49"/><b>then </b><i><font color="Green" title="E57">A18</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="helly.html#E6:49"><i><font color="Green" title="E45">A6</font></i></a>, <a class="txt" href="helly.html#E7:49"><i><font color="Green" title="E46">A7</font></i></a>, <a class="txt" href="helly.html#E15:49"><i><font color="Green" title="E51">A12</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<a NAME="E23:49"/><i><font color="Green" title="E58">A19</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="helly.html#E5:49"><i><font color="Green" title="E44">A5</font></i></a>, <a class="txt" href="helly.html#E13:49"><i><font color="Green" title="E50">A11</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<font color="Maroon" title="c6">P4</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span> = 
<font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> 

<br/>.= 
<font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
;<br/>
<a NAME="E25:49"/><b>then </b><i><font color="Green" title="E59">A20</font></i>: 
<font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="helly.html#E15:49"><i><font color="Green" title="E51">A12</font></i></a>, <a class="txt" href="helly.html#E21:49"><i><font color="Green" title="E56">A17</font></i></a>, <a class="ref" href="glib_001.html#T38" title="GLIB_001:th.38">GLIB_001:38</a></i>;<br/>
<a NAME="E26:49"/><i><font color="Green" title="E60">A21</font></i>: 
<font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="helly.html#E19:49"><i><font color="Green" title="E54">A15</font></i></a>, <a class="ref" href="helly.html#D2" target="_self" title="HELLY:def.2">Def2</a></i>;<br/>
<a NAME="E27:49"/><i><font color="Green" title="E61">A22</font></i>: 
<font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="helly.html#E25:49"><i><font color="Green" title="E59">A20</font></i></a>, <a class="ref" href="helly.html#D2" target="_self" title="HELLY:def.2">Def2</a></i>;<br/>
<a NAME="E28:49"/><i><font color="Green" title="E62">A23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E15:49"><i><font color="Green" title="E51">A12</font></i></a>, <a class="ref" href="glib_001.html#T95" title="GLIB_001:th.95">GLIB_001:95</a></i>;<br/>
<b>set </b><font color="Maroon" title="c15">P1br</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> ;<br/>
<b>set </b><font color="Maroon" title="c16">Pbc</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span>;<br/>
<a NAME="E29:49"/><i><font color="Green" title="E63">A24</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x</font>
 
<b>by </b><i><a class="txt" href="helly.html#E17:49"><i><font color="Green" title="E52">A13</font></i></a>, <a class="ref" href="glib_001.html#T23" title="GLIB_001:th.23">GLIB_001:23</a></i>;<br/>
<a NAME="E30:49"/><i><font color="Green" title="E64">A25</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x</font>
 
<b>by </b><i><a class="txt" href="helly.html#E27:49"><i><font color="Green" title="E61">A22</font></i></a>, <a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>;<br/>
<a NAME="E31:49"/><i><font color="Green" title="E65">A26</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="helly.html#E20:49"><i><font color="Green" title="E55">A16</font></i></a>, <a class="ref" href="glib_001.html#T23" title="GLIB_001:th.23">GLIB_001:23</a></i>;<br/>
<a NAME="E32:49"/><i><font color="Green" title="E66">A27</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="helly.html#E27:49"><i><font color="Green" title="E61">A22</font></i></a>, <a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>;<br/>
<b>set </b><font color="Maroon" title="c17">j</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span>;<br/>
<a NAME="E33:49"/><i><font color="Green" title="E67">A28</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="helly.html#E30:49"><i><font color="Green" title="E64">A25</font></i></a>, <a class="ref" href="glib_001.html#T30" title="GLIB_001:th.30">GLIB_001:30</a></i>;<br/>
<a NAME="E34:49"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="chord.html#T2" title="CHORD:th.2">CHORD:2</a></i>;<br/>
<a NAME="E35:49"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E36:49"/><b>then </b><i><font color="Green" title="E68">A29</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x</font>
 
<b>by </b><i><a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="ref" href="glib_001.html#T33" title="GLIB_001:th.33">GLIB_001:33</a></i>;<br/>
<a NAME="E37:49"/><i><font color="Green" title="E69">A30</font></i>: 
not <span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a>  is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 
<b>by </b><i><a class="txt" href="helly.html#E22:49"><i><font color="Green" title="E57">A18</font></i></a>, <a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="helly.html#E31:49"><i><font color="Green" title="E65">A26</font></i></a>, <a class="ref" href="glib_001.html#D24" title="GLIB_001:def.24">GLIB_001:def 24</a></i>;<br/>
<a NAME="E38:49"/><i><font color="Green" title="E70">A31</font></i>: 
not <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span> is <a href="glib_001.html#V1" title="GLIB_001:attr.1">closed</a>
 
<b>by </b><i><a class="txt" href="helly.html#E23:49"><i><font color="Green" title="E58">A19</font></i></a>, <a class="txt" href="helly.html#E30:49"><i><font color="Green" title="E64">A25</font></i></a>, <a class="txt" href="helly.html#E32:49"><i><font color="Green" title="E66">A27</font></i></a>, <a class="ref" href="glib_001.html#D24" title="GLIB_001:def.24">GLIB_001:def 24</a></i>;<br/>
<a NAME="E39:49"/><i><font color="Green" title="E71">A32</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="ref" href="glib_001.html#T93" title="GLIB_001:th.93">GLIB_001:93</a></i>;<br/>
<a NAME="E40:49"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="helly.html#E3:49"><i><font color="Green" title="E42">A3</font></i></a>, <a class="txt" href="helly.html#E4:49"><i><font color="Green" title="E43">A4</font></i></a>, <a class="txt" href="helly.html#E26:49"><i><font color="Green" title="E60">A21</font></i></a>, <a class="txt" href="helly.html#E27:49"><i><font color="Green" title="E61">A22</font></i></a>, <a class="ref" href="helly.html#T39" target="_self" title="HELLY:th.39">Th39</a></i>;<br/>
<a NAME="E41:49"/><b>then </b><i><font color="Green" title="E72">A33</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p5">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="helly.html#E39:49"><i><font color="Green" title="E71">A32</font></i></a>, <a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a></i>;<br/>
<a NAME="E42:49"/><i><font color="Green" title="E73">A34</font></i>: 
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E6:49"><i><font color="Green" title="E45">A6</font></i></a>, <a class="txt" href="helly.html#E7:49"><i><font color="Green" title="E46">A7</font></i></a>, <a class="txt" href="helly.html#E28:49"><i><font color="Green" title="E62">A23</font></i></a>, <a class="txt" href="helly.html#E31:49"><i><font color="Green" title="E65">A26</font></i></a></i>;<br/>
<a NAME="E43:49"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:49_5"/>
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 ;<br/>

<a NAME="E2:49_5"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> </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> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c18">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:49_5"/><i><font color="Green" title="E74">A35</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E5:49_5"/><i><font color="Green" title="E75">A36</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E4:49_5"><i><font color="Green" title="E74">A35</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:49_5"/><i><font color="Green" title="E76">A37</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K14" title="GLIB_001:func.14">.edges()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E4:49_5"><i><font color="Green" title="E74">A35</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c19">v1br</font>, <font color="Maroon" title="c20">v2br</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c21">n</font> being  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E8:49_5"/><i><font color="Green" title="E77">A38</font></i>: 
<font color="Maroon" title="c21">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span>
 <b>and </b><br/><a NAME="E9:49_5"/><i><font color="Green" title="E78">A39</font></i>: 
<font color="Maroon" title="c19">v1br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">n</font>
 <b>and </b><br/><a NAME="E10:49_5"/>
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E11:49_5"/><i><font color="Green" title="E79">A40</font></i>: 
<font color="Maroon" title="c20">v2br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c21">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 <b>and </b><br/><a NAME="E12:49_5"/><i><font color="Green" title="E80">A41</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c19">v1br</font>,<font color="Maroon" title="c20">v2br</font>,<font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="helly.html#E5:49_5"><i><font color="Green" title="E75">A36</font></i></a>, <a class="ref" href="glib_001.html#T104" title="GLIB_001:th.104">GLIB_001:104</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c22">v1c</font>, <font color="Maroon" title="c23">v2c</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">T</font>, <font color="Maroon" title="c24">m</font> being  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E14:49_5"/><i><font color="Green" title="E81">A42</font></i>: 
<font color="Maroon" title="c24">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E15:49_5"/><i><font color="Green" title="E82">A43</font></i>: 
<font color="Maroon" title="c22">v1c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c24">m</font>
 <b>and </b><br/><a NAME="E16:49_5"/>
<font color="Maroon" title="c18">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E17:49_5"/><i><font color="Green" title="E83">A44</font></i>: 
<font color="Maroon" title="c23">v2c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c24">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 <b>and </b><br/><a NAME="E18:49_5"/><i><font color="Green" title="E84">A45</font></i>: 
<font color="Maroon" title="c18">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c22">v1c</font>,<font color="Maroon" title="c23">v2c</font>,<font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="txt" href="helly.html#E6:49_5"><i><font color="Green" title="E76">A37</font></i></a>, <a class="ref" href="glib_001.html#T104" title="GLIB_001:th.104">GLIB_001:104</a></i>;<br/>
<a NAME="E19:49_5"/><i><font color="Green" title="E85">A46</font></i>: 
( ( <font color="Maroon" title="c19">v1br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">v1c</font> &amp; <font color="Maroon" title="c20">v2br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">v2c</font> ) or ( <font color="Maroon" title="c19">v1br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">v2c</font> &amp; <font color="Maroon" title="c20">v2br</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">v1c</font> ) )
 
<b>by </b><i><a class="txt" href="helly.html#E12:49_5"><i><font color="Green" title="E80">A41</font></i></a>, <a class="txt" href="helly.html#E18:49_5"><i><font color="Green" title="E84">A45</font></i></a>, <a class="ref" href="glib_000.html#T18" title="GLIB_000:th.18">GLIB_000:18</a></i>;<br/>
<a NAME="E20:49_5"/>
<font color="Maroon" title="c21">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c21">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E21:49_5"/><b>then </b>
<font color="Maroon" title="c21">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E8:49_5"><i><font color="Green" title="E77">A38</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E22:49_5"/><b>then </b>
( <font color="Maroon" title="c19">v1br</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c20">v2br</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 
<b>by </b><i><a class="txt" href="helly.html#E8:49_5"><i><font color="Green" title="E77">A38</font></i></a>, <a class="txt" href="helly.html#E9:49_5"><i><font color="Green" title="E78">A39</font></i></a>, <a class="txt" href="helly.html#E11:49_5"><i><font color="Green" title="E79">A40</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<a NAME="E23:49_5"/><b>then </b><i><font color="Green" title="E86">A47</font></i>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c19">v1br</font>,<font color="Maroon" title="c20">v2br</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T38" title="ZFMISC_1:th.38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E24:49_5"/>
<font color="Maroon" title="c24">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c24">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/>
<a NAME="E25:49_5"/><b>then </b>
<font color="Maroon" title="c24">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E14:49_5"><i><font color="Green" title="E81">A42</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E26:49_5"/><b>then </b><i><font color="Green" title="E87">A48</font></i>: 
( <font color="Maroon" title="c22">v1c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c23">v2c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 
<b>by </b><i><a class="txt" href="helly.html#E14:49_5"><i><font color="Green" title="E81">A42</font></i></a>, <a class="txt" href="helly.html#E15:49_5"><i><font color="Green" title="E82">A43</font></i></a>, <a class="txt" href="helly.html#E17:49_5"><i><font color="Green" title="E83">A44</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<a NAME="E27:49_5"/><b>then </b>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c22">v1c</font>,<font color="Maroon" title="c23">v2c</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T38" title="ZFMISC_1:th.38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E28:49_5"/><b>then </b>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c22">v1c</font>,<font color="Maroon" title="c23">v2c</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p4">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E19:49_5"><i><font color="Green" title="E85">A46</font></i></a>, <a class="txt" href="helly.html#E23:49_5"><i><font color="Green" title="E86">A47</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/>
<a NAME="E29:49_5"/><b>then </b>
( ( <font color="Maroon" title="c22">v1c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> or <font color="Maroon" title="c22">v1c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x</font> ) &amp; ( <font color="Maroon" title="c23">v2c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> or <font color="Maroon" title="c23">v2c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x</font> ) )
 
<b>by </b><i><a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="helly.html#E31:49"><i><font color="Green" title="E65">A26</font></i></a>, <a class="txt" href="helly.html#E41:49"><i><font color="Green" title="E72">A33</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a>, <a class="ref" href="zfmisc_1.html#T28" title="ZFMISC_1:th.28">ZFMISC_1:28</a></i>;<br/>
<b>hence </b><a NAME="E30:49_5"/>
contradiction
 <b>by </b><i><a class="txt" href="helly.html#E6:49"><i><font color="Green" title="E45">A6</font></i></a>, <a class="txt" href="helly.html#E7:49"><i><font color="Green" title="E46">A7</font></i></a>, <a class="txt" href="helly.html#E28:49"><i><font color="Green" title="E62">A23</font></i></a>, <a class="txt" href="helly.html#E18:49_5"><i><font color="Green" title="E84">A45</font></i></a>, <a class="txt" href="helly.html#E26:49_5"><i><font color="Green" title="E87">A48</font></i></a>, <a class="ref" href="glib_000.html#T21" title="GLIB_000:th.21">GLIB_000:21</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E44:49"/><b>then </b><i><font color="Green" title="E74">A49</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> is   <a href="glib_001.html#NM5" title="GLIB_001:NM.5">Path</a> of <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="helly.html#E30:49"><i><font color="Green" title="E64">A25</font></i></a>, <a class="txt" href="helly.html#E37:49"><i><font color="Green" title="E69">A30</font></i></a>, <a class="txt" href="helly.html#E38:49"><i><font color="Green" title="E70">A31</font></i></a>, <a class="txt" href="helly.html#E41:49"><i><font color="Green" title="E72">A33</font></i></a>, <a class="txt" href="helly.html#E42:49"><i><font color="Green" title="E73">A34</font></i></a>, <a class="ref" href="helly.html#T17" target="_self" title="HELLY:th.17">Th17</a></i>;<br/>
<a NAME="E45:49"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="helly.html#E29:49"><i><font color="Green" title="E63">A24</font></i></a>, <a class="txt" href="helly.html#E30:49"><i><font color="Green" title="E64">A25</font></i></a>, <a class="txt" href="helly.html#E31:49"><i><font color="Green" title="E65">A26</font></i></a>, <a class="txt" href="helly.html#E32:49"><i><font color="Green" title="E66">A27</font></i></a>, <a class="ref" href="glib_001.html#T31" title="GLIB_001:th.31">GLIB_001:31</a></i>;<br/>
<a NAME="E46:49"/><b>then </b><i><font color="Green" title="E75">A50</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">P1</font></span>)</span></span>)</span> <a href="glib_001.html#K6" title="GLIB_001:func.6">.reverse()</a> </span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> <font color="Maroon" title="c10">i'</font>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">P4</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="helly.html#E44:49"><i><font color="Green" title="E74">A49</font></i></a>, <a class="ref" href="helly.html#D2" target="_self" title="HELLY:def.2">Def2</a></i>;<br/>
<a NAME="E47:49"/><i><font color="Green" title="E76">A51</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E13:49"><i><font color="Green" title="E50">A11</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<a NAME="E48:49"/><i><font color="Green" title="E77">A52</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">P4</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E15:49"><i><font color="Green" title="E51">A12</font></i></a>, <a class="txt" href="helly.html#E21:49"><i><font color="Green" title="E56">A17</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<a NAME="E49:49"/><i><font color="Green" title="E78">A53</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E33:49"><i><font color="Green" title="E67">A28</font></i></a>, <a class="txt" href="helly.html#E36:49"><i><font color="Green" title="E68">A29</font></i></a>, <a class="txt" href="helly.html#E46:49"><i><font color="Green" title="E75">A50</font></i></a>, <a class="ref" href="glib_001.html#T88" title="GLIB_001:th.88">GLIB_001:88</a></i>;<br/>
<a NAME="E50:49"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E47:49"><i><font color="Green" title="E76">A51</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E51:49"/><b>then </b>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E7:49"><i><font color="Green" title="E46">A7</font></i></a>, <a class="txt" href="helly.html#E48:49"><i><font color="Green" title="E77">A52</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E52:49"/><b>then </b><i><font color="Green" title="E79">A54</font></i>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E53:49"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:49_6"/><i><font color="Green" title="E80">A55</font></i>: 
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 ;<br/>

<a NAME="E2:49_6"/><b>then </b><i><font color="Green" title="E81">A56</font></i>: 
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:49_6"/><b>then </b><i><font color="Green" title="E82">A57</font></i>: 
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E4:49_6"/><i><font color="Green" title="E83">A58</font></i>: 
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E2:49_6"><i><font color="Green" title="E81">A56</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:49_6"/><i><font color="Green" title="E84">A59</font></i>: 
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="txt" href="helly.html#E1:49_6"><i><font color="Green" title="E80">A55</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c19">Pax</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font>;<br/>
<b>set </b><font color="Maroon" title="c20">Pxb</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font>;<br/>
<b>set </b><font color="Maroon" title="c21">Pbx</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font>;<br/>
<b>set </b><font color="Maroon" title="c22">Pxc</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font>;<br/>
<b>set </b><font color="Maroon" title="c23">Pcx</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font>;<br/>
<b>set </b><font color="Maroon" title="c24">Pxa</font> = <font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c2">a</font>;<br/>
<a NAME="E6:49_6"/><i><font color="Green" title="E85">A60</font></i>: 
<font color="Maroon" title="c5">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="helly.html#E47:49"><i><font color="Green" title="E76">A51</font></i></a>, <a class="ref" href="helly.html#T35" target="_self" title="HELLY:th.35">Th35</a></i>;<br/>
<a NAME="E7:49_6"/><i><font color="Green" title="E86">A61</font></i>: 
<font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E49:49"><i><font color="Green" title="E78">A53</font></i></a>, <a class="ref" href="helly.html#T35" target="_self" title="HELLY:th.35">Th35</a></i>;<br/>
<a NAME="E8:49_6"/><i><font color="Green" title="E87">A62</font></i>: 
<font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c2">a</font></span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E7:49"><i><font color="Green" title="E46">A7</font></i></a>, <a class="txt" href="helly.html#E48:49"><i><font color="Green" title="E77">A52</font></i></a>, <a class="ref" href="helly.html#T35" target="_self" title="HELLY:th.35">Th35</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  = 
<font color="Maroon" title="c12">x</font>
<b>by </b><i><a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<b>by </b><i><a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
;<br/>
<a NAME="E10:49_6"/><b>then </b>
<font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E6:49_6"><i><font color="Green" title="E85">A60</font></i></a>, <a class="ref" href="glib_001.html#T94" title="GLIB_001:th.94">GLIB_001:94</a></i>;<br/>
<a NAME="E11:49_6"/><b>then </b><i><font color="Green" title="E88">A63</font></i>: 
( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  or <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 
<b>by </b><i><a class="txt" href="helly.html#E3:49_6"><i><font color="Green" title="E82">A57</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  = 
<font color="Maroon" title="c12">x</font>
<b>by </b><i><a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<b>by </b><i><a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
;<br/>
<a NAME="E13:49_6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E7:49_6"><i><font color="Green" title="E86">A61</font></i></a>, <a class="ref" href="glib_001.html#T94" title="GLIB_001:th.94">GLIB_001:94</a></i>;<br/>
<a NAME="E14:49_6"/><b>then </b><i><font color="Green" title="E89">A64</font></i>: 
( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  or <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 
<b>by </b><i><a class="txt" href="helly.html#E4:49_6"><i><font color="Green" title="E83">A58</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  = 
<font color="Maroon" title="c12">x</font>
<b>by </b><i><a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a> 
<b>by </b><i><a class="ref" href="helly.html#T27" target="_self" title="HELLY:th.27">Th27</a></i>
;<br/>
<a NAME="E16:49_6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="helly.html#E8:49_6"><i><font color="Green" title="E87">A62</font></i></a>, <a class="ref" href="glib_001.html#T94" title="GLIB_001:th.94">GLIB_001:94</a></i>;<br/>
<a NAME="E17:49_6"/><b>then </b><i><font color="Green" title="E90">A65</font></i>: 
( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  or <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 
<b>by </b><i><a class="txt" href="helly.html#E5:49_6"><i><font color="Green" title="E84">A59</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E18:49_6"/><i><font color="Green" title="E91">A66</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="ref" href="helly.html#T31" target="_self" title="HELLY:th.31">Th31</a></i>;<br/>
<a NAME="E19:49_6"/><i><font color="Green" title="E92">A67</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> 
 
<b>by </b><i><a class="ref" href="helly.html#T31" target="_self" title="HELLY:th.31">Th31</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_6_4"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_6_4"/>
( ( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  ) or ( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  ) or ( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  ) )
 </span><b>by </b><i><a class="txt" href="helly.html#E11:49_6"><i><font color="Green" title="E88">A63</font></i></a>, <a class="txt" href="helly.html#E14:49_6"><i><font color="Green" title="E89">A64</font></i></a>, <a class="txt" href="helly.html#E17:49_6"><i><font color="Green" title="E90">A65</font></i></a>, <a class="ref" href="helly.html#T31" target="_self" title="HELLY:th.31">Th31</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_6_4_1"><b>suppose </b></a><a NAME="E1:49_6_4_1"/>
( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 ;<br/><div class="add"><a NAME="E2:49_6_4_1"/><b>then </b>
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="helly.html#E18:49_6"><i><font color="Green" title="E91">A66</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:49_6_4_1"/>
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="helly.html#E1:49"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="helly.html#E47:49"><i><font color="Green" title="E76">A51</font></i></a>, <a class="ref" href="helly.html#T38" target="_self" title="HELLY:th.38">Th38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_6_4_2"><b>suppose </b></a><a NAME="E1:49_6_4_2"/>
( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 ;<br/><div class="add"><a NAME="E2:49_6_4_2"/><b>then </b>
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="helly.html#E19:49_6"><i><font color="Green" title="E92">A67</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:49_6_4_2"/>
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="helly.html#E2:49"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="helly.html#E48:49"><i><font color="Green" title="E77">A52</font></i></a>, <a class="ref" href="helly.html#T38" target="_self" title="HELLY:th.38">Th38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_6_4_3"><b>suppose </b></a><a NAME="E1:49_6_4_3"/>
( <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  &amp; <font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a>  )
 ;<br/><div class="add"><a NAME="E2:49_6_4_3"/><b>then </b>
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">x</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c12">x</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span>
 <b>by </b><i><a class="txt" href="helly.html#E19:49_6"><i><font color="Green" title="E92">A67</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:49_6_4_3"/>
<font color="Maroon" title="c18">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c12">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="helly.html#E49:49"><i><font color="Green" title="E78">A53</font></i></a>, <a class="ref" href="helly.html#T38" target="_self" title="HELLY:th.38">Th38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E54:49"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="helly.html#K2" title="HELLY:func.2">.pathBetween</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span>)</span> <a href="glib_001.html#K13" title="GLIB_001:func.13">.vertices()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">P1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="helly.html#K1" title="HELLY:func.1">maxPrefix</a> <font color="Maroon" title="c5">P1</font>,<font color="Maroon" title="c6">P4</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="helly.html#E52:49"><i><font color="Green" title="E79">A54</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div>
